Creating a dense sample of ultracold YO molecules in an
optical latticebyYewei Wu
B.S., Tsinghua University, 2014
M.S., University of Colorado, 2017

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillmentof the requirements for the degree ofDoctor of Philosophy
Department of Physics
2021
Committee Members:
Jun Ye, ChairJames K. Thompson
David J. Nesbitt
Konrad W. Lehnert
Gregory B. Rieker

iiWu, Yewei (Ph.D., Physics)
Creating a dense sample of ultracold YO molecules in an optical lattice
Thesis directed by Prof. Jun Ye

Ultracold molecules offer a new platform for quantum chemistry, strongly correlated quantum
systems, quantum information processing, and precision tests of fundamental physics. Their richinternal structure and strong anisotropic dipolar interaction provide the tools for new physics andchemistry studies. However, due to the additional ro-vibrational degrees of freedom, controlling ofmolecules becomes very challenging. The past few years have witnessed a rapid progress of laser
cooling and trapping of molecules realized by several groups around the world.
In this thesis, we show an enhanced slowing efficiency for YO molecular beams by an improved
laser coupling regime. With enough number of slowed molecules, we demonstrate the first creationof RF and DC MOT of YO, which makes YO the first oxide molecule trapped in MOT. We
systematically study various types of MOT and the gray molasses cooling of YO, achieving atemperature of 4 µK, 25 times colder than the Doppler limit. The robust cooling against large
magnetic field allows us to develop a novel scheme to significantly compress the molecular cloud
below mm. With a compressed cloud, we are able to efficiently load molecules into a 1D opticallattice for further cooling and compression. A factor of 220 and 95 increase in density and phasespace density are realized compared to the cloud before loading, creating a molecular sample withthe highest phase space density to date by direct laser cooling. By adiabatically ramping down thelattice depth, 1.0(2) µK is achieved, which is the lowest temperature realized by direct laser coolingof molecules. With a long lattice lifetime of 850(70) ms, the study of YO-YO interaction is withinreach.

Dedication

To Claire.

Acknowledgements

There are so many people who made this work possible. Although it’s guaranteed that I’m
not able to show my appreciation in a few sentences, I’ll still give it a try.
I would like to thank first and foremost my advisor, Jun Ye, for his guidance and mentorship.
He not only helped me on research, but also guide me to think and work as a physicist. Junprovides a great science environment for every young graduate student to grow in his lab. Hispassion, optimism, energy and knowledge of science have a profound impact on everyone, which is
the key to our experimental success. Somehow, he could always manage to get enough funding tosupport all of our brave ideas. Apparently, no one has found his treasure chest yet.
I also had a great team working on the YO experiment. When I joined the group, I had ashort overlap with Bo Yan, Mark Yeo and Matt Hummon. Bo Yan is an enthusastic and interesting
person. He always had a smile on his face and would encourage everyone when the experimentwasn’t working properly. Mark Yeo is an expert in frequency comb and dye laser, without which
the experiment couldn’t continue at all. Matt Hummon is an excellent teacher who showed me how
all apparatus work in the lab. For the most part of my Ph.D., I had the privilege of working with
Alejandra L. Collopy, Shiqian Ding and Ian A. Finneran. Alejandra L. Collopy was instrumental
in building up the 3D MOT apparatus. She designed the first RF MOT of YO and solved lots ofexperimental problems. Shiqian Ding was the game changer of the experiment. He always had his
eye open on every details and was brave enough for new upgrades, without which the experiment
couldn’t have proceeded smoothly. I want to say a big thank you to you for all these years andwish you best of luck in Tsinghua. Ian A. Finneran is a true microwave expert that could generate

v
all crazy microwaves to fry our molecules. It’s unfortunate that I’m unable to use your circuits for
our SWAP MOT idea but I’m sure the next generation would benefit from all your works. Justin
Burau is the young graduate student in the lab who became really experienced in the past two
years. I’m confident to leave the experiment to him and I believe he’ll bring the experiment to a
crazy high level. Also, I would like to welcome Kameron Mehling who just joined the lab last year.
He is a good talker, body builder and very energetic person. He has a curious mind which is theprerequisite for a good scientist and I really enjoy all his questions.
Ye group has people working on various front of science. It’s really helpful to share knowledges, ideas and equipment with them. I’d like to thank Hao Wu, David Reens, Tim Langen,
Chengyi Luo and Lee Liu for great advice and useful discussions.
I must also thank all the fantastic staff here in JILA. All of our experiment apparatuses havethe hard work of our machinists and electronic engineers. Thanks to Hans Green, Todd Asnicar,
Kim Hagen, Kyle Thatcher, Calvin Schwadron, James Urich, Terry Brown, Carl Sauer, J.R. Raithand David Alchenberger.
I’d like to thank my family for their support and understanding. In particular, I’m really
fortunate to meet my wife in Boulder, she has made me a better person. No matter what I decide
to do, she is always behind me. I can’t wait for our life together after graduation.

viContents

Chapter
1 Introduction

1

1.1

Why Cold Polar Molecules? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.2

Productions of Ultracold Polar Molecules . . . . . . . . . . . . . . . . . . . . . . . .

2

1.3

About This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32 YO Level Structure
2.1

2.2

2.3

Molecular Structure of Diatomic Molecules . . . . . . . . . . . . . . . . . . . . . . .

5

2.1.1

Angular Momentum Coupling-Hund’s Cases . . . . . . . . . . . . . . . . . . .

6

2.1.2

Labeling of Molecular States . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.1.3

Vibrational Energy Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.1.4

Rotational Energy Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.1.5

Λ Doubling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8Interaction with External Fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.2.1

Under Magnetic Field - Zeeman Effect . . . . . . . . . . . . . . . . . . . . . .

9

2.2.2

Interaction with Laser Beams . . . . . . . . . . . . . . . . . . . . . . . . . . .

9YO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Cryogenic Buffer Gas Source
3.1

5

14

Y2 O3 Two-stage Buffer Gas Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1.1

Charcoal Sorbs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

vii
3.2

Y2 O3 Single-stage Buffer Gas Source . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.1

Cell Heating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2.2

Coating Cell Surface with Y2 O3 Nanopowder . . . . . . . . . . . . . . . . . . 19

3.2.3

Cell Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3

Y + O2 (O3 ) Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4

Next Generation of YO Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4.1

Molecule Yield Fluctuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.4.2

Limited Pumping and Accessibility . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4.3

1 K System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4 Laser Slowing

31

4.1

Laser Slowing YO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2

Γ/13 Slowing Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.3

4.4

4.2.1

Γ/13 Repumping Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2.2

Detection Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2.3

Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Γ/8 Slowing Scheme with N=2 Decoupled . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3.1

Repumping Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.3.2

Spectroscopy for Γ/8 Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3.3

Slowing Setup and Performance . . . . . . . . . . . . . . . . . . . . . . . . . . 37
0

Slowing Scheme with A 2 ∆3/2 Repumped . . . . . . . . . . . . . . . . . . . . . . . . 41

5 3D Magneto-Optical Trap of Yttrium Monoxide
5.1

Magneto-optical Trapping Theory
5.1.1

5.2

42

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Type II MOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Experiment Setup for RF MOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.2.1

RF MOT Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2.2

First 3D RF MOT Coil Design . . . . . . . . . . . . . . . . . . . . . . . . . . 45

viii

5.3

5.4

5.5

5.2.3

New RF MOT Coil Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.2.4

Driving RF Coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.2.5

Cooling the Coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.2.6

Reducing the Scattered Light . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.2.7

Detection system for RF MOT . . . . . . . . . . . . . . . . . . . . . . . . . . 50

RF MOT Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.3.1

1D RF MOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.3.2

3D RF MOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Molecule Loss by Parity Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.4.1

N=3 Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.4.2

N=3 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

DC MOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.5.1

DC MOT Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.5.2

Detailed DC MOT Characterization . . . . . . . . . . . . . . . . . . . . . . . 62

5.5.3

Collision with Background Gas in DC MOT . . . . . . . . . . . . . . . . . . . 64

5.5.4

Remaining Issues in MOT Beams . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.5.5

Limited MOT Lifetime at High Magnetic Field Gradient . . . . . . . . . . . . 66

5.5.6

New Trapping Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6 Sub-Doppler Cooling and Compressed Trapping of Molecules
6.1

6.2

6.3

69

Gray Molasses Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.1.1

Gray Molasses Cooling Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.1.2

Gray Molasses Cooling of YO . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Λ-Enhanced Gray Molasses Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.2.1

Λ-Enhanced Gray Molasses Cooling Theory . . . . . . . . . . . . . . . . . . . 73

6.2.2

Λ-Enhanced Gray Molasses Cooling of YO

Compressed Trapping of YO. . . . . . . . . . . . . . . . . . . 74

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

ix
6.3.1

Gray Molasses Cooling with Magnetic Field . . . . . . . . . . . . . . . . . . . 78

6.3.2

Robust Cooling with Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . 79

6.3.3

A Novel Compression Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

7 Optical Trapping of Molecules
7.1

7.2

7.3

7.4

83

Optical Dipole Trap(ODT) Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
7.1.1

Molecule Interacts with Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

7.1.2

Gaussian Beam Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

689 nm ODT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
7.2.1

Experiment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7.2.2

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

1064 nm ODT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7.3.1

Experiment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7.3.2

Loading and Cooling inside ODT . . . . . . . . . . . . . . . . . . . . . . . . . 93

7.3.3

ODT Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

1064 nm Optical Lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.4.1

Loading and Cooling inside Lattice . . . . . . . . . . . . . . . . . . . . . . . . 96

7.4.2

Lattice Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

7.4.3

Molecule Loss with Low Intensity GMC Beams . . . . . . . . . . . . . . . . . 99

7.4.4

Heating at Low Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

7.4.5

Ramping Down the Lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7.4.6

Noise-induced Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Bibliography

107

Appendix
A YO Molecular Structures and Spectroscopy

119x
A.1 X 2 Σ+ → A2 Π1/2 Transition(v=0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
0

A.2 X 2 Σ+ → A 2 ∆3/2 Transition
B Dye Lasers - How to Make it Happy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
124

B.1 Why Dye Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
B.2 Sirah Matisse DR 2 Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
C Magnetic Coil127

D Compression Timing Diagram

131

xi

FiguresFigure2.1

Hund’s Cases (a) and (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

2.2

Ground State Zeeman Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3

YO Energy Levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.1First Version of Cryogenic Buffer Gas Cell. . . . . . . . . . . . . . . . . . . . . . . . 15

3.2

Schematic of Buffer Gas Cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3

Performance of Single vs Two Stage Cell. . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4

Cell Heating Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.5

Ablation Target and In-vacuum Shutter. . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.6

Coating Cell with YO Nanopowder. . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.7

Cell Performance with/out Nanopowder. . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.8

Coating on Ablation Window. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.9

Modified Cell with O2 /O3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.10 Comparison of Y+O2 (O3 ) with Y2 O3 Cell. . . . . . . . . . . . . . . . . . . . . . . . 24
3.11 Molecule Yield at Different Temperature. . . . . . . . . . . . . . . . . . . . . . . . . 26
3.12 Measurement of Molecule Yield at Different Temperature. . . . . . . . . . . . . . . . 26
3.13 Limited Pumping and Accessibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.14 Exploded-view of 1 K Cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.15 1 K Pot Drawing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

xii
4.1

Γ/13 Slowing Scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2

Doppler Sensitive Detection Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3

Slowing Result with Two Stage Cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.4

Slowing Improvement by Increasing Deceleration. . . . . . . . . . . . . . . . . . . . . 36

4.5

Γ/8 and Γ/5 Repumping Scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.6

Spectroscopy for Γ/8 Scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.7

Slowing Setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.8

Γ/8 Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.9

Slowing Scheme with A 2 ∆3/2 Repumped. . . . . . . . . . . . . . . . . . . . . . . . . 41

5.1Type I and Type II MOT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2

Different MOT Coil Designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.3

RF Coil Electronics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.4

RF Coil Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.5

Custom Vacuum Viewport. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.6

MOT Detection Layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.7

1D RF MOT Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.8

3D RF MOT Setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.9

Overslowing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

05.10 RF MOT Characterisation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.11 RF MOT Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.12 MOT Lifetime versus Power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.13 Parity Mixing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.14 N=3 Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.15 DC MOT Setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.16 DC MOT Contribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.17 DC RF MOT Comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

xiii
5.18 MOT at Different Intensities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.19 MOT at Different Magnetic Field and Detuning. . . . . . . . . . . . . . . . . . . . . 63
5.20 Limit of MOT Lifetime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.21 MOT Shape Affected by Beam Alignment. . . . . . . . . . . . . . . . . . . . . . . . . 65
5.22 Compressed MOT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.23 New Trapping Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.1

Sub-Doppler Cooling Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.2

DC MOT Setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.3

VSCPT Theory.

6.4

Temperature vs δ in Small Range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.5

Temperature vs δ in Large Range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6.6

Raman Detuning Scan Different Parameters. . . . . . . . . . . . . . . . . . . . . . . 77

6.7

Characterisation of GMC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.8

Cancellation coil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.9

B Field Cancellation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.10 Temperature under Bias Magnetic Field. . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.11 Compression of Molecular Cloud. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
7.1

Trap Depth vs Wavelength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

7.2

Gaussian Beam Profile and Light Shift . . . . . . . . . . . . . . . . . . . . . . . . . . 86

7.3

Trap Tilt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7.41064 nm Beam Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

7.5

Fiber End Cap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7.6

ODT and Lattice Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

7.7

Trapping Beam Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

7.8

ODT Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

7.9

ODT with Different Raman Detuning δ . . . . . . . . . . . . . . . . . . . . . . . . . 93

xiv
7.10 ODT with Different Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.11 ODT Lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.12 Lattice Loading Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.13 Lattice Trapping Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.14 Lattice parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.15 Lattice Loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.16 Lattice loss curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.17 Lattice Heating at Low Intensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.18 Ramping Down the Lattice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.19 Relative Intensity Noise Spectrum and E-folding Time. . . . . . . . . . . . . . . . . . 106
A.1 N=0 to J=0.5 Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
A.2 N=1 to J=0.5 Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
A.3 N=1 to J=1.5 Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
A.4 N=2 to J=1.5 Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
A.5 N=2 to J=2.5 Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
A.6 N=3 to J=2.5 Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
A.7 Delta State Lifetime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
A.8 Delta State Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
B.1 Dye Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
C.1 Calculated Coil Performances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
D.1 Compression Timing Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

Chapter 1

Introduction

The study of ultracold atoms has been a major topic in the atomic physics community
for more than 4 decades since the advent of laser cooling and trapping techniques. The study oftrapping and cooling atoms to ultralow temperatures has resulted in several Nobel Prizes. Ultracold
atoms provide a powerful platform for studying quantum degenerate gases [1, 2], strongly correlated
systems [3], quantum information [4, 5, 6, 7], quantum sensing [8] and ultra-precise atomic clocks [9].

1.1

Why Cold Polar Molecules?
Some atoms have optimal structures, making them relatively easy to cool and trap. The weaklong range interaction makes them an ideal candidate for metrology applications. Compared withatoms, molecules have rich internal structure and strong anisotropic interaction due to the body
fixed electric-dipole moment. Therefore, ultracold polar molecules [10, 11] provide opportunities formany important applications ranging from quantum simulation [12, 13, 14, 15, 16] to precision testsof fundamental physics [17, 18]. Some of these applications, particularly in quantum information
processing [12, 13, 19], many body quantum system simulation [20] and quantum-state-controlled
chemistry [21, 22], demand a high phase space density. As a result, the generation of ultracold
molecules has become a popular topic and lots of molecules have been cooled and trapped over the
past decade.
Controlling how molecules interact with each other has become increasingly popular in recent
years. For example, collisional losses in ultracold gases of alkali-metal dimers [23, 24, 25, 26] is2poorly understood. The recent observation of suppression of loss as KRb Fermi molecules enter
quantum degeneracy also awaits theory explanations. Theory predicts the presence of a reaction
complex, in the process called sticky collisions [27]. It’s only recently that bimolecular reactions
and intermediate complex have been observed directly [28]. More experiments are also focusing onstate controlled collisions [21, 29]. By controlling external fields [30], reactions can be enhanced or
suppressed [31, 32]. For example, the elastic-inelastic ratio can be tuned by the external field toenhance the evaporation cooling efficiency, which has led to a degenerate gas in 2D [33].
Molecules are also great tools for precision measurements, particularly in searching for thepermanent electric dipole moments of the electron(eEDM) [34, 35, 36, 37]. Based on the Standard
Model, the weak interaction does not preserve the CP-symmetry, implying an uneven charge distribution over the electron, which means the electron has a permanent electric dipole moment. The discovery of an eEDM would imply the violation of time reversal invariance. Compared to atoms [34],polar molecules can enhance the detection sensitivity due to its large internal electric field. The
current upper bound of the eEDM is set by the measurements using polar molecules [36, 37, 38, 39].

1.2

Productions of Ultracold Polar Molecules
The productions of atoms and molecules for cooling experiments are fundamentally different.

For example, alkali atoms are initially produced from a metal dispenser, where the dispenser canbe heated to produce a high vapor pressure. This atomic vapor can be used directly for laser
cooling. As for molecules, due to the thermal distribution, they are distributed among many
rotational and vibrational states separated by tens of GHz and several THz. These large separations
require multiple lasers to address molecules across all these states, which is an impossible mission.
Therefore, the goal is to produce a high flux of molecules at a single quantum state. This isaccomplished in two ways: indirect cooling, where molecules are assembled from ultracold atoms,
and direct cooling, where cooling is directly applied on a molecular species. With indirect methods,
several ultracold molecules have been produced [23, 24, 25, 26, 40, 41, 42]. Among these molecules,
KRb has been brought to quantum degeneracy very recently [43] and has enabled the study of

3dipolar evaporation [33] and collisional shielding [44]. Besides assembling bi-alkalis, there has been
a rapid progress in direct laser cooling and trapping of molecules. A typical and general method tocreate cold molecules is called buffer gas cooling [45]. This technique relies on the elastic collisions
between molecules and a buffer gas to cool both internal and external degrees of freedom of themolecules. With helium as the buffer gas, most molecules can be cooled such that the majority ofthe population resides at the lowest ro-vibraitonal states. Nowadays, the cryogenic buffer gas cellhas become the standard source for direct cooling and trapping of molecules [45, 46].
With molecules generated at ∼K from the buffer gas source, there are many ways to further
cool the molecules, which could be summarized in two categories depending on the evolution of thephase space density. One ”cooling” technique doesn’t change the phase space density, it works byperiodically converting the kinetic energy into potential energy, such as in a Stark/Zeeman decelerator [47, 48, 49, 50, 51] and centrifugal decelerator [52]. Direct laser cooling is another technique,where the entropy is taken away by the photons. However, laser cooling is limited to moleculeswith diagonal transitions [53], optimized angular momentum selection rules [54] and attainable highpower lasers for the transition wavelength. Starting from two proposed papers on vibration androtation closures for cooling [53, 54], the past few years have witnessed a rapid advancement inlaser cooling and trapping molecules. Magneto-optical traps have been demonstrated for diatomic
molecules such as SrF [55], CaF [56, 57], YO [58, 59] and even polyatomic molecules CaOH [60].
Sisyphus-type gray molasses cooling(GMC) together with velocity-selective coherent population
trapping was used to cool molecules to µK [59, 61, 62]. Recently, these molecules have been loaded
into the magnetic traps [63, 64, 65], optical dipole traps [61] and optical tweezer arrays [66, 67, 68]
for collisional studies.

1.3

About This Thesis
In this thesis, we will discuss the production, slowing, trapping and cooling of YO. In Chapter

2, we will introduce the molecular structure and basic properties of YO relevant to this work. Buffer
gas cooling of YO and various upgrades are detailed in Chapter 3. Chapter 4 will discuss different

4slowing mechanisms. In Chapter 5, we compare RF and DC MOT performances. Chapter 6 will
detail the sub-Doppler cooling of YO and the special compression protocol tailored by the unique
YO structure. Chapter 7 will cover the loading and cooling into a 1-D optical lattice together
with the creation of the molecular sample with the highest phase space density and the lowest
temperature by direct laser cooling.

Chapter 2

YO Level Structure

Understanding the molecular structure and interaction with external fields is critical for
slowing, cooling and trapping molecules [53]. Compared with atoms, ”a diatomic molecule is one
atom too many”, said Arthur Schawlow. The extra atom in a diatomic molecule introduces two
additional degrees of freedom, vibration and rotation, creating a complex structure. Therefore, onlymolecules with diagonal energy levels can be directly laser cooled. In this chapter, we introduce
the molecular structure of diatomics and discuss the YO energy levels relevant to this work since
it is been described in detail [69].

2.1

Molecular Structure of Diatomic Molecules
In a diatomic molecule, the nuclei are much heavier than the electrons, thus their wave func-

tions can be treated independently. In molecular spectroscopy, it means the electronic, vibrationaland rotational degress of freedom are decoupled and could be written in this approximation:
H = He + Hvib + Hrot + HSO + HSR + HHF S + HΛwhere He , Hvib , Hrot , HSO , HSR , HHF S , HΛ are the electronic, vibrational, rotational, spin-orbit,
spin-rotation, hyperfine and Λ-doubling components of the Hamiltonian. These terms are generally
well separated in energy scale, with electronic energy level spacings of 100’s THz, vibration at THz
level and rotational at the 10’s of GHz level.

6
2.1.1

Angular Momentum Coupling-Hund’s Cases

Diatomic molecules share some similarities with atoms, such as electronic spin S, electronic orbital angular momentum L and total angular momentum J=L+S. Beyond this, diatomic molecules
also have their rotational degrees of freedom. Unlike atoms with spherical symmetry, diatomic
molecules possess axial symmetry with respect to their internuclear axis. Although most angularmomenta are coupled to each other, it is useful to simplify the problem in cases where angularmomenta are coupled in a prescribed order according to their coupling energy. The angular momentum coupling of diatomic molecules can be categorized into Hund’s cases [70], proposed byFriedrich Hund. Here we describe the two most common cases, both of which describe the YO
states related to this work.

Figure 2.1: Angular momentum coupling diagram for Hund’s cases (a) and (b).

2.1.1.1

Hund’s Case (a)Figure 2.1 (a) shows the angular momentum coupling diagram for Hund’s case (a). In thiscase, the electron orbital angular momentum L is strongly coupled to the internuclear axis under theelectrostatic interactions and electron spin S is strongly coupled to L through spin-orbit coupling.
Their projections onto the internuclear axis are labeled as Λ, Σ and the sum is Ω. This cumulative
projection then couples with the rotation of the nuclei R, forming the total angular momentum

70

J=R+Ω. This case describes the A2 Π1/2 and A 2 ∆3/2 states, two excited states of YO involved in
our laser cooling scheme.

2.1.1.2

Hund’s Case (b)In Hund’s case (b), shown in Figure 2.1 (b), electron orbital angular momentum L still couples
to the internuclear axis. However, the electron spin S isn’t coupled because the spin-orbit couplingis weak. Thus, Λ couples to R to form N=R+L and eventually coupled with S to form J=N+S.
YO ground state X 2 Σ+ is a special Hund case (b) as L is zero. The electron S and nuclear spin I
are strongly coupled by the Fermi contact interaction, forming an intermediate angular momentum
G=I+S. Then it couples with molecular rotation N through spin-rotation interaction yielding
F=G+N.

2.1.2

Labeling of Molecular States

It is standard to denote electronic energy levels of diatomic molecules by letters, with X always
denoting the ground state. Electronically excited states are labeled by capital letters(A,B,C...) in
the order of the energy of the states. Sometimes, the letter ordering doesn’t follow the energy levels
when a lower state was found after the other states. In addition to the letter, electronic energy
levels are labeled by the molecular notation
2S+1

+/−

Λ|Ω|

where +/- denotes the reflection symmetry through an arbitrary plane along the internuclear axis.
Similar to atomic states where J=0,1,2,3 are labeled as S,P,D,F, molecular states with Λ=0,1,2,3
are labeled as Σ, Π, ∆, Φ. Therefore, the electronic ground state of YO is labeled as X 2 Σ+ andthe ”lowest” excited state is labeled as A2 Π1/2 . It is worth mentioning the lowest excited state is00actually A 2 ∆3/2 , and it is labeled as A since it was discovered after the A2 Π1/2 state.

8
2.1.3

Vibrational Energy Levels

The vibrational levels can be approximated as a harmonic oscillator with additional terms
representing the anharmonicity [71].
111Evib = ωe (v + ) − ωe xe (v + )2 + ωe ye (v + )3 + ...
2
22
where v is the vibrational quantum number, ωe is the vibrational constant and xe , ye are anharmonic
constants.

2.1.4

Rotational Energy Levels

The rotation of a diatomic molecule can be approximated as a rigid rotor with additionalterms representing the centrifugal distortion. It can be described as
Erot = Bv R(R + 1) − Dv R2 (R + 1)2 + Hv R3 (R + 1)3 + ...
where R is the rotational quantum number, and Bv , Dv , Hv depend on vibrational level v.
1
1
Bv = Be − αe (v + ) + γe (v + )2 + ...
2
2
These parameters represent the coupling between rotational and vibrational motion [72].

2.1.5

Λ Doubling

In Hund’s case (a), as L may precess about the internuclear axis in two directions(clockwise/ counter clockwise), its projection onto the internuclear axis can be ±Λ. These two manifolds
are degenerate if the molecule is not rotating, however, this degeneracy breaks down due to themolecular rotation. The splitting between these manifolds is called Λ doubling and it scales with
J. For Hund’s case (a) molecules in 2 Π1/2 state, the Λ splitting is|EΛ | = (p + 2q)(J + 1/2)
where p, q are the Λ doubling parameters and the sign depends on the spin-orbit interaction. Λ
doubling creates an opposite parity state close to the excited state. For example, the splitting

9
0

0

0

between A 2 ∆3/2 J = 3/2(−) and J = 3/2(+) state is so small (∼ 0.2 MHz) that these two states
are totally mixed, causing decays to unrepumped states. This will be discussed in Chapter 4.

2.2Interaction with External Fields

2.2.1

Under Magnetic Field - Zeeman Effect

In the presence of an external magnetic field, the spectral line of an atom(molecule) splits
into several components. These energy shifts are due to the Zeeman effect. The Hamiltonian isgiven by [71]Hz = gs µB S · B + gL µB L · B − gI µN I · BµB
where gs ≈ 2, gN ≈ 1, gI ≈ 5.6, µB , µN ≈ 1836
are electron spin, orbit, nuclear g factors, Bohrmagneton and nuclear magnetic moment. The Zeeman shifts of X 2 Σ+ state are plotted in Figure
2.2.
The Zeeman shift of A2 Π1/2 is calculated to be0
1 0Ez,± = ± (gl − gre )µB Bz MF
300

where ± refers to the parity of the Λ doublet. The gl and gre parameters depend on Λ doubling
parameters p and q as follows [73, 74]
0

gl =

p
2BΠ

0

gre = −qBΠwhere BΠ is the rotational constant of A2 Π1/2 state. As we can see in Figure 2.2, F=1, mF =1
states have the maximum Zeeman shift among all manifolds in A2 Π1/2 state, which is a factor of
15 smaller than the largest Zeeman shift in the X 2 Σ+ ground state.

2.2.2

Interaction with Laser Beams

When a laser beam interacts with a molecule, the electric field of the light will cause a changeof the molecular energy for different internal states. These molecular energy shifts due to the AC10fields are called AC Stark shifts, which will be detailed in Chapter 7. Here we review some basic
parameters in molecule laser interactions.
Despite the complexity of the multi-state molecule, it is useful to use a simple rate model [75,76] to predict some properties. In the model, there are ng ground states that are directly coupled
to ne excited states, thus the steady-state scattering rate is
Rsc = Γne,ng
(ng + ne ) + 2Σj=1 (1 + 4∆2j /Γ2 )Is,j /Ij

Is,j =πhcΓ
3λ3jwhere Γ, ∆j , Is,j , λj , Ij are excited state decay rate, single-photon detuning, two-level saturation
intensity, light wavelength and intensity for transition j. Assuming all transitions have similar

Figure 2.2: Zeeman structure of ground state X 2 Σ+ N=1.

11values for ∆, Is and total light intensity I0 , the equation can be simplified as
Rsc =

n2g
Γef f
sef f
2(ng + ne ) I0
2ne
,
Γ
=
Γ,
s
=
,
I
=
Is
ef
f
ef
f
s,ef
f
2 1 + sef f + 4∆2 /Γ2
ng + nen2g
Is2(ng + ne )where the Γef f , sef f and Is,ef f are effective linewidth, effective saturation rate and effective saturation intensity. One difficulty for slowing molecules is the low scattering rate caused by couplingwith many ground states, which will be detailed in the Chapter 4.

2.3

YO
89 Y16 O was chosen for several reasons. The main transition(X 2 Σ+ →− A2 Π1/2 ) is strong(Γ =

2π×4.8 MHz), thus a fast photon scattering is possible. YO has very diagonal vibrational branchings
such that molecules could scatter more than 106 photons while repumping only the three lowest
vibrational states. All transition wavelengths are accessible in the visible region where commercial
laser diodes or other systems are available. The dipole moment(4.45(7) D) [77], between the tworotation states in X 2 Σ+ , is reasonable for dipolar interactions. Because of the strong coupling
between nuclear and electronic spin, YO molecules aren’t sensitive to external magnetic field. Thismagnetic insensitivity enables the spatial compression of molecular cloud and the realization of
stable cooling, which will be detailed in Chapter 6. The relevant energy levels and decays for the
discussion in this thesis are shown in Figure 2.3.
A large amount of prior spectroscopy [78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88] had been doneon YO, which greatly simplified our spectroscopy measurement. The detailed energy levels havebeen discussed previously [69]. The spectroscopies taken by us are shown in Appendix A, so here
we highlight only the most salient features.
0

The ground and excited state of the cycling transition are N=1(-) of X 2 Σ+ and J = 1/2(+)
of A2 Π1/2 , while the rest of the states are repumped back using microwave or lasers. The N=1
state is chosen to limit the decay back to N=1 state. Decay to other rotational levels are forbidden
by parity and angular momentum selection rules [54]. The vibrational branchings are addressedby repumping X 2 Σ+ v=1 state directly back to the A2 Π1/2 v=0 state, while the X 2 Σ+ v=2 state

12

Figure 2.3: YO energy levels relevant in this thesis.

is repumped using a two step process. It first goes up to A2 Π1/2 v=1 state, which predominantly
decays to the X 2 Σ+ v=1 state, and then gets repumped back to v=0 by v=1 repumping laser. The
nuclear spin gives rise to hyperfine structure, splitting the ground state into 4 manifolds. Thesehyperfine states are addressed with AOM sidebands.
0

Ideally, with only three lasers covering X 2 Σ+ (v = 0, N = 1) →− A2 Π1/2 (v = 0, J = 1/2),
00

X 2 Σ+ (v = 1, N = 1) →− A2 Π1/2 (v = 0, J = 1/2) and X 2 Σ+ (v = 2, N = 1) →− A2 Π1/2 (v = 1, J =1/2) transitions, YO could scatter more than 106 photons. However, molecules on the main excited00state A2 Π1/2 has a ∼ 3 × 10−4 chance of decaying to an intermediate state A 2 ∆3/2 (J = 3/2(−))
and then decay to N=0(+) or N=2(+) of X 2 Σ+ ground state. This two photon process flips theparity of the molecule, causing molecular loss after 3000 photon scatterings. This is not acceptable13
even for molecular slowing, thus extra lasers and microwave are installed to plug the leak. Different
repumping schemes will be discussed thoroughly in Chapter 4.

Chapter 3

Cryogenic Buffer Gas Source

To directly slow, cool and trap molecules, a cold and bright source is required. Molecules need
to be prepared at the low temperature where most of them are residing in the lowest vibrationaland rotational states. The two main sources to create cold molecules are supersonic expansion jetsand buffer gas cooled beams. Supersonic expansion generates rotationally and vibrationally cold
molecules but the forward velocity is hundreds of m/s, which requires lots of photon scatterings anda long slowing distance. These are hard to achieve for molecules without a very diagonal structure.
Therefore, YO molecules are produced in a cryogenic buffer gas cell [45, 89]. In this chapter,
I’ll introduce basic principles of buffer gas cooling, briefly review our initial setup, introduce theenhancements and the new design for operating at lower temperature.

3.1

Y2 O3 Two-stage Buffer Gas SourceThis is the first version we had for our 2D magneto-optical trap and rotational microwave

mixing experiment [90, 91]. It’s well documented previously [69], so here we introduce it very
briefly.
Molecules are first generated by chemical reaction or laser ablation. In our case, the hotmolecules from laser ablation are cooled by buffer gas helium to ∼4K through elastic collisions. BothHe and YO escape from the cell through a small aperture, while He is absorbed later by cryogenic
charcoal sorbs. Depending on the buffer gas flow rates and cell geometry, different hydrodynamic
regimes could be used to produce a YO beam [45]. It’s also found that the forward velocity increases

15linearly with gas flow, which is called the boosting effect [45]. This is not desirable for slowing themolecules. Thus, for this setup, we operate in the effusive regime to realize the slowest forward
velocity of the molecules. A leaky second stage is also added to further slow down the moleculesby creating an intermediate region where molecules experience several collisions on its way out.

Figure 3.1: (a). Side view of two stage buffer gas cell. Helium is cooled to 4K by the copper bobbin
before entering the cell. (b). Front view of two stage buffer gas cell and charcoal sorbs. Fourcharcoal panels are typically installed on the 4K cold head to absorb the unwanted helium.

Figure 3.1 shows the two stage buffer gas cell and charcoal sorbs underneath the cell. Typically, there are four charcoal panels installed on the 4K cold head to absorb the unwanted helium,
which is not shown in this figure. The 1st stage of the cell is made out of a 1.5”×1.5”×1.25”

16long oxygen-free high thermal conductivity (OFHC) copper block. The cell cavity is formed by
two through holes of 0.85” diameter. The beam exists through a ∼3 mm aperture in the front.
The second stage is made out of a 1.5”×1.5”×0.38” long OFHC copper block, standing off 2.8 mm
away from the first stage. In addition, two rectangular vents on the side of the second stage provide
additional leakage and the exit aperture is 9 mm in diameter. These leakages creates a intermediate
region which holds a pressure between the 1st stage and low vacuum region. Our second stage isvery similar to the design from the Doyle group in Harvard [92].
In order to keep the temperature at 4 K, cell and charcoal sorbs are directly anchored to the
4 K stage of a two-stage pulse tube cryocooler(Cryomech PT410). The cooling capacities at 40
K and 4.2 K stages are 40 W and 1 W. Therefore, if the cell and charcoals are directly exposed
to vacuum chamber at room temperature, the heat load from black body radiation would be ∼4.5
W, which overwhelms the 4 K stage cooling capacity. We therefore apply two layers of radiation
shielding, as shown in Figure 3.2. The inner shield is thermally anchored to the 4 K stage and theouter shield is thermally connected to the 40 K stage to block the radiation from the chamber atroom temperature. The heat load on cell and charcoal sorbs is reduced from 4.5 W to 1.4 mW,
negligible compared to the cooling capacity of the 4 K stage.

3.1.1

Charcoal Sorbs

As we mentioned above, both He and YO escape from the cell through a small aperture
after elastic collisions. Helium exiting from the aperture needs to be pumped away immediately
before colliding with YO again. However, enclosing the cell with radiation shields means that the
conductance to the external turbo pumps is very low. The typical compression ratio for helium isalso low, leading to a poor vacuum. Therefore, the buffer gas would build up and deteriorate the
YO beam. The solution is to use cryogenic, activated charcoal as a cryopump [93]. When activatedcharcoal is cooled below 10 K, it becomes a cryopump for helium with ∼ 10 Liter/(s·cm2 ) pumping
speed and could hold up to 1 liter(STP) of helium per gram. With activated charcoal(Spectrum
Chemical C1221) epoxied(Loctite STYCAST 2850FT) to the inner surface of 4 K shield and extra

17

Figure 3.2: Top view of complete buffer gas cell setup.

4 K panels, as shown in Figure 3.1 (b), we achieve a pumping speed of ∼100 L/s and it should lastfor weeks under normal gas loads [94, 95]. If the charcoals are saturated with helium, it’s necessary
to warm up the sorbs above ∼ 35 K [96] and pump out the desorbed helium with a mechanicalpump.
Initially, our fresh cell worked only for ∼ 30 minutes before a warm up, which is much shorter
than the estimated runtime we mentioned above. It’s because our 4 K enclosure wasn’t covered
nicely thus the sorb regenerated itself when the desorbing helium bounced off a surface which wassignificantly hotter than the sorb. A hot helium atom can hit the sorb and cause a few cold helium
atoms to desorb, which can then be heated up by the hot surface and release cold atoms again [97].
The cell runtime was significantly improved to several weeks by sealing the 4 K stages with only a2”-diameter hole for pumping and a 1”-diameter aperture for YO exiting the chamber.

18

3.2

Y2 O3 Single-stage Buffer Gas Source
We never explored the two-stage cell geometries such as the mesh size, spacing and aperturesize. Instead, we took away the second stage and made a few changes to get a single-stage cell.
The differences are shown in Figure 3.3. As for a single-stage cell, the forward velocity of themolecule beam increases with the helium flow, as predicted [45]. While in a two-stage cell, it
remains consistently low since the boosting effect is reduced by the second stage. Removal of thesecond stage increased the forward velocity by more than 30 m/s, as shown in Figure 3.3 (a), butalso increased the molecule number by a factor of 100, as shown in Figure 3.3 (b). The deceleration
distance increases by a factor of two, resulting in a diffusion loss of 75%. As a result, the numberof slowed molecules increases by more than an order of magnitude by removing the second stage
cell. It doubles the number of photon scattering to slow molecules down to rest but it is nota limit to our experiment at the moment. To achieve better thermalization and slower forward
velocity, we installed a diffuser and spacer [98] to slow down the helium before it collides with YO.
Unfortunately, it didn’t make a noticeable difference.

Figure 3.3: Performance of single-stage vs two-stage cell. (a). Forward velocity of molecular beamversus different helium flow rates. The forward velocities of the two-stage cell are independent of
helium flow, as the boosting effect is reduced by the second stage. While it increases linearly withthe helium flow rate in the single-stage cell, as expected. (b). Molecule yield at different helium
flow rates. The leaky second stage reduces the molecule number by a factor of 100.

19
3.2.1

Cell Heating

Previously, the experiment was running at a repetition rate of 10 Hz for fast data acquisition. Then we found that the buffer gas cell generated many more molecules while the ablation
is operating at a low repetition rate. As shown in Figure 3.4 (a), three times more molecules are
generated per shot at ablation rate of 1.4 Hz than 10 Hz, while the forward velocities are very
similar. We’ve tried ablating at lower repetition frequency but it didn’t make any difference. The
theory behind this change is due to the heating of the ablation target and the cell. A 5 mJ laser
ablating at 10 Hz introduces 50 mW into the 4 K stage, where the cooling capacity is only ∼ 1 W.
To cool the Y2 O3 ceramic more efficiently, instead of mounting on the ring, as shown in Figure 3.1,
where the thermal conductivity is terrible, now the Y2 O3 pellets are directly epoxied on a copper
base which is directly mounted on the 4 K cell, as shown in Figure 3.5 (a). This didn’t solve theproblem, we therefore operated the entire experiment at 1 Hz. Similar molecule reduction is also
observed when a ∼20 mW off-resonant laser is always pointing into the cell, as shown in Figure
3.4 (b). This confirms our theory of molecule loss resulting from incidental heating of the cell. To
reduce any possible heating of the cell, our experiment runs at a low rep rate(1 Hz) and two in-vac
shutters(Vincent Associates Uniblitz VS14S1T0ECE) were installed to block any laser beams after
the molecules have passed the shutter location, as shown in Figure 3.5 (b). The seal is realizedby buna-N O-rings and the shutters are thermally heatsunk to the aluminum beambox or vacuum
flanges.

3.2.2

Coating Cell Surface with Y2 O3 Nanopowder

We have experimented with a couple of different cell geometries to generate more and slower
molecules. None of these have worked better than our original design. After attempting thesealternative designs, we couldn’t even recover the molecular beam using our original cell. Eventually,
we found that the coating of Y2 O3 powder on the inner side of the buffer gas cell plays an important
role.

20

Figure 3.4: Molecule yield affected by cell heating. (a). Molecule yields per shot at different
ablation rate. More molecules are generated at low rep rate as less heat is introduced to the cell.
(b). Molecule yields at different heating power given by a off-resonant CW laser. It proves ourtheory that molecule yield is affected by the cell heating.

Figure 3.5: (a).Y2 O3 pellets expoxied on the copper mount. Laser ablation leaves black marks on
the surface. (b). In-vacuum shutter installed on the inner surface of the beambox. There is anotherone installed ∼ 15 cm away.

Unlike CaF [99], Y2 O3 cell doesn’t accumulate dust after weeks of operation, as shown in
Figure 3.6 (a)(b). However, a clean cell doesn’t behave the same as a ”marinated” cell. There is
still a very thin coating affecting the molecule yield. Therefore, we coated the cell by brushing
the Y2 O3 nanopowder dissolved in isopropanol onto the interior cell surfaces. Currently, we’re notable to precisely control the thickness of the coating which affects the molecule yield, as shown in
Figure 3.6 (c)-(e), but we’re able to repeatedly hit a nearly optimal performance.

21

Figure 3.6: (a). CaF2 cell after two weeks of running. Courtesy of Loic Anderegg. (b). Y2 O3 cell
after years of operation. (c). Y2 O3 cell coated with thin layer of Y2 O3 nanopowder(Sigma Aldrich
544892). (d). Y2 O3 cell with thick coating. (e). Molecule yields with different coating. The Y2 O3coating on the cell significantly affects the molecule yield, we therefore apply a thin coating toboost up the molecule yield.

Figure 3.7: Cell behaviour with/without powder. (a).Molecule number. (b). Forward Velocity.
With a powdered cell, more molecules with a low forward velocity can be generated at low helium
flow rate.

The nanopowder coating also affects the hydrodynamics inside the cell, as shown in Figure 3.7.
With coating, the cell can operate at a lower helium flow rate(<2 sccm), creating more molecules
at a slower forward velocity. This really helps reducing the pressure at the science chamber.
Unfortunately, our knowledge is still empirical and the physics behind this yield enhancement

22
requires further investigation.
Lower helium flow rates introduce a problem by coating the ablation window. At low helium
flow, the molecular plume produced by ablation has a higher chance reaching the ablation window,
which contaminates the window and affect the ablation efficiency. This coating can’t be removedby the ablation laser, thus the window has to be replaced after two days. To prevent this, a skinnysnorkel [98] with the length of 1” is added to move the ablation window farther from the pellets.
This resulted in replacing the ablation windows bimonthly.

Figure 3.8: (a). Ablation window after weeks of runtime. The window is coated and the coating
can not be removed by the ablation laser. (b). A long snorkel is introduced to create a gap between
ablation window and target to reduce the coating effect.

3.2.3

Cell Performance

For a specific cell geometry, there are several parameters that affect the molecule yield including helium flow rate, ablation energy, ablation focus and ablation spot. For a single stage Y2 O3cell with nanopowder coating, we typically operate at low helium flow(0.25 sccm) and high ablationenergy(18 mJ), providing ∼ 107 molecules with the forward velocity of 120 m/s. Higher helium
flow and ablation energy will produce more molecules at higher forward velocity, however this increases the slowing distance and thus decreases the useful flux to the MOT region. Furthermore,
it is typically ideal to focus the ablation laser on the sample surface where a brightest and slowest

23
molecule beam is generated.

3.3

Y + O2 (O3 ) Source
To generate more CaF molecules, Tarbutt group opted for a chemical source using a calcium

metal and SF6 gas [89]. In their setup, the ablation of metals in a buffer gas cell is very reliable andit provides very high fluxes. Using this chemical source, they generated a flux of 5×1010 molecules
per steradian per pulse in a single rotational state with a mean speed of ∼150 m/s. Similar increases
for YO has been observed by the presence of oxygen at room temperature [100]. So we introduced
the O2 and O3 into the cell for chemical interaction. O2 (O3 ) sublimates at 54 K(∼81 K), so thevapor pressure at ∼100 K would be high enough to prevent clogging. We sent O2 (O3 ) directly into
the cell from a modified back plate, as shown in Figure 3.9 (a). The gas line was designed to have aweak thermal connection to the 40 K shield with a resistive heater epoxied to maintain at ∼120 K.
A thin(1/16” OD) stainless steel tube was used to reduce the thermal conductivity and a thermal
diode(Lakeshore DT-670-CU) was installed at the entrance to monitor the temperature. The gasline penetrated through the diffuser, spacer and was isolated from the 4 K cold cell with a small
Ultem spacer, as shown in Figure 3.9 (b).

Figure 3.9: Inserting a O2 (O3 ) line into the cell. (a). Back plate of the cell. (b). Modified diffuser,
spacer and black plate. A Ultem spacer is used to prevent the O2 (O3 ) from touching the 4K copper.
A resistive heater is also epoxied to the line to maintain the temperature at ∼ 120 K.

24Figure 3.10: Comparison of Y+O2 (O3 ) with Y2 O3 cell. (a). Molecule free flight signal. (b).
Molecule forward velocity versus ablation lens position. (c). Molecule number at different ablationlens position. (d). Molecule number at different O3 levels. Y+O2 (O3 ) chemical source provide
more molecule but at higher forward velocity, which is bad for molecule slowing experiment. The
O3 helps improving the molecule yield, but it is still worse than directly ablating Y2 O3 pellet.
However, all these were tested without the thin coating mentioned above. A more systematic study
with the Y2 O3 nanopowder coating is required.

We placed both Y2 O3 and Y metal inside the cell to directly compare their yield. Y metal
with O2 provides more but faster YO molecules than Y2 O3 pellet, as shown in Figure 3.10 (a). A
fast forward velocity is detrimental for slowing, so we scanned the ablation focus for both Y2 O3 celland Y+O2 cell, as shown in Figure 3.9 (b)(c). For Y+O2 , it’s hard to generate molecules at small
forward velocity, which is not ideal for molecule slowing experiment. We also tried more volatile
oxidizer like O3 which may be more reactive with Y metal. As we can see in Figure 3.9 (d), thepresence of O3 helps increase the molecule yield but doesn’t change the velocity distribution at all.

25
It’s worth mentioning that the chemical reactions were tested before we realized the importanceof the nanopowder coating. So the chemical source needs to be investigated more seriously withthe powdered cell. In the end, we didn’t use this approach in our experiment but switched back toablating pure Y2 O3 ceramic pellets.

3.4

Next Generation of YO Source
With all the upgrades mentioned above, we could generate ∼107 molecules with the forward

velocity of 120 m/s. For the nanopowder coated cell, we found that the molecule yield is decent
even at very low helium flow rates(0.25 sccm). A single spot on the Y2 O3 pellet enables ∼104
ablations, so the whole pellet provides hundreds of thousands of shots. In addition, under such alow helium flow rate, the cryogenic sorbs won’t saturate for months. Thus, the total runtime of thecell is mainly limited by the coating of the ablation window, which takes about a month. In thenext section, I list several drawbacks remaining in the current system and then introduce the next
generation of YO buffer gas cell.

3.4.1

Molecule Yield Fluctuation

The spacing between rotational levels is on the order of tens of GHz, as described in Chapter
2. This energy scale is on the thermal scale of a few Kelvin. Figure 3.11 (a) shows the calculated
occupation of rotational levels as a function of temperature. Since our experiment focus on N=0,1
and 2 states, to have sufficient population, temperatures of 4 K or less are required, as shown in
Figure 3.11 (b). So the cell at lower temperatures could generate more useful molecules.
We measured the dependence of molecular yield on temperature, as shown in Figure 3.12 (a),by turning off or on the pulsetube while ablating molecules. The cell temperature is measured by athermal diode(Lakeshore DT-670-CU) attached directly under the cell. Molecule number increases
with lower temperature at different helium flow rates, which matches the model calculated in
Figure 3.11 (b). Due to the nature of the pulsetube, the cell temperature is fluctuating by ∼0.2
K at ∼1.4 Hz. If the experiment is not synchronized with the pulsetube, the molecule yield would

26

Figure 3.11: Molecule yield at different temperature. (a). Calculated thermal occupation of rotational levels for YO. (b). Calculated occupation of the 3 lowest rotational states(N=0,1,2) versus
cell temperature. A cell at lower temperature can generate more molecules at N=0, 1, 2 states,
which are useful in our experiment.

fluctuate by 20%, as shown in Figure 3.12 (b), resulting in an unstable signal. In our experiment,
we synchronized the experiment cycle to the pulsetube cycle to achieve a stable yield. We therefore
operate the experiment at 1.4 Hz, the same as pulsetube. The synchronization is realized bymonitoring the cell temperature and trigger the experiment at the correct timing.

Figure 3.12: Measurement of molecule yield at different cell temperature. (a). Molecule yield at
different cell temperature. The molecules yield at 2.5 sccm has a stronger dependence than 6.0
sccm, as the thermalization is better in the latter case. (b). Fluctuation of molecule yield dueto the nature of pulsetube. The ablation operates at ∼1.3 Hz, different from the rep rate of thepulsetube(1.4 Hz).

27
3.4.2

Limited Pumping and Accessibility

As discussed previously in section 3.2.1, two in-vacuum shutters are installed to preventthe cell heating by blocking the laser beams into the cell. In addition, they also help maintainthe pressure of the science chamber by blocking the helium. As we can see in Figure 3.13 (a),the science chamber pressure increases with helium flow but remains to be ∼10−9 Torr. Without
these shutters, the pressure would be more than 10−8 Torr, limiting the trap lifetime to less than asecond. This indicates that the helium exiting the cell is not pumped out sufficiently. It could be
improved by installing more cryogenic sorbs in the region between the cell aperture and the front
4 K shield. Currently, they are only ∼5 cm apart, so more sorbs can’t be inserted.
As mentioned above, the cell runtime is currently restricted by the coating on the ablation
window, which is also limited by our beam box dimension. A longer snorkel would reduce theamount of YO powder reaching the ablation window, which requires more space between cell and4 K shields, as shown in Figure 3.13 (b) and (c). The limited space also makes it extremely hardto swap the sample and targets.
Another issue is the copper plates get oxidized overtime thus their reflectivity reduces as well,which eventually increases the heat load into the cell. An oxygen resistant gold coating should beapplied to the surface to prevent the copper blackening.

3.4.3

1 K System

A new 1 K system is designed to overcome all these problems. In the current setup, thecell is cooled to 4 K directly by the 4 K stage of the cryocooler(Cryomech PT410). In the newsetup, the cryogenic buffer gas cell is cooled to 1 K via a thermal connection to a 1 L pot of
helium which is pumped by a roughing pump(Edwards XDS 10). With a pumping speed of 10
L/s and a heating rate of 100 mW, the pot temperature is ∼ 1.4 K [101]. A 1 L pot of liquid
helium provides a runtime of about 7 hours between refills, which should be more than enough fordaily operation. At 1.4 K, the new cell generate ∼50% more molecules than the current 4 K cell,

28

Figure 3.13: (a). Science chamber pressure versus helium flow rate with shutters open 8 ms every
second. (b). Back view of the cell, snorkel included. The cell is directly anchored on the 4K cold
head. (c). Front view of the cell, snorkel not installed. We can see the space is very limited.

according to the calculation in Figure 3.11 (b). The molecule yield should also be very stable since
the cell temperature doesn’t fluctuate with the pulsetube. Our experiment timing doesn’t need
to be synchronized to the pulsetube any more. In addition to the temperature, the cell wouldn’t
physically oscillate together with the pulsetube as well. Therefore, the cell pointing should bestable, resulting in a much stable and bright source. The 4 K and 40 K pulsetube stages arethermally connected to radiation shields by copper braids(not shown) to decrease the black bodyradiation onto the cell. The heat loads are estimated to be about 30 mW, 300 mW and 20 W on 1

29
K, 4 K and 40 K stages. Besides, all shields are supported from the bottom with the thin stainlesssteel rods isolating the heat exchange between different stages.

Figure 3.14: Beambox view for each layer. (a). Beambox. (b). 40 K shields. (c). 4 K shields. (d).
1 K pot and cell.

The 1 K design is shown in Figure 3.14 and 3.15. Here I list several features for the new
design. In the previous design, the entire 4K and 40K copper enclosures are directly mounted on
the pulsetube. As a result, there are ∼20 kg of copper while the recommended loads are only 5 kg
on 4K stage and 10 kg on 40K stage. This can potentially introduce a leak into the system, also it
was very hard to access the panels without disassembling everything. A very thin stainless steel rod
is used to support most of the things from the bottom. We choose 41 ”-20 threaded rod as a support
to reduce possible heat transfer between each layer. Special care is taken in the 1K pot design as
it experiences a large temperature gradient from 300 K to 1 K. The 0.065” thick tubing is used
to reduce the cross section for low thermal conductance. To increase the pumping performance,a CF 6” flange is designed on the top panel to directly pump out the chamber. A KF 25 flange
is left at the corner to pump out the hot helium from the pot, as shown in Figure 3.14 (d). It is
worth mentioning that there is 1K system available from Cryomech, which is a closed system that
doesn’t require filling in helium. We can implement this in the future if we want to simplify our 1
K system. Currently, the new beambox has been made and hopefully it will be assembled pretty
soon.

30

Figure 3.15: Section view of the new beam box.

Chapter 4

Laser Slowing

Molecules exiting the buffer gas cell move at ∼ 120 m/s. In order to capture molecules
into a magneto optical trap(MOT), they need to be slowed down to the MOT capture velocity
q
~kγD
vc =
[102], which is on the order of 5 m/s. In atomic physics experiment, people havemdeveloped several techniques to slow atoms but it remains challenging for molecules due to theircomplex structure. Slowing the molecules down to trappable velocity takes us three years and it
remains to be the most inefficient step in the experiment. In this chapter, we introduce the basic
slowing theory, slowing setup, detection method, slowing upgrades and a potential scheme with
better slowing efficiency.

4.1

Laser Slowing YO
The idea of a radiative scattering force on free atoms being velocity dependent and therefore

useful for cooling a gas was proposed in Refs. [103, 104, 105]. The Zeeman slower [106] and chirped
slowing [107] are the two main techniques used in the cold atom community. In order to achieve
the continuous photon scattering, these techniques adopt different ways to compensate the Doppler
shifts since the scattering is strongly velocity dependent. In both cases, a laser beam is directed
opposite to an atomic beam.
Zeeman slower is a simple and stable deceleration method, where a tapered magnetic field is
employed to cover a range of initial velocities. This works by utilizing a spatially varying magnetic
field to compensate the changing Doppler effects by the correspondingly adjusted Zeeman shifts.

32
The magnetic field is specially designed for specific atomic species thus the atoms are always
resonant to the laser beam during the entire deceleration. This design relies on the fact thatthe atoms have a large Zeeman shift in the excited state and limited number of ground states.
Unfortunately, molecules typically don’t posses these properties. As shown in Figure 2.2, YO
molecules have 12 ground states with distinct Zeeman shifts, which means the molecules can decay
into both high and low field seeking states. In addition, the excited state A2 Π1/2 has a verysmall Lande g factor, making the Zeeman slower even harder. In our experiment, we chirp laser
frequencies to slow the molecules. Recently, various methods for molecule cooling including, adifferent type of Zeeman slower and stimulated cooling with adiabatic transfer are proposed [108,109, 110, 111, 112, 113] to cool molecules more efficiently.

4.2

Γ/13 Slowing Scheme
The generation of molecules from a cryogenic buffer gas cell is described previously in Chapter

3, which provides relatively low initial forward velocities. With a forward velocity of ∼120 m/s anda recoil velocity of 6.2 mm/s, it takes 2×104 photon scatterings to slow down to rest, thus a closed
cycling transition is required. With two vibrational repumps(v=1 and 2), molecules can scatter
more than 106 photons before getting dark.

4.2.1

Γ/13 Repumping Scheme

The most relevant details of our Γ/13 slowing scheme are shown in Figure 4.1 where thevibrational repumps are not shown for simplicity. X 2 Σ+ N=1(-) and A2 Π1/2 J’=1/2(+) are theground and excited state for the main cycling transition. The N=1 state is chosen to alleviate
the need of rotational repumping due to parity and angular momentum selection rules of ∆N=0,±1 [54]. In this case, the repumping scheme is very simple where only one laser is required on each
vibrational level. Therefore, only three lasers are required for slowing molecules. Unfortunately,00

there is an intermediate level A 2 ∆3/2 (J = 3/2(−)) lying at a lower energy than the excited state0

A2 Π1/2 , making the cycling transition more complicated. The A2 Π1/2 to A 2 ∆3/2 transition is33
electric dipole forbidden, however, it does occur due to the mixing of the nearby A2 Π3/2 with the00

A 2 ∆3/2 [78], resulting in a 3×10−4 chance of decaying to A 2 ∆3/2 state. Since it is a two photon
0

process, molecules that decay to X 2 Σ+ via A 2 ∆3/2 end in the N=0 or 2 levels where it becomesdark to the cooling laser. To maintain the continuous scattering, microwaves are applied to directly
mix the N=0 and N=2 states with the N=1 state, depicted as blue arrows in Figure 4.1. Therefore,
v=0 N=0-2, v=1 N=1 of X 2 Σ+ and J’=1/2(+) of A2 Π1/2 are all directly connected in the main
cycling transition. In this scheme, there are 4 manifolds coupled in the excited state(ne = 4) and 48
manifolds involved in the ground state(ng = 48). This results in an effective scattering rate [75, 76]eΓScatter = ngn+n
Γ of Γ/13.
e

In this scheme, there are 4 manifolds coupled in the excited state(ne = 4) and 48 manifolds
involved in the ground state(ng = 48). This results in an effective scattering rate [75, 76] ΓScatter =ne
ng +ne Γ of Γ/13.

Figure 4.1: Γ/13 slowing scheme. (a). Configuration of main slowing beam and microwave repumpers. Vibrational repumpers are not shown for simplicity. (b). Detailed setup for mainslowing beams addressing different hyperfine manifolds.

34

Figure 4.2: Detection method. (a). Single photon detuning ∆ corresponds to the Doppler shift,which is related to the detection velocity. (b). Experiment apparatus for slowing and velocity
sensitive detection. The detection beam is 45 degree with respect to the molecule beam.

4.2.2

Detection Method

The detection of slowed molecules is tricky for the molecules with many hyperfine splittings.
The splitting between G=0 and G=1 is 750 MHz, corresponding to 650 m/s at 45◦ detection. With
the multiple hyperfine states of YO separated by 20 MHz(∼17 m/s at 45◦ detection), we apply
two lasers detecting G=0 and G=1 states separately, as shown in Figure 4.2 (a). This two-laser
detection is sensitive to the distribution of hyperfine states, which would underestimate the speedof molecule by ∼10 m/s. In experiment, we vary the single photon detuning ∆ to detect molecules
at different velocities. This velocity sensitive light induced fluorescence(LIF) signal is detected by a
PMT(Hamamatsu R10699), feeds to a home-built preamplifier and then filtered by a multichannel
scaler(Stanford Research Systems SR 430) that sets the threshold for photon counting. The counts
are collected by a NI-DAQ card and then processed with Matlab. The PMT collection effieciency
is ∼ 3 × 10−4 which is calculated according to the geometry.
The initial slowing result is unstable due to the low slowing efficiency and the unstablemolecule yields between shots. To understand the slowing performance, it is crucial to take avelocity distribution of the free molecules and the slowed molecules. This is achieved by modulating
the one photon detuning ∆ at high frequency(1 kHz) and extract the velocity distribution basedon the modulation timing.

35

Figure 4.3: Doppler sensitive detection. (a). Initial velocity distribution of the two stage cell. (b).
Detecting 10 m/s molecules, slowing beams are off at 33 ms. Our initial slowing with second stage
cell is terrible.

4.2.3

Performance

The detection method works great for detecting a velocity distribution, the velocity distribution from our two stage cell is shown in Figure 4.3 (a). For optimal slowing to 10 m/s, theslowing laser was applied 5 ms after the ablation pulse and was on for 28 ms. The slowing beams
are broadened by EOMs to cover a broader velocity group of molecules. Unfortunately, we’re neverable to slow more than a hundred of molecules to 10 m/s due to the low initial molecule number
and the poor slowing efficiency(<1%) [90], as shown in Figure 4.3 (b). The two stage cell generates ∼4000 molecules peaked at 70 m/s. The initial molecule number gets boosted up to ∼106
by taking away the second stage together with all the upgrades previously mentioned in Chapter
3. After this upgrade, we’re able to slow more than a thousand of molecules to 10 m/s. The low
slowing efficiency is primarily due to the the small deceleration rate that is limited by the effective
scattering rate of this scheme, Γ/13.

4.3

Γ/8 Slowing Scheme with N=2 Decoupled
In order to slow more molecules, we tried to increase the deceleration rate by decouplingstates from the cycling transition. With the fixed initial and final velocities, a larger deceleration
leads to a shorter slowing distance. In this case, the transverse diffusion is reduced, as shown in36

Figure 4.4: (a). Transverse diffusion with different deceleration rate. A high decelerationrate(bottom) reduces the transverse spread, increasing the number of molecules in the MOT region.
(b). Detecting 5 m/s molecules at different scattering rate, slowing beams are off at 21 ms. The
number of slowed molecules increases by ∼20 times with Γ/8 pumping scheme.

Figure 4.4 (a), resulting in an increased number of molecules captured in the MOT.

4.3.1

Repumping Scheme

To increase the effective scattering rate, we decouple the X 2 Σ+ N=2 from the cycling transition by removing the N=1 ↔ N=2 microwave but directly optical pumping N=2 to A2 Π1/2
0

J = 3/2, as shown in Figure 4.5 (a). From Section 2.2.2, we see by decoupling N=2, we now havee
28 ground states(ng = 28) instead of 48, giving us an effective scattering rate ΓScatter = ngn+nΓeof Γ/8. With increased deceleration, ∼20 times more 5 m/s molecules are slowed than the Γ/13
scheme, as shown in Figure 4.4 (b). A further increase could be achieved by decoupling the vibra0tion repumping v=1 N=1 state, from the cooling excited state A2 Π1/2 J = 1/2 by pumping to0

A2 Π1/2 J = 3/2 state where two v=1 repumps are required, as shown in Figure 4.5 (b). In thisscheme, we have 16 ground states(ng = 16) and 4 excited states(ne = 4), resulting in an effectiveescattering rate ΓScatter = ngn+n
Γ of Γ/5. Unfortunately, we’ve never seriously explored the Γ/5escheme due to the increased number of vibration repumping lasers. It is still worth a try to get

37
more molecules slowed for the MOT.

4.3.2

Spectroscopy for Γ/8 Scheme
00

The N=1→J = 3/2 and N=2→J = 3/2 spectroscopy is taken to implement the new Γ/8
repumping scheme. We excited the ground state molecules with a low intensity laser beam perpendicular to the motion of molecules and then collected the fluorescence. The laser frequency ismodulated as described in Section 4.2.2, thus the entire spectrum is obtained in a single experiment. The results are shown in Figure 4.6. In our experiment, the N=2 repumper is set at theright peak in Figure 4.6 (b) for the best slowing performance.
4.3.3

Slowing Setup and Performance

A dye laser was used to repump molecules on X 2 Σ+ N = 2(+) state, parking at the rightpeak shown in Figure 4.5 (b). With increased deceleration rate, the diffusion was suppressed since
the slowing distance is reduced by 40%. As a result, the number of slowed molecules increased bya factor of 20, as shown in Figure 4.4 (b).
With so many lasers involved in chirped slowing, it is important to simultaneously sweep alllaser frequencies to compensate for the Doppler shifts during the entire slowing. Our main slowing
laser and vibrational repumpers are directly locked on an erbium frequency comb to achieve kHz
stability. So, there are two ways to modulate these laser frequencies: either chirping lasers together
with the comb or modulating them independently. Back in 2015 [90], we modulated the repetition
frequency of the frequency comb thus all lasers locked on the comb would be modulated accordingly.
This simple method is convenient when the wavelengths are close enough, which is true in our case.
Our transition wavelengths are 614 nm, 648 nm and 649 nm. Therefore, the Doppler shifts oneach transition are very similar. Considering the flexibility, we switched to a different scheme
where the frequency comb remains static but the lasers are modulated by their locking acoustooptic modulators(AOM). A slowing laser setup is shown above in Figure 4.7. The detailed locking
schemes are discussed in Appendix B of [114].

38

Figure 4.5: (a). Γ/8 repumping scheme. The N=1↔N=2 microwave is removed, while the N=20
is directly repumped to A2 Π1/2 J = 3/2 by a laser. The v=0 N=2 state is therefore decoupledfrom the cooling ground state v=0 N=1, resulting in an effective scattering rate of Γ/8. (b). Γ/50repumping scheme. The v=1 repumper is replaced by two lasers pumping into A2 Π1/2 J = 3/2
state. v=1 N=1 state is therefore decoupled from the cooling excited state A2 Π1/2 J 0 = 1/2(+),
resulting in an effective scattering rate of Γ/5.

0

Figure 4.6: (a). X 2 Σ+ N = 1(−) → A2 Π1/2 J = 3/2(+) spectroscopy, peaks are F=1 and F=2.
0(b). X 2 Σ+ N = 2(+) → A2 Π1/2 J = 3/2(−) spectroscopy, peaks are F=1 and F=2. N=2 repumper
is parked at the right peak for the best slowing performance.

39

Figure 4.7: Slowing setup for chirped slowing. The vibrational repumpers v=1 and v=2 are injection
locked and then amplified by the tapered amplifier. The main N=1 transition and vibrational
repumps are combined by dichroic mirrors and PBS.

A 1 W Raman fiber amplifier(MPB RFA) is used to address the main slowing transition.
Since the N=2 repumping is 9.617 GHz away from the main slowing transition, a commercial dyelaser(Sirah Matisse DR) is used to repump the N=2 dark state. RF sidebands produced by a seriesof AOMs address all hyperfine transitions. The beam combination is achieved by dichroic mirrors
and polarizing beam splitter(PBS). In order to address more velocity groups, a 10 MHz EOM
could be inserted to broaden the slowing spectrum. In addition, the combined beams go through a
Pockels cell which switches the polarization between s and p to distrupt the optical pumping into
the dark Zeeman states. The Pockels cell also introduces sidebands into the lasers, broadening thespectrum together with AOMs. The collimated slowing beams are slightly focused at the entranceof the science chamber to provide a transverse confinement and maintain a good mode match tothe molecule beams. This technique doubles the number of slowed molecules. The solution for thecell heating by slowing beam is described in Section 3.2.1

40

Figure 4.8: Γ/8 slowing performance. (a). Slowing at different deceleration rate. (b). Slowing
result at optimal slowing parameters

We first explored the chirped slowing by scanning the deceleration rate as shown in Figure 4.8(a). In the experiment, we kept the initial(vi =110 m/s) and final(vf =20 m/s) velocities fixed while
only varying the deceleration rate a. In this case, the deceleration distance s changes accordingly,
vf2 − vi2 = 2a × s. The optimal deceleration rate is ∼6000 m/s2 , indicating a scattering rate of
1 MHz. It is a factor of 3 smaller than the effective scattering rate Γ/8 calculated based on therepumping scheme. We’ve checked that all transitions are well saturated and properly mixed, thus
the discrepancy in decelerations remains unclear.
We also varied the Pockels cell frequency for slowing. Pockels cell chops the polarization ofslowing beam to prevent the polarization dark state. Since the scattering rate is ∼1 MHz, there is
no strong dependence from 1 MHz to 5 MHz.
For a 100-20 m/s slowing, slowing beams are typically switched on at ∼2 ms after the Yag
ablation pulse. This is mostly due to the exit time of YO from the cell, which is ∼1.5 ms.
Combining all the upgrades, the Γ/8 scheme delivered ∼2×105 molecules within the trappablevelocity. The slowing efficiency from 120 m/s to 5 m/s is ∼4%. This provides enough slow molecules
for the trapping stages.

41

4.4

0

Slowing Scheme with A 2 ∆3/2 Repumped
To prevent the leakage into N=0 and N=2 dark states, we can also directly repump the00

A 2 ∆3/2 (J = 3/2(−)) state into B 2 Σ+ (J = 1/2(+)) state, as shown in Figure 4.9. The B 2 Σ+ toX 2 Σ+ transition is very diagonal with most of the decays into v=0, 1 and 2 where the vibrational
states are already repumped. The proposed scheme decouples N=0 and N=2 from the main groundstate N=1, which increases the photon scattering rate by 15% but most importantly, reduce theloss during cooling. The coupling to the N=1 state deteriorate the cooling, which will be detailed in
section 6.1.2. In the current repumping scheme, to achieve a cold temperature, the N=0 rotational
repumper is switched off during the gray molasses cooling, resulting in a 50% of molecules loss.
This loss will be prevented in the new scheme. In the new scheme, there are 4 manifolds coupledin the excited state(ne = 4) and 24 manifolds involved in the ground state(ng = 24). This resultsein an effective scattering rate [75, 76] ΓScatter = ngn+n
Γ of Γ/7.
e00Figure 4.9: (a). Current repumping scheme. (b). New repumping scheme with A 2 ∆3/2 (J =3/2(−)) directly repumped to B 2 Σ+ . This scheme doesn’t significantly increase the scattering rate
but prevent the loss during the gray molasses cooling.

Chapter 5

3D Magneto-Optical Trap of Yttrium Monoxide

After slowing the molecules, it’s important to trap them and keep them locally confined.
Magneto-optical trap(MOT) is a widely used technology in atomic physics to produce samples ofcold, trapped, neutral atoms. It combines laser cooling and a spatially-varying magnetic field tocreate the trapping forces. Since the first proposal on making a molecular MOT in 2008 [54], over the
past 12 years, there are only a few molecules that have been trapped in MOT [91, 55, 56, 57, 58].
In this chapter, we discuss different MOT schemes on a type II cooling transition, present theimplementation of the MOT in three-dimensions along with the comparison between RF and dc
MOT performances.

5.1

Magneto-optical Trapping Theory
Building on laser cooling, the first magneto-optical trap(MOT) was demonstrated in 1987 [115].

A typical MOT is formed from the intersection of a weak quadruple magnetic field and three pairsof circularly-polarized red-detuned beams. A simplified 1D MOT configuration is shown in Figure
5.1.
A magnetic field gradient is generated by a pair of anti-Helmholtz coils, creating a spatiallyvarying energy level due to the Zeeman effects. We first focus on the traditional MOT setup(TypeI MOT), as shown in Figure 5.1 (a). For a J=0 to J=1 transition, the magnetic field splits thethree sublevels(mj = 0, ±1) of the excited state, whereas the ground state remains unchanged. A
pair of red detuned lasers with σ + and σ − polarizations are sent from opposite directions. Because

43

Figure 5.1: Arrangement for a MOT in 1D. (a). Type I MOT. In the magnetic field gradient, theZeeman splitting of mj = 0, ±1 states depends on the position of the atom. The counter propagating
beams with different polarization and the transition selection rules lead to an imbalance in theradiative force from the laser beams that pushes the atom back towards the centre of the trap. (b).
Type II MOT. Trapping force doesn’t exist due to the dark manifolds in the ground state.

of the transition selection rule, atoms are excited from ground state to mj = −1 state by absorbinga σ − photon. Similarly, atoms are excited from ground state to mj = +1 state by absorbing a σ +photon. If the atoms are displaced to the right of the origin, it preferentially absorbs the laser fromthe right which is closer to resonance, and thus receives a kick back towards the origin. Similarly,
if the atoms are displaced to the left, it prefers the photon from the left, and thus receives a kicktowards the origin as well. The excited state atoms would then decay back down to J=0 state,
resulting in a force averaged to zero and the whole process continues. The total force [102] on theatoms is given by the sum of σ + and σ − beams where
−

+

σ
σ
FMOT = Fscatt(ω − kv − (ω0 + βz)) − Fscatt(ω + kv − (ω0 − βz)) ' −2∂F∂F
kv + 2βz,∂ω∂ω0with Fscatt as the scattering force from a single beam
Fscatt = ~kI/IsatΓ.
2 1 + I/Isat + 4δ 2 /Γ2

The term ω0 + βz is the resonant absorption frequency for the ∆mj = +1 transition at position z.
Similarly, ω0 − βz is that for the ∆mj = −1. The Zeeman shift at displacement z isβz =gµB dBz,~ dz

44
where g = gj . Therefore, the force depends on the frequency detuning δ = ω − ω0 , so
FMOT = −αv −

αβ
z,
k

α=

∂F
=
∂ω

8~k 2 ∆I/Isat2Γ 1 + I/Isat + 4∆
Γ2

2 .

This is the expression describing a damped harmonic oscillator. Therefore, the atoms are confined
inside the trap under the restoring and viscous force.

5.1.1

Type II MOT

Unlike atoms, a molecular MOT is more difficult due to its complex energy structure. For atypical type I MOT on a J→J+1 transition, as shown in Figure 5.1 (a), excited atoms always decay
back to the same ground state. Therefore, a large number of photon scatterings becomes possible.
However, in order to maintain the rotational closure for molecules [54], N=1 is chosen as the groundstate, resulting in a F→F-1 transition, a type II MOT. As a result, there are more ground states
than the excited states where molecules can be pumped into dark states in the ground [116] undera fixed laser polarization and magnetic field gradient, as shown in Figure 5.1 (b). For example,
molecules on mj = +1 can absorb a σ − photon and get pumped to mj = 0 excited state. The
become dark to the σ − laser if they decay to mj = 0, −1 states. To avoid these dark states, there
are two solutions: rf MOT [117] and dc dual frequency MOT [118, 119].

5.2

Experiment Setup for RF MOT
As first described in Ref. [91], in an rf MOT, we modulate both magnetic field direction andlaser polarization at a rate faster than the optical pumping rate. Typically, the optical pumping
rate into dark state is on the order of 1 MHz. The switching needs to be fast enough for the change
to be non-adiabatic.

5.2.1

RF MOT Coils

The typical MOT coil is realized by two spools of magnet wires in an anti-Helmholtz configuration. However, a normal drive for the coils can not create B field gradient of ∼10 Gauss/cm

45
oscillating at MHz, which is limited by the required current and voltage at such high frequency. We
use a resonant tank approach to drive the coils sinusoidally, as implemented in Ref. [91]. Several
vacuum compatible coils are designed and constructed.
Switching current at high frequency gives rise to a large inductive spike, creating a hugevoltage. The stray electric field then mixes the opposite parity states and causes extra loss into
the wrong parity states, which will be detailed in Section 5.4. To reduce the inductance, coils are
made small and placed inside the vacuum chamber. In this case, heating becomes an issue inside
the vacuum. At RF frequencies, the current in the conductor is localized near the surface in alimited thickness called skin depth
r
δ=

2ρ
,
ωµ

where ρ, ω, µ are resistivity of the conductor, angular frequency of the current and permeability of
the conductor. The skin depth of copper at 5 MHz is ∼35 µm. Therefore, the resistivity is large
due to the small the cross section, which produces lots of heat.

5.2.2

First 3D RF MOT Coil Design

We use a coil directly bonded on an amorphous aluminum nitride(AlN) substrate that has avery high thermal conductivity(∼200 W/m·K). Therefore, the heat generated by the copper coils
is quickly conducted to the insulated AlN board. However, AlN is much harder than alumina,
making the fabrication very difficult. All our coils are designed and drawn by ourselves and thenfabricated by REMTEC.
The first coil design used in 3D rf MOT paper [58] was previously described in [114], so here
we only emphasize the most salient details. As shown in Figure 5.2 (a), four boards with twoslightly different designs are used to increase the magnetic field. There is one copper spiral on bothsides of the board and a Kapton film is sandwiched between the boards to avoid direct contact andthe possible arcing. There are 4 layers and total 28 turns on each half of the MOT coil. A copper
C clamp is installed on the left side to conduct the heat to the water cooled copper finger. With
this coil setup, we generated a magnetic field gradient of ∼20 Gauss/cm modulating at 5 MHz

46

Figure 5.2: Different MOT coil designs.(a). First MOT coil design used in 3D rf MOT paper. There
are 7 turns on each side of the board. 2 boards are used on each half of the coil. (b). Current
MOT coil design used in 3D dc MOT. (c). Coil mount for good thermal conductivity. (d). Coilmount for better pumping conductance. The blackening is achieved by the black paint, MH2200.

with a working temperature of 50 ◦ C. To reduce the unwanted light scatter, the coil is blackenedby oxidizing [120] the copper traces while the AlN substrate remains reflective. This design has
several drawbacks. The high voltage capacitors were installed inside the vacuum, therefore, theresonant frequency of the LC tank circuit can’t be tuned without opening the vacuum. The coils
weren’t centered properly for years due to the limited accesses. In addition, the coils remained hot
during normal operation due to the limited thermal contact.

47
5.2.3

New RF MOT Coil Design

To overcome these problems, a new pair of coils was designed. The pictures of a single board
and the coil assembly are shown in Figure 5.2 (b) and (c). Compared with the previous design,
we nearly doubled the number of traces on each surface for higher field gradient and introduced acopper layer on the edge for better heat conductance. The center hole is larger than that of theold coil, allowing a larger MOT beam to capture more molecules. The boards are cut for potential
optics inside the vacuum, for example, an in-vacuum lens. The detailed drawing of the coils are
displayed and discussed in Appendix C.

5.2.4

Driving RF CoilFigure 5.3: (a). Measure the reflection of new coils to determine the resonant frequency(f0 =0.8
MHz) and the quality factor(Q∼40). (b). Impedance matching circuit diagram for rf MOT coils.

The new boards, Figure 5.2 (b), consist of a 12 turns copper spiral bonded on both side of the
AlN substrate. The spiral is 0.012” thick with a width of 0.025” and a gap of 0.025”. Comparedwith the previous design, the new design increases the inductance(resistance) by a factor of 4.6(2.3).
A high voltage variable capacitor is located outside the vacuum, giving a tunable frequency between
0.5 to 2 MHz. With a capacitance of ∼500 pF, the quality factor Q of the coil is ∼40 and theresonant frequency is 0.8 MHz, as shown in Figure 5.3 (a). For this configuration, we tested thatthe arcing didn’t occur at 4 kV/cm where the magnetic field gradient is 40 Gauss/cm.

48

Figure 5.4: (a). Axial magnetic field measurement. The field is very linear in a 8 mm region.
(b). Calculated axial magnetic field with different coil configuration. Both configurations provide
a good linearity within 1 cm.

To drive the RF coil, we use a commercial RF amplifier(RM Italy HLA-305V) that produces∼65 W, resulting in a field gradient of 20 Gauss/cm at 0.8 MHz. The impedance matching isachieved by a wrapped toroidal transformer. The magnetic field is quite linear in a 8 mm region,
as measured in Figure 5.4 (a), matching the calculated result in Figure 5.4 (b). 11 Gauss/cm·A ismeasured along the axial direction, in agreement with the calculation. The new coils are directly
mounted to the stainless steel vacuum flanges as shown in 5.2 (c). Therefore, the coil center isvery well aligned to the geometric center of the chamber. At the beginning, the coil was connected
in series to ensure that they are driven with the same current. Later, we switched to parallel
configuration as shown in Figure 5.3 (b) to reduce the potential E field associated loss. We will
discuss this in Section 5.4.

5.2.5

Cooling the CoilWhen driving the coils with 20 Gauss/cm(RMS), 50 watts of heat are generated inside thevacuum. With limited thermal convection, the thermal conductance becomes critical to prevent
outgassing and themal gradients. In the new design, a copper layer was bonded on the edgeof the board for better thermal contact. The copper ”horse shoe” which mounts the coils were49
attached onto four 0.5” copper feedthroughs. An indium foil was sandwiched between all joints
to increase the thermal conduction. These copper feedthroughs were water cooled at the outsideof the vacuum. Using a water-ethylene glycol(EG) mixture in the chiller, the cooling water weremaintained at -20 ◦ C. This allows the coils to run at full duty cycle with a temperature of ∼40 ◦ C
in vacuum. The thermal performance was measured by two thermistors located at the highest andlowest temperature spots of the coil. The temperature difference on the board is less than 10 ◦ C.

Figure 5.5: (a). Stress inside the window, checked via polarized stress tester. The color is due tothe birefringence, indicating a strong stress in the window. (b). Window glued on thin wall vacuum
flange. The stress is greatly reduced. (c). Scattered light from our custom viewport.

5.2.6

Reducing the Scattered LightIn our experiment, YO molecules are detected using light induced fluorescence(LIF). Therefore, it’s necessary to reduce the light scattered by the stainless steel chamber and all coil accessories. There are many blackening methods including copper blackening [121] and various typesof black paints. Previously, we oxidized a series of copper shields and put them inside vacuum toblock all scattered light. The method involves bringing a sodium hydroxide(NaOH) and sodium
chlorite(NaClO2 ) solution to a boil and immersing the copper for several minutes. However, it
only works for copper surfaces and it’s prohibitively hard to machine this copper to fit all surface
necessary to block scattered light. In addition, the copper oxide coating can be easily removed
by rubbing the surfaces. For an improved solution, we spray a black paint(Alion MH2200) all50
over our chamber due to the ease of application and great performance. This paint is silica-based,
nonconductive, UHV compatible and scratch resistive [122, 123, 124]. It can be easily applied toall surfaces including aluminum, copper, stainless steel and aluminum nitride. We sprayed thepaint over all surfaces using an air brush and baked them in air at 200 ◦ C for 4 hours to eliminate
possible outgassing. Figure 5.2 (b) and (d) shows the coil before and after the blackening. The
only drawback is that the coating is hard to remove.
It is suggested [99] that a custom window should be used to further reduce the light scatter. During the brazing process, the commercial UHV windows are covered with a thin layerof grime which causes high scattering. We tried to epoxy a 40 mm N-BK7 window with NIR I
coating(Edmund optics 83-476) onto a CF to KF adapter(Kurt J. Leskser F0275XQF40). The
epoxy(Epotek 353 ND) [125] we used requires a minimum cure temperature of 80 ◦ C and 150 ◦ C
for full bonding strength according to the specification sheet. The high cure temperature combinedwith the mismatch of thermal expansion coefficient between stainless steel and N-BK7 introduces
a large stress in the window, as shown in Figure 5.5 (a). If fused silica is used for better surface
quality, the window would even crack after the cure due to its small thermal expansion coefficient.
To overcome these problems, we machined the vacuum flange to 0.01” thickness which reduces thestress, as shown in Figure 5.5 (b). This was originally developed by Housekeeper for direct metal
to glass seal where the thickness is normally ∼0.001”. The epoxy is also applied on the side of
the window for better performance. With this design, the stress in the window is greatly reduced.
However, the viewports still scatter ∼0.25-1% of laser light, as seen in Figure 5.5 (c). This canbe attributed to the grime introduced during the curing at high temperature. In the future, a lowtemperature epoxy(Epotek 032-3M) should be used which is able to cure at room temperature.

5.2.7

Detection system for RF MOT

The detection system shown in Figure 5.6 was used for the 3D rf MOT [58]. We detected
614 nm fluorescence and filtered the 648, 649 nm vibrational repumpers with color filters(Edmund
84-118). Irises are placed in the image plane between lens sets to block the unwanted scattering. A

51

Figure 5.6: Detection system for the rf MOT. Two 2 inch, 150 mm focal length and two 1 inch,
75 mm focal length lenses are used on each side. An iris is placed at the focal plane to block theunwanted light scatter. There is a color filter blocking the vibrational repumpers.

PMT(Hamamatsu R10699) provided time resolved signals and a CCD(Apogee Alta U47) recorded
spatial information. PMT receives the photons and generates the photon current. The current
goes through a transimpedance amplifier and is then counted by a multichannel scaler(SRS 430).
The amplifier was designed and built by the electronic shop in JILA. With a high photon flux, thephoto current pulses have a high chance to overlap with each other. In this case, the multichannel
scaler can not distinguished the pulses, resulting in a saturation. This can be improved by insertinga correction factor [126]. Both PMT and CCD systems are similarly designed and orthogonal tothe molecule beam. The collection efficiency of the PMT(CCD) is 3.3×10−4 (1.4×10−3 ). The CCDalignment is confirmed by imaging a notched threaded rod in the MOT center [114].

5.3

RF MOT Performance

5.3.1

1D RF MOT

To study the 3D RF MOT, we first explored the 1D rf MOT. The slowing was unnecessary
since the transverse velocity of the beam is on the order of ∼5 m/s, comparable to the trapping
velocity. 1D MOT allowed for optimization of the correct phase between the laser polarization andthe magnetic field direction.

52

Figure 5.7: 1D RF MOT. (a). Phase between laser polarization and magnetic fields in rf MOT.
(b). 1D rf MOT at opposite phase. The signal is phase subtracted(φ − (φ + 180◦ )). Molecules
are generated at time zero. (c). Differential 1D MOT signal at different phase. 50◦ is the optimal
MOT phase.

Three lasers are red detuned to address G=0 F=1, G=1 F=0 and G=1 F=1,2 states. We sent
3 pairs of beam into the chamber and looked at the fluorescence detected by a beam with limited
size. As discussed in the previous section, both magnetic field direction and laser polarization are
modulated at a rate faster than the optical pumping rate to prevent molecules from going dark.
When the correct phase is chosen, the molecule beam is compressed due to the trapping force.
Similarly, if the phase is wrong, the trapping force becomes weak and even expand the beam. Witha small detection beam, a compressed beam has more counts than an expanded beam, as shownin Figure 5.7 (b). The phase is scanned to reach the optimal trapping condition, as shown in
Figure 5.7 (c). The data was measured at a detuning of 5 MHz and a magnetic field gradient of 10
Gauss/cm.

5.3.2

3D RF MOT

To capture molecules in a 3D rf MOT, it’s necessary to slow molecules down to 5 m/s. As
it has been discussed previously in Section 3.2 and 4.3.3, we removed the second stage of thebuffer gas cell, coated the cell, installed an in-vacuum shutter and implemented the slowing schemefrom Γ/14 to Γ/8. We first checked that we can slow molecules down to ∼5m/s. It takes ∼ 16
ms to slow molecules from 120 m/s to 5 m/s. Then we looked for a slow decay signal of trapped

53

Figure 5.8: Experiment layout for 3D rf MOT Setup. MOT beams are circulated for a strong
intensity.

molecules using a PMT. Limited by the laser intensity of v=0 and v=1, we circulated the trapping
and repumping beams instead of using three independent pairs. The beam first entered through thebottom port, then reflected down to the octagonal plane, as shown in Figure 5.8. After reflecting
into the last port, the beam was retroreflected back.
We had been struggling with a weak MOT signal for a very long time until we extended theslowing sequence by an extra 12 ms, which was first discovered by the Harvard group. Apparently, they underestimated the molecular beam velocity and overestimated the trapping velocityof the MOT. In our case, the Doppler sensitive detection would only overestimate the velocities,
as described in Section 4.2.2. Therefore, we believe it’s the over slowing that helped load more
molecules into the MOT. As we can see in Figure 5.9 (a), more molecules were loaded into the
MOT with more slowing time and reached saturation at ∼11 ms. The optimal slowing time of 28
ms almost doubled the time we had seen as the arrival time of 10 m/s molecules, which was only
∼16 ms. Figure 5.9 (b) shows a Doppler detection at the end of the slowing, molecules are slowed

54

Figure 5.9: (a). 3D rf MOT loading with different extra slowing time, ∆ = 2π × 5 MHz. The
original slowing time is 16 ms. The trace is phase subtracted (φ − (φ + 180◦ )). Extra slowing timeafter the original slowing sequence helps the MOT loading. (b). Doppler detection at the end ofslowing with different extra slowing time. The center velocity is shifted from ∼18 m/s to 0 m/s
with extra 12 ms at the end of the original slowing sequence. This ”over slowing” apparently helps
the MOT loading.

further to about 0 m/s and they’re even ”over slowed” with the extra slowing time. Apparently,
the trapping velocity of the rf MOT is really lower than expected.
The MOT beams have a 1/e2 beam waist of 10 mm and can have a maximum of 25 mW
v=0 of light per beam. The power on each hyperfine states were set to be equal. v=1 and v=2
repumpers are typically 25 and 8 mW per MOT beam. The light induced fluorescence detected by
PMT with various parameters is shown in Figure 5.10. MOT loading is optimal with a 12.5 mW
trapping laser of 5 MHz red detuning. Initially, the MOT loading is limited by the magnetic field
gradient which only reaches 13 Gauss/cm. With some technical upgrades, we achieved a rms field
gradient of 20 Gauss/cm with 60 W input. The phase dependence was not very strong as well.
The temperature of the MOT was determined by time-of-flight(TOF) expansion. A thermal
cloud would expand in free space where the expansion rate depends on the temperature. In our
experiment, we turn off MOT beams and magnetic field simultaneously for various amount of timet, followed by a 2 ms resonant beam for detection. A short detection time(2 ms) and typicalintensity(1.3 mW/cm2 ) are used to reduce any heating effects during imaging. The images of thereleased molecular cloud are shown in Figure 5.11 (a), with the cloud becoming larger at longer

55

Figure 5.10: Characterisation of 3D rf MOT. (a). Different v=0 detunings. (b). Different v=0
powers. (c). Different magnetic field gradients. (d). Different phases φ between magnetic field
direction and laser polarization.

Figure 5.11: Time-of-flight expansion for temperature measurement. (a). Image of released
molecule cloud, the size of each image is 1 cm × 1 cm. We can see the cloud expands withtime. (b). The measurement of the Gaussian width σ of the cloud as a function of free flight timet. The slope is proportional to the temperature. We extract the radial and axial temperature of
the MOT to be 4.1(5) and 3.8(5) mK.

56
release time. We extracted the radial and axial temperature by fitting the Gaussian width σ withthe release time t
σt2 − σ02 =1/3

kB T 2t
mY O

2/3

and the temperature of the cloud is T = Taxial Tradial .
Unlike typical type I MOT, the temperature is much hotter than the Doppler temperature,
TD =116 µK. This has been observed in all molecular MOT [57, 127, 56] using type II transitions.
It’s theorized that the hot temperature is resulted from the Sisyphus heating mechanism [128]. The
heating might also come from the unwanted sidebands on the MOT beams, which are introducedby the Pockel cell for polarization chopping. Since the hyperfine splittings are ∼tens of MHz, we
reduced the Pockel cell chopping rate from 5 MHz to 1 MHz after coil modification, but it didn’t
make a difference. To further cool the molecules, intensity can be ramped after trapping. However,
the molecular cloud’s size would increase rapidly due to the limited restoring forces. Instead, weapply gray molasses cooling which is detailed in the following Chapter 6.

5.4

Molecule Loss by Parity Mixing
The MOT lifetime was determined by measuring the decay of the MOT fluorescence. As we

can see in Figure 5.10 (b), MOT loading was enhanced with more trapping power while the lifetime
become shorter at higher scattering rates. The MOT decay time versus power curve is plotted in
Figure 5.12. The fitting is inversely proportional to power, indicating the molecules are pumped
into dark states. This limits the number of trapped molecules and our MOT lifetime.
00

As we mentioned earlier in Section 4.1, YO possesses an intermediate state A 2 ∆3/2 J =3/2(−) which introduces extra loss into opposite parity states due to the two photon process. The000Λ splitting between A 2 ∆3/2 J = 3/2(−) and J = 3/2(+) is only ∼0.2 MHz. These states canbe mixed by an external electric field, for example, our rf MOT coil. Therefore, molecules on
0

J = 3/2(+) state would decay into N=1 and N=3 state where N=3 is not repumped, as shown in57

Figure 5.12: MOT lifetime at different intensities of the trapping beam. The solid line is a fit to
the function t = a/P + b, where a and b are fitting parameters. This indicates the molecules are
pumped into dark state, limiting our MOT lifetime

Figure 5.13 (a). The remixing rate into N=3 dark state is:(dA0 E/3)21
0=
2 + Γ2 /4 Rsc qAA ,τ4ωΛωΛ ≈ 0.1M Hz

dA0 = 7.5D [77],0where dA0 , ωΛ , Rsc , qAA0 are half of Λ doubling splitting, A 2 ∆ state electric dipole moment,0scattering rate and branching ratio from A2 Π1/2 to A 2 ∆3/2 .
The top and bottom coils are connected in a parallel configuration to reduce the stray electricfield. For coils run at 1 MHz with 10 Gauss/cm and the electric field of ∼1 V/m leads to a lifetimeof ∼20 ms at the scattering rate of 1 MHz. As a result, the leaking into N=3 is limiting our rf
MOT lifetime.

58
5.4.1

N=3 Spectroscopy0

The N=3→ J = 5/2 spectroscopy is taken to repump the v=0 N=3 state. We excited the0molecules on N=3 state to A2 Π1/2 J = 5/2(+) with a low intensity laser beam perpendicular to
the motion of molecules and then collected the fluorescence. The laser frequency is modulated as
described in Section 4.2.2, thus the entire spectrum is obtained in a single experiment.

00Figure 5.13: (a). Loss into v=0 N=3(-) due to the parity mixing on A 2 ∆3/2 (J = 3/2) state. The0
red arrow is the N=3 repumper. (b). X 2 Σ+ N = 3(−) → A2 Π1/2 J = 5/2(+) spectroscopy, peaks
are F=2 and F=3. N=3 repumper is parked at the right peak(488.473144 THz) for the best MOT
performance.

5.4.2

N=3 Performance

As mentioned previously in Section 4.3.3, a dye laser was used to repump the X 2 Σ+ N = 2(+)
state. The N=3 repumper is set on the right peak in Figure 5.13 (b), which is ∼9.8 GHz lower
than the N=2 repumper. We generate sidebands on the dye laser by an EOM(Qubig EO09775M2)
to address the N=3 state. It is worth mentioning that the cooling transition on N=1 is ∼9.6 GHz
higher than the N=2 repumper. Therefore, one of the EOM sidebands is only ∼ 200 MHz from themain cooling transition, which can potentially interact with molecules.

59
We studied the N=3 performance in the dc MOT, which is different from rf MOT and will
be discussed in the follow section. By inserting a resistor between the top and bottom coils, we canincrease the electric field from 0.3 V/cm to 37 V/cm. The MOT traces without N=3 repumper are
shown in Figure 5.14 (a). In both cases, the number of trapped molecules and the MOT lifetimes00

are equal, indicating the A 2 ∆3/2 J = 3/2(±) parity has been fully mixed, even at 0.3 V/cm. With
the N=3 repumper, as shown in Figure 5.14 (b), the MOT lifetime increases from 34(1) to 57(1)ms and the molecule number increases by a factor of 2.

Figure 5.14: Repumping N=3 state in dc MOT. The trace is subtracted(molecule on-molecule off)
to take away the back ground scattering. (a). MOT without N=3 repumper at different electricfield. (b). DC MOT with/without N=3 repumper. The electrc field is 0.3 V/cm.

5.5

DC MOT
Instead of an rf MOT, A dc MOT [128, 119] can be exploited to remix the dark states as well.

In the rf MOT, the remixing relies on diabatically switching the magnetic field. In the dc MOT,
besides the red detuned laser, a blue detuned laser with opposite polarization is added to address
the dark magnetic sublevels, as shown in Figure 5.15 (a). The laser setups of RF and dc MOT
are shown in Figure 5.15 (b). We add another laser L4 with opposite detuning and polarization toaddress the dark magnetic manifolds.

60

Figure 5.15: The optimal polarization scheme for a YO MOT. (a) Simplified dual frequency MOT
setup. F=2 is the ground state and F=1 is the excited state. Compared to rf MOT with a single
red detuned σ − laser, a blue detuned σ + beam is added to address the dark manifolds such asmF = −1, −2. (b). rf MOT setup of YO. Only ground states are shown for simplicity. All beams
are red detuned and polarizations are set based on the g factor. (c). DC MOT setup of YO. Only
ground states are shown for simplicity. L3 and L4 with opposite polarizations around G=1 F=2
provide trapping, while the L1 and L2 mainly repump the states.

5.5.1

DC MOT Performance

To generate the dc MOT beams, we equally split the main cooling laser into four beams L1,
L2, L3, L4 with a diameter of 8.2 mm. We set a nominal intensity I = 1.4I0 , where I0 = 2.7
mW/cm2 is the estimated saturation intensity. At this intensity, the optimal detunings for thehyperfine components, from top to bottom in Figure 5.15 (c), are tuned to be -5.8, -9, -5.8 and+2.6 MHz, resulting in a MOT lifetime of 90 ms. The magnetic field gradient is 12 Gauss/cm.
Under these conditions, the molecular sample has a 2σ diameter of 2.8 mm (3.9 mm) along theaxial (radial) direction and a temperature of 2 mK, 2 times colder than the rf MOT(4 mK). The
number of trapped molecules is 1.1×105 , 7 times that reported in the work of rf MOT [58] andthe peak spatial density is ∼1×107 cm−3 . I should mention that we increased the cell yield by ∼5times after the rf MOT paper [58] was published.
The dual-frequency MOT results from the trapping on G=1 F=1,2 states and also has contributions from the other two trapping mechanisms, red-detuned Type-I and red-detuned Type-II

61
MOT [118, 129]. To determine their relative contributions, we disable the blue-detuned component
L4 in Figure 5.15 (c) and compare the MOT performance at different polarization settings of L1, L2and L3. As we can see in Figure 5.16 (a), all states including G=0 F=1 and G=1 F=0,1 contributeto trapping under the correct polarization. When L4 is unblocked, the MOT produces 5 times more
molecules and twice the lifetime as compared to the MOT with L4 blocked, as shown in Figure 5.16(b). This feature clearly demonstrates that the dual-frequency trapping mechanism dominates thetrapping force for the MOT [118].

Figure 5.16: Test the dc MOT contribution. We plot differential MOT fluorescence between two
opposite quadruple field directions. (a). Red detuned dc MOT with different polarizations. Polarizations of G=0 F=1 and G=1 F=0,1 beam are labeled in the legend. All beams contribute totrapping if the polarization is correct. (b). DC MOT with and without the blue detuned component. Apparently, the dual-frequency trapping mechanism dominates the trapping force for the
MOT.

The YO dual-frequency MOT further benefits from the close spacing (3.5 MHz) of G=1 F=1
and G=1 F=2, in comparison to the cooling transition linewidth of Γ=2π×4.8MHz [130]. Therefore,
G=1 F=1 and G=1 F=2 both contribute to the dual-frequency trapping mechanism, increasing theoverall trapping frequency. This feature may be responsible for our observation that the dc MOT
traps approximately 20% more molecules than the rf MOT given that the other conditions remain
the same, contrary to the results reported for CaF [57] and SrF [76].
We experimentally determine that the red detuned MOT shown in Figure 5.15 (b) already
employs the correct polarization for both laser components addressing the G=1 manifold. For

62the two closely spaced states of G=1 F=1 and 2, the corresponding laser polarization produces
trapping for G=1 F=2 and antitrapping for G=1 F=1 [129], which shows that the force from G=1F=2 overwhelms that from G=1 F=1, consistent with the observation in [131] for SrF molecules.

Figure 5.17: DC rf MOT comparison. We plot differential MOT fluorescence between two opposite
quadruple field directions. (a). DC and rf MOT under same intensity (12 mW/cm2 , 4.4 I0 ) andmagnetic field gradient (12 Gauss/cm). (b). Time of flight expansion of dc and rf MOT for
temperature measurement. The temperature of dc MOT is 2 mK, colder than rf MOT (4 mK).

In general, we trap ∼7 times more molecules in dc MOT (1.1×105 molecules [59]) comparedto the rf MOT (1.5×104 molecules [58]). I should mention that a factor of ∼5 increase is attributed
to the cell modification. As a result, dc MOT traps 20% more molecules than rf MOT shown in
Figure 5.17 (a). The cloud volume of dc MOT is a factor of 3.4 smaller than the rf MOT. The
temperature of dc MOT is 2 mK, colder than the rf MOT which is 4 mK, as shown in Figure 5.17(b). Therefore, dc MOT is about 4 times denser and 50 % colder than the rf MOT. Under the same
intensity, dc MOT lifetime is ∼50% longer than the rf MOT. DC MOT is also technically simple torealize since it doesn’t require magnetic field and polarization modulation. Therefore, we proceedwith the dc MOT to trap YO molecules.

5.5.2

Detailed DC MOT Characterization

The optimal dc MOT parameters are described in the previous section. Here we show all the
optimization we did for the dc dual frequency MOT to maximize the loading and MOT lifetime.

63

Figure 5.18: (a). MOT loading at different v=0 trapping power. We choose 2 mW for optimalloading. (b). MOT fluorescence at different v=1 and v=2 power. The 100% repumper power of
v=1 and v=2 on each hyperfine component is 20 mW. Both v=1 and v=2 repumpers fully saturate
the transition.

Figure 5.19: (a). MOT loading at different magnetic field gradient. The solid line is a guide forthe eye. (b). MOT loading versus various detunings of L3 and L4.

The dc MOT saturates at ∼ 2 mW for a beam of diameter of 8.2 mm, as shown in Figure 5.18 (a).
The loading becomes worse at high trapping power, potentially resulting from the scattering loss.
We can see in Figure 5.18 (b) that both v=1 and v=2 beam fully saturate the transition. We also
applied the v=3 repumper but it didn’t make any difference, as expected since it takes more than
105 photon scatterings [88] into v=3 state. We did more lifetime study in the next section.
The MOT loading at various magnetic field gradients and detunings are shown in Figure
5.19. The optimal loading is ∼ 12 Gauss/cm while a higher gradient doesn’t increase the loading

64
efficiency any more. Scanning the frequency of the L3 and L4 showed a optimal detuning at ∼-3.2
MHz and ∼+4.2 MHz for 10-40 Gauss/cm. Eventually we chose -5.8 MHz and +2.6 MHz for MOT
loading.

5.5.3

Collision with Background Gas in DC MOTIn order to figure out what’s limiting our MOT lifetime, we first scanned the lifetime atdifferent helium flow rates. The lifetime decreases to 35 ms when the helium flow becomes 2×10−8
Torr at 2 sccm, as shown in Figure 5.20 (a). If we measured the MOT lifetime at different scattering
rates and then fit the lifetime against scattering rate, as shown in Figure 5.20 (b), we can see there
is a constant loss that is limiting the lifetime. This indicates that the MOT lifetime is limited by
the collision with background gas. To prevent the helium from reaching the MOT region, a second
shutter was installed inside the molecular beam box. This in-vacuum shutter also helps reducethe cell heating effect, which is mentioned in Section 3.2.1. The pressure is reduced to 3×10−9
Torr with both shutters open for about 8 ms during the whole experiment and the vacuum lifetime
should increase to ∼ 1 second. The shutter motor is in direct contact with a large piece of aluminum
to dissipate the heat. This is critical to reduce the outgassing and lengthen the shutter lifespan.

Figure 5.20: MOT lifetime limited by helium. (a). MOT lifetime at different helium flow rate.
It’s clear that the helium limits the MOT lifetime at high flow rates. (b). MOT lifetime t versus
scattering rate Rsc . The blue line is a fit to the function t=a/Rsc where a is the fitting parameter.
The red line is a fit to the function t=a/Rsc +1/T, where T represents the lifetime limited by the
background gas.

65
5.5.4

Remaining Issues in MOT Beams

When we first made the MOT work, the MOT shape was changing every day. There areseveral reasons for this instability. First, the MOT beams propagate about three meters before
they see the molecules. This long beam path amplifies any pointing fluctuation introduced by the
optics. Secondly, the shape of the beams are terrible due to the acousto optical modulator(AOM),
tapered amplifier(TA) and Pockel cell. A non TEM00 mode introduces a spatially dependent
trapping force which degrades the MOT performance. Thirdly, all components of the MOT beam
(v=0,1,2 and hyperfine components) need to match the mode to each other. These problems are
solved by coupling the beams into a PM fiber before the beams are directed to the molecules. Witha fiber, the length of the beam path is reduced to less than one meter. As a spatial filter, the fiber
cleans up the mode and ensures the mode matching of all MOT beams.

Figure 5.21: (a). MOT with good alignment. (b). MOT with mis-aligned retroreflection(∼0.5◦
off).

In a regular atomic MOT, beam alignment is not very critical. However, our dc MOT relies
on a perfect alignment of the counter-propagating beams. Since the MOT beams are circulated
through three orthogonal directions, the counter-propagating alignment is optimized by coupling
the beam back into the fiber using the retro-reflected mirror. A well optimized and a mis-aligned
MOT image is shown in Figure 5.21. The mis-alignment affects both the MOT shape and thenumber of trapped molecules. One possible reason is the power imbalance in the MOT beams dueto the circulation of beams. As previously mentioned in Section 5.2.6, the MOT windows have

66
considerable loss in transmission. Therefore, the beams are attenuated by ∼ 12% before retroreflection. To compensate this power loss, the MOT beams are slightly focused to compensate thisattenuation, but it can not balance each MOT direction nicely. A proper way is to decouple thesethree directions if we have extra laser power and replace all MOT windows with lower loss.

5.5.5

Limited MOT Lifetime at High Magnetic Field Gradient

To further compress the molecule cloud, one would reduce the MOT temperature or increase
the trapping frequency, as T∝ kσ 2 where T, k σ are cloud temperature, spring constant and cloud
radius. One route is to ramp up the magnetic field after loading to increase the trapping frequency.
This is known as compressed MOT (cMOT) [132]. In our experiment, we first load MOT at 12
Gauss/cm for 32 ms, then ramp to a higher magnetic field gradient in 32 ms and eventually measure
the cloud size and lifetime.

Figure 5.22: Compressed MOT. (a). MOT size 2σ at different magnetic field gradient. The solidlines are fits to the function σ = √ 1
where dB/dl represents the magnetic field gradient . The
dB/dlcloud size shrinks accordingly at large magnetic field gradient. (b). MOT lifetime at different
magnetic field gradient. The solid line is a guide for the eye.

We can see from Figure 5.22 (a), the cloud shrinks at higher magnetic field, following σ ∝(dB/dl)−0.5 where dB/dl represents the magnetic field gradient. In addition, we find that the loss
gets enhanced at higher field gradient, as shown in Figure 5.22 (b). This loss mechanism is unclear00

and yet to be discovered. The X 2 Σ+ N = 3(−) leaking from A 2 ∆3/2 (J = 3/2(+)) state has been

67
repumped by the N=3 repumper. Based on the Frank-Condon factors [88], it takes ∼3000 photons
0

to pump molecules into A 2 ∆3/2 state and it has ∼10% chance leaking into v=1 state. With thescattering rate of 0.5 MHz, the calculated lifetime is ∼60 ms if v=1 N=0,2,3 are not repumped.
00Therefore, it’s very likely that the leakage comes from A 2 ∆3/2 (J = 3/2). Currently, the lifetimeof the MOT is long enough for the transfer of the compressed cloud to a conservative trap, in which
there would be no resonant light-assisted collisions and the further cooling is feasible.

5.5.6

New Trapping Scheme

We propose a new trapping scheme employing A2 Π3/2 as the main excited state. The A2 Π3/2
state has similar magnetic moment as that used in atomic cooling experiments, as shown in Figure5.23(b), which will largely improve the capture velocity and trapping force of the MOT [129]. In
addition, as recently demonstrated for rubidium atoms [116], applying the blue-detuned MOT,
shown in Figure 5.23 (b), to the trapped YO molecules using the excited state with a large Landég-factor will compress the molecular cloud and increase the spatial density by a few orders ofmagnitude.
The proposed scheme involves more excited states, which increases the photon scattering
rate by more than a factor of two compared with the current one we’re using(Γ/8). In the newscheme, there are 8 manifolds coupled in the excited state(ne = 8) and 20 manifolds involved inethe ground state(ng = 20). This results in an effective scattering rate [75, 76] ΓScatter = ngn+nΓ ofe2Γ/7. According to section 4.3, we expect it to increase the number of slowed molecules by at least
an order of magnitude [58] as a result of the higher deceleration rate. Combined with the potential
enhancement from the compression, we expect to increase the phase space density by several ordersof magnitude.
An extra 597 nm laser is required to implement this scheme. The dye laser can be use if the
new fiber laser(Precilaser) generates the N=2 repumper.

68

A23/2v=0(a)J'=3/2 (-)(b)
F=1, 2(g=1, 0.6)

J'=3/2

A21/2

(+)

(+)
(-)

X2

+

v=0

597 nmJ'=1/2614 nm

v=0

(-)

F=2

772 MHz
F=1, 2, 3

N=2(+)
N=1(-)
N=0(+)

Figure 5.23: (a). Lasers for creating cycling transitions in YO molecules. Orange arrows: thecurrent scheme that optimizes angular momentum closure [54], which only requires a single laser.
Green arrows: the proposed scheme that involves the excited A2 Π3/2 state. This state has aconsiderable magnetic dipole moment, which is crucial for improving the MOT trapping force. The
solid (dashed) arrows represent the laser-driven transitions (spontaneous emissions). (b). Scheme
for capture and compression of molecular cloud. Red: red-detuned MOT [129] for capturing themolecules. Blue: blue-detuned type-II MOT [116] for compression.

Chapter 6

Sub-Doppler Cooling and Compressed Trapping of MoleculesOnce the molecules are trapped in the MOT, the goal is to further cool and compress themolecular cloud and eventually load them into a conservative trap. In this chapter, we first introduce
the theory of sub-Doppler cooling, including gray molasses cooling(GMC) and Λ-enhanced graymolasses cooling. Next, we discuss the performance of YO with these cooling methods. Then, weshow a novel compressed trapping scheme tailored for the unique structure of 89 Y16 O. With the
combination of these techniques, we produced a laser-cooled molecular sample with the highest
phase space density in free space [59].
In this chapter, I reproduce the work published in [59] with modifications.

6.1

Gray Molasses Cooling
Gray molasses is a method of sub-Doppler cooling and is widely used in atomic species withpoorly-resolved hyperfine structure. Typically, atoms trapped in MOT can be cooled below the
Doppler limit with the quadrupole magnetic field removed. This cooling method is called opticalmolasses as the trapping force disappears. Then, atoms can be cooled even further by the graymolasses employing the Sisyphus cooling together with a ”dark” state, which is not coupled to
the light. Compared to traditional optical molasses, gray molasses cooling can achieve a colder
temperature, with cold atoms/molecules shielded from interacting with the light.

70
6.1.1

Gray Molasses Cooling Theory

Before the invention of gray molasses cooling, atoms were first cooled with optical molasses
after the MOT. By removing the quadruple magnetic field, atoms can be cooled well below the
Doppler limit [133], which is an order of magnitude colder compared to the MOT. Typically, there
are two configurations for the optical molasses: lin⊥lin and σ + σ − . In the first case, lin⊥lin, shownin Figure 6.1 (a), there is a spatially varying light shift of the ground-state sublevels(M=±1/2),
where the polarization cycles from linear to circular to orthogonal linear to opposite circular in
the space of half a wavelength. M=1/2 atoms starting at z=0 climb up the potential hill as they
approach λ/4 point, where the polarization becomes σ − . At this point, they’re very likely to
be excited due to the transition selection rule and eventually decay to M=-1/2 state. The sameprocess continues for M=-1/2 until it climbs up to λ/2 and get excited by σ + beam. The energy
gets dissipated during each scattering since the atom absorbs less energy compared to the emission,
resulting in a low temperature. As for σ + σ − configuration, there is no spatially varying lightshift thus the cooling doesn’t rely on the Sisyphus effect. It has been shown that the damping
force is introduced by the differential scatterings caused by the imbalance in the population, which
results from the time lag between the atomic orientation and the local field [134]. In addition tothese configurations, a light field of constant polarization combined with a magnetic field could
also produce sub-Doppler cooling [135]. In this case, the polarization is fixed(σ + ) but the lightintensity is oscillating in space because of the interference, as shown in Figure 6.1 (b). For Jg =1/2
to Je =3/2 transition, ground state M=1/2 is more strongly coupled than M=-1/2, resulting in alarger light shift. Starting at z=0, atoms must climb a potential hill as they approach the nodes
at λ/4. Under a small transverse magnetic field, atoms may merge into the M=-1/2 state throughLarmor precession. As the M=-1/2 state is weakly coupled, atoms gain less energy as they movetowards the antinode at λ/2. At this point, where the laser intensity is the strongest, atom canabsorb a photon and possibly decay back to M=1/2 state. Each optical pumping results in theabsorption of a photon at lower frequency than the emission, taking away the energy.

71

Figure 6.1: Simplified diagram for different sub-Doppler cooling configurations. Excited states
are not shown for simplicity. (a). Optical molasses, lin⊥lin. (b). Magnetically induced cooling.
(c). Gray molasses, lin⊥lin. C represents coupling state(”bright”), NC represents non-couplingstate(”dark”).

Gray molasses cooling(GMC) works on type-II transitions and relies on position-dependent
dark states that are formed from the spatial variation of the laser polarization and intensity, as
shown in Figure 6.1 (c). Unlike most Doppler cooling techniques, light in the gray molasses mustbe blue-detuned from its resonant transition. As a result, all ”bright” coupling states are always
Stark shifted upwards above the ”dark” non-coupling state. The ”bright” state has a spatiallyvarying light shift due to the polarization gradients while the ”dark” state remains unchanged. A
molecule in the ”dark” state can evolve into the ”bright” state through non-adiabatic process at
the node where the minimal energy gap is located. Then, the molecule rides up the hill, get excitedby the laser and eventually decay back to the ”dark” state. Molecules get cooled as they absorb a
photon at a lower frequency than the emission. It is worth mentioning that the blue-detuned lasercauses Doppler heating, but it is offset by this polarization-gradient cooling. This provides coolingin lin⊥lin case. It has been calculated [128] that for F⇔F and F⇔ F-1 transition, both lin⊥lin andσ + σ − configuration of GMC provide cooling in 3-D.

6.1.2

Gray Molasses Cooling of YO

In Figure 6.2 (a)-(b), we show the simplified molecular structure and laser configuration
relevant to dc MOT and GMC. Once the dc MOT is loaded, we blue detune L1 , remove the
red-detuned component of L2 , switch off L3 and the quadrupole magnetic field for gray molasses

72

Figure 6.2: (a). Lase setup for DC MOT. (b). Laser setup for GMC. (c). GMC temperature
without/out N=0⇔N=1 microwave.

cooling. Unlike other molecules, YO has a large frequency gap(753.8 MHz) between G=0 and
G=1, as shown in Figure 6.2 (a). Therefore, L1 (L2 ) covers G=0(G=1) individually. The magnetic
gradient is switched off in less than 100 us, during which time the laser beams are switched off
by AOMs and detuned accordingly by relocking the main laser. All the vibrational and rotational
repumpers are left untouched at the initial stage of cooling.
We first tried the GMC cooling with laser intensity I=3.1 I0 (I0 =2.7 mW/cm2 ), single photon
detuning ∆/2π=10 MHz and Raman detuning δ/2π=-3.5 MHz. As we can see in Figure 6.2 (c), we
achieved a temperature of 25(4) µK, which is two orders of magnitude lower than the temperatureinside the MOT(2 mK). During this cooling, microwave remixing between N=0⇔N=1 was kept on00

to repump the leakage from A 2 ∆3/2 (J = 3/2(−)) state. However, any field addressing the groundstate, such as magnetic or electric field, is detrimental since the cooling relies on the light shift of theground state. Therefore, with microwave switched off, the temperature was significantly reduced to8(1) µK. By doing so, we lost 15% of molecules as N=0 and N=2 states are not repumped back to
the main cycling transition. This loss is not significant since it requires ∼3000 photon scatterings
00

to A 2 ∆3/2 (J = 3/2(−)) state and GMC doesn’t scatter many photons as long as the molecules
are cold. The GMC temperature reduces with single photon detuning ∆ and intensity I as the73
momentum diffusion is reduced [134].

Figure 6.3: Three level system showing velocity selective coherent population trapping(VSCPT).

6.2

Λ-Enhanced Gray Molasses Cooling
Λ-Enhanced gray molasses combines the gray molasses with velocity selective coherent pop-

ulation trapping(VSCPT) [136]. It introduces a dark state which is more stable compared to the”dark” state in gray molasses cooling. Therefore, the cold molecules can not scatter photons andeventually a colder temperature can be achieved.

6.2.1

Λ-Enhanced Gray Molasses Cooling Theory

The theory can be explained using a three level system, as shown in Figure 6.3 (a). With
two circularly polarized, counter propagating beams of specific frequencies, a coherent dark stateis formed for molecules with specific velocity(v∝ δ/M ), therefore, the molecules at velocity v can
not scatter any photons. This is because, in the molecular frame, the two counter propagating
beams form a Raman resonance, creating a superposition of ground state g1 and g2 with transition
amplitudes destructively interfere. Therefore, the cooling ”center” is determined by the Raman
detuning δ. If δ is zero, then the molecules with zero velocities will be trapped by the VSCPT
effect. However, VSCPT is not very efficient by itself due to its stochastic nature. Combined with

74
the GMC where the energy is effectively dissipated, Λ-enhanced GMC can reach extremely low
temperature with very limited photon scatterings. This technique was first demonstrated in alkali
atoms [137], creating a dense lithium atom sample at ∼60µK.

6.2.2

Λ-Enhanced Gray Molasses Cooling of YO

In our YO setup, two lasers are applied to address G=0 and G=1 states separately, due
to their large frequency gap. This significantly reduces the parameter space. To explore the Λenhanced feature, we set I=3.2I0 , leave L1 fixed at ∆/2π=40 MHz and vary the frequency of L2 .
As we can see in Figure 6.4 (a), a low temperature is achieved if the Raman detuning δ=0, where acoherent dark state is formed between G=0 F=1 and G=1 F=2. A similar feature is also observedat δ/2π=-3.5 MHz where a coherent dark state is formed between G=0 F=1 and G=1 F=1. Unlike
typical Λ-enhanced feature, we do not see a lower temperature at resonance, but instead, there areextensive heating peaks around the Raman resonance.

Figure 6.4: Temperature vs Raman detuning around different Raman resonance, with I=3.2I0 andsingle-photon detuning ∆/2π=40 MHz. (a). Temperature vs Raman detuning around G=0 F=1
and G=1 F=1 Raman resonance. (b). Temperature vs Raman detuning around G=0 F=1 and G=1
F=2 Raman resonance. We do not see a lower temperature at resonance, but there are extensive
heating peaks around the Raman resonance.

To understand the performance of GMC around a Raman resonance, we next investigate thecooling on each hyperfine state by putting L1 or L2 on resonance. We keep I=3.2I0 , leave L1 fixed75
at ∆/2π=40 MHz and vary the frequency of L2 in a much larger range, as shown in Figure 6.5. For
δ/2π=-43.5 MHz, the remaining component of L2 is on resonance with G=1, F=1. Thus, cooling(to9 µK) arises purely from the G=0, F=1 manifold. Similarly, if we set L1 on resonance with G=0
while having L2 blue detuned from G=1, the cooling temperature reaches as low as 15 µK. We thus
conclude that both G=0 and G=1 states are responsible for cooling, and their combination leads
to an efficient sub-Doppler cooling of YO to the lowest temperature while being robust against the
Raman detuning δ in a wide range. This is very different compared to an atomic system, where
one laser provides cooling while the other is mostly responsible for repumping. Therefore, in YO
setup, L1 and L2 beams share the same intensity in our setup.
As we can see in Figure 6.4, when δ is tuned slightly away from zero, we observe striking risesof temperature, followed with quick decreases back down to 4 µK when |δ| becomes sufficiently

Figure 6.5: Temperature vs Raman detuning δ, with I=3.2I0 and single-photon detuning∆=8.3Γ(2π×40 MHz). The solid line is a guide for the eye.

76
large of a few hundred kHz. The two resonancelike features are symmetrically located around δ=0.
This feature has been observed previously in other molecules [61] without explanations.
To understand the heating peaks around the Raman resonance, we explore the cooling performance with various parameters, as shown in Figure 6.6. As we can see in Figure 6.6 (a), theobserved peak width and splitting between the two temperature peaks increase with the laser intensity. As for the single-photon detuning ∆, shown in Figure 6.6 (b), the peak width and splitting
decreases with ∆. Our understanding for this effect is the following. Gray molasses cooling depends
on transient dark states [128, 138] and generally, a less stable dark state causes more momentum
diffusion and leads to a higher temperature. Near the Raman resonance condition(δ = 0, −3.5
MHz), dark states formed in both G=0 F=1 and G=1 F=1(2) can be destabilized by their crosscoupling. It leads to enhanced photon scattering and deteriorated cooling over a range on the orderof the two-photon Rabi frequency, ΩR ∝ Ω1 Ω2 /∆, consistent with our observation. This result isdifferent from the δ=0 situation, where a new stable dark state is formed with the superposition of
Zeeman sublevels from different hyperfine states [61, 62], resulting in a Λ-type GMC.
In addition to the peak width and separation, we can see the lowest temperature changes
with the laser intensity and single-photon frequency ∆. The temperature depends on the molasses
beam intensity and single-photon detuning ∆ in a way consistent with theory [128]. As shown in
Figure 6.7 (b) and (c) for δ=0, the temperature increases linearly with the intensity and decreases
with the detuning before settling down to a constant. The momentum diffusion coefficient Dp
increases(decreases) with intensity(detuning), while the damping coefficient α is both intensityand detuning insensitive [128]. The temperature is determined by kB T=Dp /α, where kB is theBoltzmann constant. The fittings in Figure 6.7 (b) and (c) are consistent with this model. Thisbehaviour is similar to the sub-Doppler cooling with type-I transitions [134], where T∝ |Ω|2 /∆. Ω√is the Rabi frequency, which is proportional to I.

77

Figure 6.6: Temperature vs Raman detuning δ. (a). ∆=12.5Γ with different intensity I. (b). I=3.2I0
with different single-photon detuning ∆. The peak width and separation increases(decreases) withI(∆). The lowest temperature also depends on the intensity and single-photon detuning ∆, consistent with theory [128].

78

Figure 6.7: Characterization of GMC. (a). Configuration of laser detunings. (b). Temperature
versus intensity I with single-photon detuing ∆=8.3Γ and Raman detuning δ=0 between the G=0
F=1 and the G=1 F=2 manifolds. The solid line is a linear fit. (c). Temperature versus ∆ with
I=3.2I0 and δ=0. The solid line is a fit to the function Tavr =1/∆+T0 , where T0 represents abackground tempreature. The error bars in the plots correspond to 1σ statistical uncertainty, andthe fittings are consistent with the theoretical predictions in [128].

With δ=0, ∆/2π=40 MHz and I=1.2I0 , we achieve a YO sample at 4 µK, which represents
the coldest laser cooled molecules in free space. It is worth mentioning that, for an intensity smaller
than the minimum value(I=1.2I0 ) shown in Figure 6.7 (b), the molasses becomes too weak to holdmolecules against gravity, leaving an unexplored territory.

6.3

Compressed Trapping of YO

6.3.1

Gray Molasses Cooling with Magnetic Field

It has been shown previously in Figure 6.2 (c) that microwave coupling between the N=0 and
the N=1 state increases the lowest temperature of GMC. The temperature increases as long as theground state is perturbed by an external field. The ground state can be shifted by Zeeman effectas well. Bias magnetic field also remixs the bright and dark state, reducing the cooling efficiency.
Therefore, Earth’s field was roughly cancelled when the chamber was open by the cancellation coils
shown in Figure 6.8. These Helmholtz coils provide a small region of homogeneous field along
NS(1.16 gauss/A), EW(-1.14 gauss/A) and Z direction(-14.2 gauss/A). Figure 6.9 shows the cloud
temperature versus different bias magnetic field. These scans are repeated several times until thelowest temperature is achieved.

79

Figure 6.8: Cancellation coil pairs. They are made with magnetic wire using the winding tools
designed by the machine shop. Aluminum rings are machined by the shop to hold coils in place.
Three pairs of coils cancel three directions independently.

Figure 6.9: Cancellation coil scans. (a). Z coil. (b). North/South coil. (c). East/West Coil.

6.3.2

Robust Cooling with Magnetic Field

Considering the negligibly small Lande g factor for G=0, it’s interesting to explore how wellgray molasses performs in the presence of B. We apply a magnetic field along the axial direction
with a pair of cancellation coils and measure the temperatures both along and perpendicular to
B with δ=0. Typically, the temperature would continue to rise with a stray magnetic field. Thisturns out not to be the case for YO. As we scan over a large range of bias field, we see the GMC
is surprisingly robust over a large range of magnetic field strength, along with a few remarkable

80

Figure 6.10: Temperature under a uniform B applied along z, with I=3.2 I0 , ∆=8.3Γ and δ=0.
The blue open circles (purple filled points) represent the temperature measured along (transverseto) B. The inset shows the temperature from 0 to 3 gauss.

features.
First, the temperature appears to have a pronounced peak near 0.3 gauss. This resonancelikefeature is attributed to the Zeeman shifts of the G=1 F=2 sublevels destabilizing the dark state
formed both in its own manifold through Larmor precession and in the G=0 F=1 manifold throughRaman coupling. The temperature dependence on magnetic field then becomes flat between 0.6
and 4 gauss, regardless of whether L2 is tuned on resonance with G=1 F=2(δ/2π=-43.5 MHz) or
remains on Raman resonance with L1 (δ=0). This observation reveals that, within this range, GMC
arises mostly from G=0 F=1, where relatively a stable dark state is formed due to its small Landeg factor.
At approximately 4 gauss, the temperature starts to rise with B, indicating the dark statein G=0 F=1 becomes unstable. The temperature measured in the direction perpendicular to B
rises slower than that along B and reaches a plateau after approximately 10 gauss. This effect is
attributed to the magnetically induced Sisyphus cooling [139, 140, 141, 142, 143], introduced in

81Section 6.1.1, after the original GMC becomes less effective. The laser field pumps YO into adark state, which is remixed with a bright state via Larmor precession. This process damps themolecular motion in a Sisyphus fashion [142]. In the direction transverse to B, the spatially varying
dark and bright state mixing is much stronger than that along B. Therefore the temperature is lower
in the transverse direction. The magnetically induced Sisyphus cooling works at approximately 25
gauss for YO, which is substantially larger than the field(∼1 gauss) applied to any other atoms or
molecules [139, 140, 141, 142, 143]. Such an exceptional magnetic insensitivity must be attributed
to the small Lande g factor of G=0 F=1 state.

6.3.3

A Novel Compression Method

Such exceptionally robust GMC against the magnetic field brings an intriguing capability. In
the presence of the quadrupole magnetic field applied for the MOT, molecules can still be cooled
via GMC to a temperature much lower than that for the MOT. Thus, with the quadrupole field
turned on continuously, we can alternate the laser beams between MOT and GMC parameters so
as to apply the strong trapping force of the MOT to the ultralow-temperature molecular sample
prepared by GMC. This scheme works effectively, as the GMC process is fast relative to MOT
heating, such that the compression from the MOT dominates over the expansion during the GMC.
We first measure the cooling (heating) rate of GMC (MOT) by recording the temperature fordifferent GMC (MOT) pulse durations. The GMC cooling rate increases with the laser intensity
and is not sensitive to the single-photon detuning ∆ between 1Γ and 6.2Γ. As shown in Figure 6.11(a), with full laser power 30I0 and detuning 3.1Γ, molecules are cooled from 2 mK to 100 µK witha 1/e time constant τ ∼94 µs. As for the MOT heating process, shown in Figure 6.11 (b), takes
approximately 1 ms to 1 mK.
To explore the MOT compression, we first ramp the magnetic field gradient of the dc MOTfrom 12 to 47 G/cm in 5 ms and hold at this value for another 5 ms for initial compression [132, 144].
This is known as compressed MOT(cMOT) and its performance has been described previously in
Section 5.5.5. The MOT stabilizes with a diameter of 1.4 mm (2.4 mm) along the axial (radial)

82

Figure 6.11: Compression of the molecular cloud by combining the GMC with the dual-frequency
dc MOT at a B gradient of 47 G/cm. (a) Temperature versus the duration of the GMC pulse, with
I=30I0 , ∆=3.1Γ, and δ=0. The solid line is an exponential fit with 1/e time constant as 94(3)µs.
(b),(c) Temperature and in situ diameter of the molecular cloud versus the duration of a single
MOT pulse, which is applied after the 2 ms GMC pulse.

direction. We then apply a 2 ms GMC pulse to cool the molecules followed by another MOT pulse
with a varying duration for compression. The cloud size is measured right after the MOT pulse,
as shown in Figure 6.11 (c). The cloud size shrinks until approximately 4 ms and is significantly
smaller than the equilibrium MOT size. This compression process is dynamical, and the cloud
expands to eventually reach the original MOT size.
For our optimized compression sequence, we repeat the GMC-MOT cycle 3 times in 10 ms
after the initial 5 ms MOT hold pulse, as shown in Appendix D. We do not observe considerable
molecule loss during the compression except those optically pumped into the unaddressed darkstates(50%). After the compression, the cloud has a diameter of 0.69 mm (0.93 mm) along theaxial (radial) direction. The corresponding volume is approximately 10 times smaller than that
before the compression, with approximately 5×104 molecules remaining and a peak spatial densityof 5.4×107 cm−3 . The molecules are then cooled to 4 µK with a final 8 ms GMC pulse, creating amolecular sample with a peak phase space density of 3.3×10−8 . The 4 µK temperature is about 8times the recoil limit.
Even though G=0 and G=1 both contribute to cooling, we should still explore the hyperfine
ratio since the G=0 state is more robust against the variations of experiment conditions.

Chapter 7

Optical Trapping of Molecules

After the realization of the ultracold molecule sample in freespace, it is important to transfer
molecules into a conservative trap for interesting applications, ranging from ultracold chemistry toquantum simulation. Typically, a cold and dense sample in the conservative trap is desired. In
recent years, many indirectly cooled molecules have been loaded in optical traps [23, 24, 25, 26,
40, 41, 42, 145]. For directly cooled molecules, we have both Stark-decelerated molecules and laser
cooled molecules loaded in various conservative traps [63, 64, 65, 61, 66, 67, 68, 146].
Conservative traps for neutral atoms have been studied extensively over the past few decades.
Magnetic and optical traps are the two main setups used in the cold atom community. Magnetic
traps have high trap depths on the order of 100 mK, while it could only trap molecules on low fieldseeking state. This is not ideal for molecules with a complex structure. However, optical trapping
could be independent of internal states if the trapping laser is far detuned. This is critical forcooling inside the trap since the cooling strongly depends on the coherent dark states that could bedestroyed by the differential ac Stark shifts, as described in Chapter 6. In this chapter, we discuss
how the YO molecules are cooled and loaded into optical dipole trap(ODT) and optical lattice.

7.1

Optical Dipole Trap(ODT) Theory
Optical dipole traps are formed when an atom or molecule interacts with a strong, far detuned,and focused laser beam. Here we follow the derivation of [147] to calculate the basic equations byconsidering the atom as a simple oscillator to the classical radiation field.

84
7.1.1

Molecule Interacts with Laser

When an atom/molecule is interacting with a laser beam, the electric field E induces anatomic dipole moment p oscillating at the driving frequency ω. The complex polarizability α is∼∼defined as p = α(ω)E. The interaction potential Udip is [147]11Udip = − hpEi = −Re(α)I22ε0 c∼

where I = 2ε0 c|E|2 and a 12 factor is introduced as the dipole moment is induced. Thus, the dipole
force results from the gradient of the interaction potential Fdip (r) = −∇Udip (r) = 2ε10 c Re(α)∇I(r).
We can see that there is a net force pointing towards the intensity maxima if Re(α) is positive. In
order to calculate the polarizability α(ω), we first consider the Lorentz’s oscillator model. In thispicture, an electron is considered to be bound elastically to the core where the oscillation eigenfrequency ω0 corresponds to the optical transition frequency. The radiative energy loss introduces
damping to the system. We can write down the equation of motion ẍ + Γω ẋ + ω02 x = − eE(t)me for22

ωthe electron, where Γω = 6πεe0 m
3 is the classical damping rate. Integrate the equation, we could
ec

get
α=

e2
1
Γ/ω02
3
=
6πε
c
0
2
2
me ω0 − ω 2 − iωΓωω0 − ω 2 − i(ω 3 /ω02 )Γ

where we introduce the on-resonance damping rate Γ = Γω0 = (ω0 /ω)2 Γω . This gives a dipole
potential in the case of large detunings and negligible saturation situation:


Γ
3πc2
Γ
Udip (r) = − 3+I(r)2ω0 ω0 − ω ω0 + ωThus for red(blue) detuning, ω − ω0 < (>)0, dipole force points toward highest(lowest)
intensity. In the case of dipole trapping, the saturation effects can be neglected. The damping rate
Γ can be determined by the dipole matrix element between ground and excited state,Γ=ω03|he|µ|gi|23πε0 ~c3

For a multilevel system, the damping rate becomes a sum over all relevant states:Γ=ω03 X X
|hei |µij |gj i|2
3πε0 ~c3ij85

Figure 7.1: YO trap depth as a function of wavelength. Here I assume a 100 watt trapping beamwith a beam waist of 20 micron.

0

Considering all nearby electronic states A2 Π, B 2 Σ+ , A 2 ∆, we can calculate the trap depthof YO at different trapping wavelength, as shown in Figure 7.1. The dashed lines represent theresonant transition wavelength. We tried a near resonant optical trap(NROT) at 689 nm and a
far-off-resonance optical dipole trap (FORT) at 1064 nm, which will be detailed in the following
sections.

7.1.2

Gaussian Beam Profile

Single beam ODT is a focused-beam trap as shown in Figure 7.2 (a). The intensity distribution follows:I(r, z) = Io

wo
w(z)

2


exp

−2r2
w2 (z)

In the case of low saturation, atoms/molecules spend most of the time in the ground state and we
can calculate the light-shifted ground state as the trapping potential of atoms, illustrated in Figure
7.2 (b)(c). When atoms/molecules are cold enough compared to the trap depth, they occupy thebottom of the trap. Therefore, the trap properties can be calculated under harmonic approximation:

86

Figure 7.2: (a). Gaussian beam profile. A focused gaussian beam is used to provide both radial
and axial trapping. (b). Energy shifts from the trapping laser. A red-detuned trapping beam
shifts the ground state energy lower. (c). Spatially varying potential due to Gaussian beam profile.
Atoms/molecules are trapped at the intensity maximum where the trap is the deepest. (b) and (c)are reproduced from Ref. [147].

s
ωr =

4Udip
mw02

Radial Frequency

s

2Udip
mzr2

3/2
m
no = Nωr2 ωz2πkB Tωz =Axial Frequency
Peak Density

If the atoms/molecules are hot or trap is shallow, the harmonic approximation breaks down.
Typically, a focused-beam ODT is aligned perpendicular to the direction of gravity. In this case,the strong radial force ∼ Udip /w0 prevent the molecule from falling under gravity. Normally, theradial trapping frequency is about a hundred times larger than the axial trapping frequency due
to the focused beam geometry. If a shallow trap is tilted, atoms/molecules can leave the trap byfalling along the axial direction, as shown in Figure 7.3. The linearly polarized light is usually theright choice for a dipole trap, as the magnetic sub-levels of certain hyperfine manifold are shiftedby the same amount.

87

Figure 7.3: Here I plot the trap depth along the axial direction. Atoms/molecules can leave theshallow trap if there is a tilt. For a shallow trap, a trap alignment becomes critical.

7.2

689 nm ODTBased on the polarizability derived in the last section, we found that the trap depth Udip =3πc2 Γ
1
3πc2 Γ 2
1
I(r) scales as ∆while the scattering rate Γsc = 2~ω
3 ( ∆ ) I(r) scales as ∆2 . A simple relation
2ω03 ∆
00Γexists between the trap depth and scattering rate Γsc = ~∆Udip . With a narrow A 2 ∆ state, we

could create a near-resonant optical trap(NROT) with low power.

7.2.1

Experiment Setup

We obtain a 100 mW of 689 nm beam from a tapered amplifier(EYP-TPA-0690-00250-2003CMT02-0000) and then focus to a beam waist of 50 µm. According to the calculation, this produces
a trap depth of 15 µK, with scattering rate of 1 Hz. The ODT beam is aligned to the molecular
cloud by depleting molecules into N=0/2 dark states, creating a hole at the center of the molecule00cloud. We lock the 689 nm beam on A2 Π1/2 (N = 1, G = 0, F = 1) ⇐⇒ A 2 ∆3/2 (J = 3/2, F = 2)
transition. The beam is aligned perpendicular to gravity to prevent molecules from falling.

88
7.2.2

Discussion

We briefly tried this 689 nm ODT for 2 months, but didn’t trap any molecules. The possible
reasons are:
(1) Low trap depth: Our trap depth is limited by the 689 nm TA power, which is only 250 mW.
A 15 µK is hard to trap molecules with the temperature of 10 µK if cooling is not working
in the lattice. A deeper trap can be achieved with a lower detuning, but the scattering loss
Γwill be enhanced, following Γsc = ~∆Udip . This can be improved with a SFG laser from

Precilasers which generates watts of power at 689 nm.
(2) Amplified spontaneous emission(ASE): Our trapping beam is amplified by a TA, whichcontains a broadband ASE. The close-resonance ASE would scatter molecules quickly which
limits the trap lifetime. ASE filters with GHz bandwidth can be used to block the unwanted
light. A SFG laser can also solve this problem.
(3) Gravity: For a weak trap, a small(0.5◦ ) angle would be enough for molecules to fall undergravity, as described previously in Figure 7.3.

Figure 7.4: 1064 nm beam preparation and optical setup. The high power AOM is used to turn
1064 nm beam on and off. The whole setup is surrounded by aluminum enclosure to prevent dust
and possible scattering. The entire system takes 1.5 hours to warm up.

89

7.3

1064 nm ODTAccording to Figure 7.1, we decided to create a deeper optical trap of YO at 1064 nm where

single frequency, high power, low noise amplifier is available. Compared with 689 nm ODT, 1064 nm
ODT has deeper trap depth, lower scattering rate and smaller differential AC stark shift between
hyperfine manifolds. We focused 11 W of light to a beam waist of 50 µm, creating a trap depth of 20µK with radial(axial) trapping frequencies ωr (ωz ) = 2π × 220(0.96) Hz. In this case, the scattering
rate is about 0.3 Hz, which is long enough for us at the moment. The full beam preparation andoptical setup for 1064 nm ODT are shown in figure 7.4.

7.3.1

Experiment Setup

A low noise, narrow bandwidth 1064 nm seed from Coherent Mephisto laser is amplified bya thousand times(15mW→50W) using a fiber amplifier(Nufern NUA-1064-PV-0050-D0), as shownin Figure 7.4. A high power AOM is used to switch and stabilize the trapping beam intensity.
This high power beam was delivered to the vacuum chamber via a fiber. A normal step-index fiber
can not handle power higher than 2 W, mostly due to stimulated Brillouin scattering(SBS). SBS
arises from the light coupling with the phonon modes where the forward-traveling photons scatter
into a phonon and a backwards-traveling photon. In this case, an interference pattern is formed,

Figure 7.5: (a) Fiber end cap. A 1 mm long fused silica end cap is bond at the fiber tip to increase
the beam size at the air-to-gap interface that protect the tip from burning. (b) Copper ferrule.
The shining orange light is the miscoupled beam. The hollow structure allows these light to escapewithout causing extra heat. In this picture, we couple 614 nm laser just for demonstration. (c)Custom-made water cooling block.

90
which modulates the local density of the fiber. This is a stimulated, non-linear process since thisinterference pattern enhances the back scattering of the photon. A power threshold exists when
the back-scattered power is comparable to the input power[148]. The threshold is determined by
the fiber length, core diameter, dielectric material, and the wavelength of the light. For example,
the threshold is only ∼3 watt for coupling 1064 nm laser if a 5 meter long, step-index, fused silica
fiber with 5 µm core is used [149, 150]. To overcome this problem, we use a photonic crystal
fiber(NKT LMA-PM-15) where a large mode area(12.6 µm) is achieved by guiding light throughits photonic structure. Besides, a fused silica end cap(Tratech Fiberoptics HP 2.5), shown in Figure
7.5 (a), covers the input and the output of the fiber to prevent the possible burning at the fiber
tip. This reduces the intensity at the air-to-end cap interface by increasing the beam diameter.
A custom-made copper block is used to holds the copper ferrule for water-cooling, as shown in
Figure 7.5 (c). We attach a thermocouple to the copper ferrule(close to the fiber tip) and programa temperature interlock system to protect the fiber from overheating. If the temperature exceeds
40◦ C, the interlcok will disabled the AOM, leaving all laser power on the beam dump, as shown in
Figure 7.4. When operating the fiber constantly at high power (>10 W), the temperature stays ataround 40◦ C. This can be improved with better cooling power.
Care must be taken when working with high power lasers. Under high intensity, thermal
lensing and unexpected reflection are problematic for stability and safety. Special optics are used
to minimize these effects[151]:• All reflective/transmissive optics are HR/AR V-coated at 1064 nm to minimize the transmission/reflection.
• All transmissive optics are fused silica to reduce the thermal expansion and absorption.
Compared to N-BK7, CaF2 and MgF2 , fused silica has comparable transmittance but
much lower coefficient of thermal expansion(5.5 × 10−7 /◦ C) which reduces thermal lensing
effect.
• Low power polarizing beamsplitter cubes are epoxied together, which can be easily damaged

91
by high power laser beams. This can be prevented by using optical bonding or thin-film
polarizer. In our experiment, we use thin-film plate polarizers(CVI TFPN-1064-PW-1025UV) to further reduce the back-reflection.

Figure 7.6: ODT and lattice optics beam paths and imaging optics. In ODT, the trapping beam
is dumped at the top of the figure while the beam is retroreflected in 1D optical lattice.

An overview of the optical layout is shown in Figure 7.6. Limited by the optical access, 1064
nm beam shares the same path with the imaging system. The 1064 nm beam first go througha telescope for a smaller beam waist. Then, an isolator is used, specifically for optical lattice,
to block the retro-reflected beam. The trapping beam is coupled into the chamber by a dichroic
mirror(Semrock: FF749-Sdi01) and then collimated, dumped(retro-reflected) on the other side of
the chamber for ODT(lattice) setup. S polarization is chosen to minimize the transmission throughthe dichroic mirror, which reduces the amount of retro-reflected light leaking into the camera.
The transmitted light from the dichroic mirror is coupled into a single mode fiber for alignment
and power stabilization. It is worth mentioning the isolator should be placed far away from the92
molecular cloud since the laser cooling is sensitive to the magnetic field.

Figure 7.7: We use 689 nm depletion to align the 1064 nm beam. We first deplete the moleculeswith a weak 689 nm beam and then overlap 1064 nm trapping laser to the 689 nm beam. (a)Molecule cloud after GMC, without depletion. (b) With weak 689 nm depletion. A well aligned
689 nm beam depletes a hole at the center of the cloud.

In order to align ODT beam on the molecular cloud, we first depleted molecules with 689
nm light, as shown in Figure 7.7 and then overlapped 1064 nm beam to the 689 nm beam. After
this initial alignment, the fine tuning was done by examining the position of trapped molecules.
The ODT beam should be perpendicular to the direction of gravity to prevent leaking. This will
be detailed in Section 7.3.3. Once the beam was aligned, the focus was adjusted to maximize thenumber of trapped molecules, as shown in Figure 7.8 (a).

Figure 7.8: (a). Number of loaded molecules vs lens position. (b). Number of loaded molecules
into the ODT as a function of loading time with GMC cooling. The timing diagram is shown in
the inset.

93
7.3.2

Loading and Cooling inside ODTIn order to capture more molecules in the optical trap, the ODT light was switched on at
the beginning of the GMC compression sequence, as shown in the inset of Figure 7.8 (b). Since theloading efficiency depends on the ability to cool molecules in the trap, we explore the dependenceof trapped molecule number on various cooling parameters. We first scanned the loading curve by
varying the overlap duration between GMC and ODT. As shown in Figure 7.8 (b), we found thatthe number of trapped molecules increased by a factor of 5 and reached the peak at 70 ms. We
didn’t perform a direct loading measurement to prove the cooling enhances the loading. But thepeak loading efficiency(∼4%) is much higher than simply trapping the molecules within the beam
waist(<1%). This implies that GMC cools the nearby molecules and helps them fall into the trap.
In an optical trap, the trapping potential relies on the spatially varying Stark shift where
differential Stark shifts are also created between hyperfine manifolds. These differential Stark shifts
impede efficient cooling inside the trap by breaking the coherence needed for GMC. Therefore, wefirst varied the Raman detuning δ. As shown in Figure 7.9 (b)(c), we observe the loading peaks
are slightly offsetted from the Raman resonance condition in freespace by ∼tens of kHz. This on
the same order of the estimated differential ac Stark shift arising from the ODT.

Figure 7.9: Dependence of ODT loading on Raman detuning δ. (a). GMC configuration. (b).
Fluorescence of trapped molecules vs Raman detuning δ. Blue and red dashed lines represent G=0
F=1, G=1 F=1 Raman resonance and G=0 F=1, G=1 F=2 Raman resonance. (c). Zoom in of (b)around δ = 0. The data points are not enough to determine the exact optimal δ but the optimalloading detuning is ∼ tens of kHz compared to the Raman resonance condition in free space.

94
Unfortunately, Raman resonance condition can not be fulfilled at each location of the trap
due to the spatially varying Stark shift. In order to load more molecules, a high intensity GMC
beam can be applied to broaden the Λ-enhanced cooling feature. We investigate the loaded number
dependence on the intensity I while keeping Raman detuning δ/2π=20 kHz and the single-photon
detuning ∆/2π=+40 MHz (8.3Γ/2π). We find that the loaded number increases with GMC intensity, shown in Figure 7.10, consistent with the idea that increased intensity reduces the sensitivity
to δ. We confirmed this statement by scanning the loading dependence on δ in lattice with different
cooling intensities. The results are detailed in Section 7.4.1.

Figure 7.10: Number of loaded molecule versus GMC intensity at a trap depth of 20 µK. We keep
the Raman detuning δ/2π=20 kHz and the single-photon detuning ∆/2π=+40 MHz.

7.3.3

ODT Lifetime

Our first ODT was very short-lived(31(4) ms), as shown in Figure 7.11 (a) in blue. This
short lifetime also limits the loading process described in the previous chapter. This leakage resultsfrom the molecule falling under gravity and it is limited by the longitudinal trapping frequency, as
described previously in Figure 7.3 . After a better alignment, the lifetime increased significantly to
83(8) ms, as shown in Figure 7.11 (a) in red. This is still too short compared to the estimated lifetime
from ODT scattering(> 3s) and background collision(∼s). In order to exclude the background95

Figure 7.11: (a). Loss of trapped molecules in a trap. Molecules leave the trap at a faster rate if
the trap is tilted. (b). ODT lifetime at different pressures. The pressure is adjusted by changing
the helium flow and the opening time of the in-vacuum shutters. Collision with background gas is
not limiting the current ODT lifetime. The typical operating pressure is ∼ 3 × 10−9 Torr.

collision, we performed the lifetime measurement at different pressures by varying the helium flowrate and the opening time of the in-vacuum shutters, as shown in Figure 7.11 (b). Apparently, thebackground collision is not limiting the ODT lifetime at the moment. We suspect that molecules
are still leaving from the axial direction as the axial trapping frequency is only ∼ 1 Hz. There are
two ways to enhance the trapping along axial direction: shrinking the focused beam waist, which
reduces the loading efficiency, or adding another trapping laser to form a crossed ODT/opticallattice. We chose the 1D lattice for efficient trapping.

7.41064 nm Optical Lattice
If the ODT beam is directly retro-reflected by a mirror shown in Figure 7.6, it forms aninterference pattern with the incoming beam, creating a 1D lattice structure. Thanks to thelattice structure, the longitudinal trapping frequency is greatly enhanced. A deeper trap is createdwith the same trapping intensity. A 11 W 1064 nm light creates a trap depth of 60 µK withradial(longitudinal) trapping frequencies ωr (ωz ) = 2π × 0.44(93) kHz and a scattering rate of 1.2
Hz. The full beam preparation and optical setup for 1D optical lattice are shown in Figure 7.4 and
7.6.

96
7.4.1

Loading and Cooling inside Lattice

The loading and cooling is very similar to the ODT setup. After 50 ms cooling inside thelattice, the cooling light was switched off for 40 ms to allow the untrapped molecules to escape fromthe detection region. Figure 7.12 shows the loading and cooling of molecules into the optical lattice.
Since a deeper trap is formed in the lattice, we first varied the Raman detuning δ with single-photon
detuning ∆/2π for G=0 F=1 fixed at +40 MHz (8.3Γ/2π) and I = 3I0 , where I0 =2.7 mW/cm2 isthe estimated saturation intensity. As shown in Figure 7.12(b), the optimal two-photon detuningδtrap in the trap is shifted by ∼2π×70 kHz compared to the Raman resonance δf ree =0 in free-space,on the same order as the calculated differential Stark shifts between G=0, F=1 and G=1, F=2. It
is about 4 times larger than the optimal Raman detuning in ODT, as expected. Since the spatial
varying Stark shift is inevitable, one way to reduce the sensitivity on Raman detuning δ and achievea lower temperature is to increase the single-photon detuning ∆. With I=5.5I0 and δtrap = 2π×70
kHz, the loading increases with single-photon detuning ∆ and saturates at ∼2π×20 MHz, shownin Figure 7.12(c). Another way to load more molecules is to increase the cooling intensity. With ahigh GMC intensity, the Λ cooling feature is broadened at the cost of raising the lowest attainabletemperature. We investigated the loaded number dependence on the intensity I while keeping
Raman detuning δtrap = 2π × 70 kHz and the single-photon detuning ∆/2π=+40 MHz (8.3Γ/2π).
As shown in Figure 7.12(d), the loaded number increases with intensity and eventually saturated
at ∼2I0 . To prove it is the case, we scanned the Raman detunings δ at different intensities andobserved a broader Raman feature at higher GMC intensity, shown in the inset of Figure 7.12 (d).
The lowest temperature also increases with high intensity, consistent with the theory [134]. These
confirm our previous hypothesis that the loading dependence on Raman detuning δ decreases withintensity I or single-photon detuning ∆.

97

Figure 7.12: Dependence of lattice loading on GMC parameters. (a). GMC configuration. (b).
Lattice LIF vs Raman detuning δ. (c). Lattice LIF vs One photon detuning ∆. (d). Lattice LIF vs
GMC intensity. The inset shows the Λ-enhanced feature at different intensities. The δ dependence
decreases with intensity I.

7.4.2

Lattice Characterization

The important lattice parameters are lattice trapping frequency, lifetime and heating rate.
As for the trapping frequency, we haven’t performed a direct measurement yet. Instead, thetrapping frequency is currently inferred from the ODT transverse trapping frequency and the latticegeometry. I should be clear that the correct way is to directly measure the trapping frequencies
by introducing intensity(pointing) noise into the trapping beam. But let me briefly explain what
we’ve performed.
We measured the transverse trapping frequency of ODT by oscillating the center of the
trap. This is achieved by modulating the beam pointing using a piezo actuated mirror. If the

98

Figure 7.13: Measure the trapping frequency of the lattice by oscillating the center of the trap.
If the center of the trap oscillates at the trapping frequency, molecules are heated and therefore
escape from the trap.

trap is oscillating at the trapping frequency, molecules would be heated and then escape from thetrap [152]. We loaded molecules into the trap, oscillated the trap center at various frequencies
and observed the number of remaining molecules after oscillation. As shown in Figure 7.13, thetransverse trapping frequency of the ODT is 2π×222 Hz. Assuming the perfect retro-reflection,
the transverse trapping frequency of the lattice is 2π×0.44 kHz. With a 50 µm beam waist at thefocus, the longitudinal trapping frequency of the lattice is 2π×93 kHz.
The other properties of an optical lattice are the lifetime of trapped molecules and the heating
rate induced by the lattice beams. After loading molecules into the lattice, we switched off all theother beams except the lattice light, and measured the number of remaining molecules after various
amount of time. The results are shown in Figure 7.14 (a), from which we extract the lifetime to
be 850(70) ms. Our vacuum pressure is ∼3×10−9 Torr, and we attribute the limitation of lifetime
to collisions with background gas. To determine the heating rate, we switched off the GMC beams
after cooling molecules to 7 µK, and measured how their temperatures evolve over time using thestandard ballistic expansion method. As shown in Fig. 7.14 (b), no noticeable heating is observed
within 500 ms.

99

Figure 7.14: Characterization of 1D optical lattice. (a) Measurement of lattice lifetime. The solidline is an exponential fit with a 1/e constant of 850(70) ms. (b) Measurement of molecules heating
rate inside the lattice. The error bars in the plots correspond to 1σ statistical uncertainty. The
extracted heating rate is −0.4(0.7)µK.

With optimized parameters(∆ = 8.3Γ, δ = 2π × 70 kHz, Iloading = 5.5I0 , Icooling = 3.0I0 ,trap depth 60 µK, ωt = 2π × 440 Hz, ωl = 2π × 93 kHz, scattering rate 1.2 Hz), 1200 molecules
are transferred into the 1D lattice with a temperature of 7.0(6) µK. The peak density is 1.2×1010
cm−3 and the phase space density is 3.1×10−6 . This is the highest phase space density of molecules
achieved by direct laser cooling.

7.4.3

Molecule Loss with Low Intensity GMC Beams

Once the lattice is loaded, we apply an extra GMC pulse with different parameters comparedto the loading. In this final stage, the cooling powers are still equally distributed between two
components, but the intensity I is lowered to achieve a low temperature. We keep Raman detuningδ = 2π×70 kHz where the loading is the most efficient. After 8 ms of GMC, we measure thetemperature using the standard ballistic expansion method. As shown in Figure 7.15 (b), thetemperature decreases linearly with the intensity which we attribute to the reduced momentum
diffusion, consistent with theoretical prediction [128].
In our previous work [59], we also observed that the temperature of YO gray molasses infree space decreases with light intensity. The trend stops when the intensity is too low to hold the

100

Figure 7.15: Molecule loss in lattice enhanced by low intensity GMC beams. (a). YO level structure with possible loss mechanism. (b). Temperature versus GMC intensity I with ∆=8.3Γ and
δ=2π×70 kHz. The solid line is a linear fit. (c). Number of remaining molecules versus GMC
intensity I with ∆=8.3Γ and δ=2π×70 kHz.. The solid line is a fit to the function N=N0 -k×ρee (I)where ρee represents the excited state A2 Π1/2 population calculated in the theoretical predictions
in Ref. [153]. Molecules in A2 Π1/2 state could be lost after scattering 1064 nm photons.

molecules against gravity. With molecules trapped inside the lattice, we ramped down the GMC
intensity in order to obtain an even lower temperature. However, we observed a striking molecularloss near GMC intensity of I=0.21 I0 , shown in Figure 7.15 (c).
With a non-zero Raman detuning δ, molecules can be populated up to A2 Π1/2 state at low0

GMC intensity [153] and then become lost through A 2 ∆3/2 decay channels. In the X 2 Σ+ stateof YO, there is a close splitting between G=1 F=1 and G=1 F=2 manifolds(3.5 MHz). In thiscase, even a Raman resonance condition is fulfilled between G=0 F=1 and G=1 F=2, there is stilla non-zero Raman detuning δ between G=0 F=1 and G=1 F=1 states, populating molecules to
A2 Π1/2 state. Even if the Raman resonance condition is fulfilled at the trap center, the spatiallyinhomogeneity breaks the resonance at the edge of the trap. To verify that the molecules excited0

to A2 Π1/2 state are not leaking into A 2 ∆3/2 state, we measured the decay curve at intensity
I = 0.21I0 , as shown in Figure 7.16. Based on the branching ratio 3 × 10−4 and the fitted decay
time constant 41(2) ms, the calculated scattering rate is 8 × 104 s−1 , which is more than two orders
0of magnitude larger than the GMC scattering rate. Therefore, the loss is not due to the A 2 ∆3/2
state leakage.

101

Figure 7.16: Molecule loss in the lattice with low power GMC beam(I=0.21I0 ). The solid line is anexponential fit. The 1/e time constant is 41(2) ms.

We attribute this loss to excitation to D2 Σ+ through A2 Π1/2 with a 1064 nm photon [87].
Among all electronic states, D2 Σ+ is ∼230 THz higher than our excited state A2 Π1/2 [87]. Therefore, a 1064 nm photon(280 THz) is reasonably close to the A2 Π1/2 → D2 Σ+ transition. Molecules
first get excited to A2 Π1/2 state by low intensity GMC beam, then get pumped up to D2 Σ+by the 1064 nm photon and eventually decay back. This is a three-photon process, as a result,molecules decay to rotational states with opposite parity compared with the initial X 2 Σ+ states in
the X 2 Σ+ →− A2 Π1/2 cycle. Currently, we’re taking more data to explore the remaining molecule
number dependence on intensity I, single-photon detuning ∆ and Raman detuning δ. These data
can help us gain a better understanding of the loss mechanism.

102
7.4.4

Heating at Low Intensity

In addition to the molecule loss, the excitation into A2 Π1/2 is undesirable for reaching a lowtemperature due to the momentum diffusion. In Figure 7.17, we observe a heating rate of 84(18)µK/s with ∆/2π =40 MHz, δtrap /2π = 70 kHz and I=0.06 I0 . As has been observed [61, 62, 154, 155]and discussed [134] previously, the temperature T = Dp /(α×kB ) would decrease with single-photon
detuning ∆ as the momentum diffusion coefficient Dp is reduced, while the friction coefficient α isindependent of ∆. To suppress the one photon scattering, we increase the single-photon detuning∆/2π from +40 MHz to +120 MHz. At +120 MHz, the heating rate becomes unnoticeable but
the lowest temperature remains at ∼7 µK. The current low temperature limit in the lattice might
be caused by another mechanism such as the interference/dephasing between the lattice and GMC
beams.

Figure 7.17: GMC heating inside the lattice with δtrap /2π = 70 kHz and I=0.06 I0 . The heating is
suppressed with a large single-photon detuning ∆.

103
7.4.5

Ramping Down the LatticeOnce the molecules are cooled inside the lattice, all the lasers are removed except the 1064
nm trapping beams. We next linearly ramped down the trap depth in 50 ms and holded at the final
depth for another 6 ms. Since the CCD is aligned along the lattice axis, the ballistic expansion
measurements determine the temperature in the transverse direction. As shown in Figure 7.18,
the temperature decreases as the trap depth gets shallower. This is expected as density decreases
during the expansion, temperature should be reduced if the phase space density is conserved. Similar observation has been reported in other systems [156, 157], but our transverse temperatures
seem to decrease a little faster than expected. Assuming the molecules are fully thermalized that
longitudinal temperature is the same as the transverse one, we plotted the calculated temperature (solid) and its 95% confidence interval (dashed) from fitting the molecule number associatedwith the molecular loss and a constant phase space density. Clearly, the transverse temperature
decreases faster than what is assumed under a conserved phase space density. A sharp molecule
loss at low trap depth is also observed. A systematic longitudinal temperature measurement andthermalization study is required to understand the physics.

104

Figure 7.18: Achieving the coldest temperature by ramping down the trap depth. We load themolecules at the trap depth of 60 uK, ramp down to different final trap depth in 50 ms andhold for 6 ms. The red dots represent the temperature measured along the transverse direction.
The red solid line shows the calculated temperature under conserved phase space density, with 95%
confidential interval showing in dashed. The blue dots represent the remaining number of molecules
after the ramp.

105
7.4.6

Noise-induced Heating

There are two main sources of heating in far-off-resonance optical traps. Heating rates are
estimated in terms of the intensity and position noise power spectrum measured for fiber amplifier.
Intensity noise causes fluctuations in the trapping frequency resulting in exponential heating, while
beam-pointing noise introduces fluctuations of the trap center and leads to heating at a constantrate. In this section, we consider a molecule in a one-dimensional harmonic-oscillator potential
with a fluctuating spring constant and a fluctuating equilibrium position.
The heating rate by intensity noise can be calculated as follows [152]. For a focused Gaussian∼laser beam with field amplitude E and beam waist a, the potential can be approximated as −V0 +
∼

|E|2
V0
1
2
2 kx , where α is the polarizability, V0 = α 4 is the maximum light shift and k = 2 a2 is the spring

constant. Since both V0 and k are proportional to the laser intensity I(t), the spring constantfluctuates in time. This leads to an effective Hamiltonian:H=
where ωtr =

q

p2
1
2
+ M ωtr[1 + (t)]x22M2I(t)−I0
k0
is the fractional fluctuation
M is the averaged trapping frequency and (t) =I0of the spring constant due the laser intensity. Using the 1st order perturbation theory, one could
find that the average energy increases exponentially:hĖi = Γ hEi
where the rate constant Γ is2Γ = π 2 νtrS (2νtr )Here the νtr is the trapping frequency in Hz, S (2νtr ) is the power spectral density at twice thetrapping frequency and TI = 1/Γ is the time to increase the energy by a factor of e, known as
e-folding time. The energy e-folding time TI directly limits the time that molecules can stay inside
the trap. Molecules will leave the trap when their energy is similar to the trap depth. In a 3D
trap, the heating rate will be the mean of the rates along all directions [152]. Similarly, pointing

106
fluctuation introduces heating with the effective Hamiltonian:
H=

p2
1
2
+ M ωtr[x − (t)]22M2where (t) is the fluctuation of the trap center [158]. We could get
hĖi =π4M ωtr
Sx (ωtr )2

where the heating is independent of the trap energy, Sx (ω) is the power spectrum of the position
fluctuations in the trap center.
Our optical trapping light is not suffering noticeable heating at the moment. The seedlaser(Coherent Mephisto) has extraordinary low noise [159] and we’re mostly limited by our fiber
amplifier, characterized in [151]. Here I attach the relative intensity noise(RIN) spectrum of ourtrapping light and the calculated e-folding time TI . In Figure 7.19 (a), we could see the intensity
servo suppress the intensity noise thus the e-folding time TI is not limiting the trap lifetime. It is
worth mentioning that when the intensity is servoed, the witness photo diode observed more noises
at several frequencies(466 Hz, 933 Hz, 1 kHz) and it is also much more noisier than the photo
diode in the loop. The in loop photo diode detects the light from a fiber, which would convert the
pointing noise into intensity noise. This can be solved by monitoring the intensity from free space.

Figure 7.19: Relative intensity noise spectrum and e-folding time. (a). RIN of 1064 nm laser. (b).
e-folding time TI from intensity noise.

Bibliography[1] Mike H Anderson, Jason R Ensher, Michael R Matthews, Carl E Wieman, and Eric A Cornell.
Observation of bose-einstein condensation in a dilute atomic vapor. science, 269(5221):198–
201, 1995.
[2] Brian DeMarco and Deborah S Jin. Onset of fermi degeneracy in a trapped atomic gas.
science, 285(5434):1703–1706, 1999.
[3] Immanuel Bloch, Jean Dalibard, and Wilhelm Zwerger. Many-body physics with ultracoldgases. Reviews of modern physics, 80(3):885, 2008.
[4] Chris Monroe, David M Meekhof, Barry E King, Wayne M Itano, and David J Wineland.
Demonstration of a fundamental quantum logic gate. Physical review letters, 75(25):4714,
1995.
[5] Mark Saffman, Thad G Walker, and Klaus Mølmer. Quantum information with rydberg
atoms. Reviews of modern physics, 82(3):2313, 2010.
[6] Kihwan Kim, M-S Chang, Simcha Korenblit, Rajibul Islam, Emily E Edwards, James K
Freericks, G-D Lin, L-M Duan, and Christopher Monroe. Quantum simulation of frustrated
ising spins with trapped ions. Nature, 465(7298):590–593, 2010.
[7] Markus Greiner, Olaf Mandel, Tilman Esslinger, Theodor W Hänsch, and Immanuel Bloch.
Quantum phase transition from a superfluid to a mott insulator in a gas of ultracold atoms.
nature, 415(6867):39–44, 2002.
[8] Dmitry Budker and Michael Romalis. Optical magnetometry. Nature physics, 3(4):227–234,
2007.
[9] Andrew D Ludlow, Martin M Boyd, Jun Ye, Ekkehard Peik, and Piet O Schmidt. Opticalatomic clocks. Reviews of Modern Physics, 87(2):637, 2015.
[10] Lincoln D Carr, David DeMille, Roman V Krems, and Jun Ye. Cold and ultracold molecules:
science, technology and applications. New Journal of Physics, 11(5):055049, 2009.
[11] John L Bohn, Ana Maria Rey, and Jun Ye. Cold molecules: Progress in quantum engineeringof chemistry and quantum matter. Science, 357(6355):1002–1010, 2017.
[12] David DeMille. Quantum computation with trapped polar molecules. Physical Review
Letters, 88(6):067901, 2002.

108[13] SF Yelin, K Kirby, and Robin Côté. Schemes for robust quantum computation with polar
molecules. Physical Review A, 74(5):050301, 2006.
[14] Mallikarjun Karra, Ketan Sharma, Bretislav Friedrich, Sabre Kais, and Dudley Herschbach.
Prospects for quantum computing with an array of ultracold polar paramagnetic molecules.
The Journal of chemical physics, 144(9):094301, 2016.
[15] Kang-Kuen Ni, Till Rosenband, and David D Grimes. Dipolar exchange quantum logic gatewith polar molecules. Chemical science, 9(33):6830–6838, 2018.
[16] Jacob A Blackmore, Luke Caldwell, Philip D Gregory, Elizabeth M Bridge, Rahul Sawant,Jesús Aldegunde, Jordi Mur-Petit, Dieter Jaksch, Jeremy M Hutson, BE Sauer, et al. Ultracold molecules for quantum simulation: rotational coherences in caf and rbcs. Quantum
Science and Technology, 4(1):014010, 2018.
[17] MS Safronova, D Budker, D DeMille, Derek F Jackson Kimball, A Derevianko, and Charles W
Clark. Search for new physics with atoms and molecules. Reviews of Modern Physics,
90(2):025008, 2018.
[18] David DeMille, John M Doyle, and Alexander O Sushkov. Probing the frontiers of particle
physics with tabletop-scale experiments. Science, 357(6355):990–994, 2017.
[19] Axel André, David DeMille, John M Doyle, Mikhail D Lukin, St Ex Maxwell, Peter Rabl,
Robert J Schoelkopf, and Peter Zoller. A coherent all-electrical interface between polar
molecules and mesoscopic superconducting resonators. Nature Physics, 2(9):636–642, 2006.
[20] Andrea Micheli, GK Brennen, and Peter Zoller. A toolbox for lattice-spin models with polar
molecules. Nature Physics, 2(5):341–347, 2006.
[21] Roman V Krems. Cold controlled chemistry.
10(28):4079–4092, 2008.

Physical Chemistry Chemical Physics,[22] N Balakrishnan. Perspective: Ultracold molecules and the dawn of cold controlled chemistry.
The Journal of chemical physics, 145(15):150901, 2016.
[23] Tetsu Takekoshi, Lukas Reichsöllner, Andreas Schindewolf, Jeremy M Hutson, C Ruth
Le Sueur, Olivier Dulieu, Francesca Ferlaino, Rudolf Grimm, and Hanns-Christoph Nägerl.
Ultracold dense samples of dipolar rbcs molecules in the rovibrational and hyperfine groundstate. Physical review letters, 113(20):205301, 2014.
[24] Peter K Molony, Philip D Gregory, Zhonghua Ji, Bo Lu, Michael P Köppinger, C Ruth
Le Sueur, Caroline L Blackley, Jeremy M Hutson, and Simon L Cornish. Creation of ultracold rb 87 cs 133 molecules in the rovibrational ground state. Physical review letters,
113(25):255301, 2014.
[25] Jee Woo Park, Sebastian A Will, and Martin W Zwierlein. Ultracold dipolar gas of fermionicna 23 k 40 molecules in their absolute ground state. Physical review letters, 114(20):205302,
2015.
[26] Mingyang Guo, Bing Zhu, Bo Lu, Xin Ye, Fudong Wang, Romain Vexiau, Nadia BouloufaMaafa, Goulven Quéméner, Olivier Dulieu, and Dajun Wang. Creation of an ultracold gasof ground-state dipolar na 23 rb 87 molecules. Physical review letters, 116(20):205303, 2016.

109[27] JFE Croft, N Balakrishnan, and BK Kendrick. Long-lived complexes and signatures of chaos
in ultracold k 2+ rb collisions. Physical Review A, 96(6):062707, 2017.
[28] M-G Hu, Yu Liu, David D Grimes, Y-W Lin, Andrei H Gheorghe, Romain Vexiau, Nadia
Bouloufa-Maafa, Olivier Dulieu, Till Rosenband, and K-K Ni. Direct observation of bimolecular reactions of ultracold krb molecules. Science, 366(6469):1111–1115, 2019.
[29] Goulven Quemener and Paul S Julienne. Ultracold molecules under control!
Reviews, 112(9):4949–5011, 2012.

Chemical[30] Mikhail Lemeshko, Roman V Krems, John M Doyle, and Sabre Kais. Manipulation ofmolecules with electromagnetic fields. Molecular Physics, 111(12-13):1648–1682, 2013.
[31] Jie Cui and Roman V Krems. Elastic and inelastic collisions of 2 σ molecules in a magnetic
field. Physical Review A, 88(4):042705, 2013.
[32] AV Gorshkov, P Rabl, G Pupillo, A Micheli, P Zoller, MD Lukin, and HP Büchler. Suppression of inelastic collisions between polar molecules with a repulsive shield. Physical review
letters, 101(7):073201, 2008.
[33] Giacomo Valtolina, Kyle Matsuda, William G Tobias, Jun-Ru Li, Luigi De Marco, and Jun
Ye. Dipolar evaporation of reactive molecules to below the fermi temperature. Nature,588(7837):239–243, 2020.
[34] BC Regan, Eugene D Commins, Christian J Schmidt, and David DeMille. New limit on theelectron electric dipole moment. Physical review letters, 88(7):071805, 2002.
[35] Jacob Baron, Wesley C Campbell, David DeMille, John M Doyle, Gerald Gabrielse, Yulia V
Gurevich, Paul W Hess, Nicholas R Hutzler, Emil Kirilov, Ivan Kozyryev, et al. Order ofmagnitude smaller limit on the electric dipole moment of the electron. Science, 343(6168):269–
272, 2014.
[36] Vitaly Andreev and NR Hutzler. Improved limit on the electric dipole moment of the electron.
Nature, 562(7727):355–360, 2018.
[37] William B Cairncross, Daniel N Gresh, Matt Grau, Kevin C Cossel, Tanya S Roussy, Yiqi
Ni, Yan Zhou, Jun Ye, and Eric A Cornell. Precision measurement of the electron’s electric
dipole moment using trapped molecular ions. Physical review letters, 119(15):153001, 2017.
[38] Jonathan J Hudson, Dhiren M Kara, IJ Smallman, Ben E Sauer, Michael R Tarbutt, and
Ed A Hinds. Improved measurement of the shape of the electron. Nature, 473(7348):493–496,
2011.
[39] Huanqian Loh, Kevin C Cossel, MC Grau, K-K Ni, Edmund R Meyer, John L Bohn, Jun Ye,
and Eric A Cornell. Precision spectroscopy of polarized molecules in an ion trap. Science,
342(6163):1220–1222, 2013.
[40] K-K Ni, S Ospelkaus, MHG De Miranda, A Pe’Er, B Neyenhuis, JJ Zirbel, S Kotochigova,
PS Julienne, DS Jin, and Jun Ye. A high phase-space-density gas of polar molecules. science,
322(5899):231–235, 2008.

110[41] Frauke Seeßelberg, Nikolaus Buchheim, Zhen-Kai Lu, Tobias Schneider, Xin-Yu Luo, Eberhard Tiemann, Immanuel Bloch, and Christoph Gohle. Modeling the adiabatic creation ofultracold polar 23 na 40 k molecules. Physical Review A, 97(1):013405, 2018.
[42] Timur M Rvachov, Hyungmok Son, Ariel T Sommer, Sepehr Ebadi, Juliana J Park, Martin W
Zwierlein, Wolfgang Ketterle, and Alan O Jamison. Long-lived ultracold molecules withelectric and magnetic dipole moments. Physical review letters, 119(14):143001, 2017.
[43] Luigi De Marco, Giacomo Valtolina, Kyle Matsuda, William G Tobias, Jacob P Covey, and
Jun Ye. A degenerate fermi gas of polar molecules. Science, 363(6429):853–856, 2019.
[44] Kyle Matsuda, Luigi De Marco, Jun-Ru Li, William G Tobias, Giacomo Valtolina, GoulvenQuéméner, and Jun Ye. Resonant collisional shielding of reactive molecules using electricfields. Science, 370(6522):1324–1327, 2020.
[45] Nicholas R Hutzler, Hsin-I Lu, and John M Doyle. The buffer gas beam: An intense, cold,and slow source for atoms and molecules. Chemical reviews, 112(9):4803–4827, 2012.
[46] S Truppe, HJ Williams, NJ Fitch, M Hambach, TE Wall, EA Hinds, BE Sauer, and MR Tarbutt. An intense, cold, velocity-controlled molecular beam by frequency-chirped laser slowing.
New Journal of Physics, 19(2):022001, 2017.
[47] Stephen D Hogan, Michael Motsch, and Frédéric Merkt. Deceleration of supersonic beams
using inhomogeneous electric and magnetic fields. Physical Chemistry Chemical Physics,
13(42):18705–18723, 2011.
[48] Sebastiaan YT van de Meerakker, Hendrick L Bethlem, Nicolas Vanhaecke, and Gerard Meijer. Manipulation and control of molecular beams. Chemical reviews, 112(9):4828–4878,
2012.
[49] Edvardas Narevicius and Mark G Raizen. Toward cold chemistry with magnetically decelerated supersonic beams. Chemical reviews, 112(9):4879–4889, 2012.
[50] David Reens, Hao Wu, Alexander Aeppli, Anna McAuliffe, Piotr Wcislo, Tim Langen, and
Jun Ye. Beyond the limits of conventional stark deceleration. Physical Review Research,
2(3):033095, 2020.
[51] Hao Wu, David Reens, Tim Langen, Yuval Shagam, Daniela Fontecha, and Jun Ye. Enhancing radical molecular beams by skimmer cooling. Physical Chemistry Chemical Physics,
20(17):11615–11621, 2018.
[52] Xing Wu, Thomas Gantner, Manuel Koller, Martin Zeppenfeld, Sotir Chervenkov, and Gerhard Rempe. A cryofuge for cold-collision experiments with slow polar molecules. Science,
358(6363):645–648, 2017.
[53] MD Di Rosa. Laser-cooling molecules. The European Physical Journal D-Atomic, Molecular,
Optical and Plasma Physics, 31(2):395–402, 2004.
[54] Benjamin K Stuhl, Brian C Sawyer, Dajun Wang, and Jun Ye. Magneto-optical trap forpolar molecules. Physical review letters, 101(24):243002, 2008.

111[55] JF Barry, DJ McCarron, EB Norrgard, MH Steinecker, and D DeMille. Magneto-opticaltrapping of a diatomic molecule. Nature, 512(7514):286–289, 2014.
[56] S Truppe, HJ Williams, M Hambach, L Caldwell, NJ Fitch, EA Hinds, BE Sauer, and
MR Tarbutt. Molecules cooled below the doppler limit. Nature Physics, 13(12):1173–1176,
2017.
[57] Loı̈c Anderegg, Benjamin L Augenbraun, Eunmi Chae, Boerge Hemmerling, Nicholas R Hutzler, Aakash Ravi, Alejandra Collopy, Jun Ye, Wolfgang Ketterle, and John M Doyle. Radio frequency magneto-optical trapping of caf with high density. Physical review letters,
119(10):103201, 2017.
[58] Alejandra L Collopy, Shiqian Ding, Yewei Wu, Ian A Finneran, Loı̈c Anderegg, Benjamin L
Augenbraun, John M Doyle, and Jun Ye. 3d magneto-optical trap of yttrium monoxide.
Physical review letters, 121(21):213201, 2018.
[59] Shiqian Ding, Yewei Wu, Ian A Finneran, Justin J Burau, and Jun Ye. Sub-doppler cooling and compressed trapping of yo molecules at µ k temperatures. Physical Review X,
10(2):021049, 2020.
[60] Louis Baum, Nathaniel B Vilas, Christian Hallas, Benjamin L Augenbraun, Shivam Raval,
Debayan Mitra, and John M Doyle. 1d magneto-optical trap of polyatomic molecules. Physicalreview letters, 124(13):133201, 2020.
[61] Lawrence W Cheuk, Loı̈c Anderegg, Benjamin L Augenbraun, Yicheng Bao, Sean Burchesky,
Wolfgang Ketterle, and John M Doyle. λ-enhanced imaging of molecules in an optical trap.
Physical review letters, 121(8):083201, 2018.
[62] L Caldwell, JA Devlin, HJ Williams, NJ Fitch, EA Hinds, BE Sauer, and MR Tarbutt.
Deep laser cooling and efficient magnetic compression of molecules. Physical review letters,
123(3):033202, 2019.
[63] DJ McCarron, MH Steinecker, Y Zhu, and D DeMille. Magnetic trapping of an ultracold gasof polar molecules. Physical review letters, 121(1):013202, 2018.
[64] S Jurgilas, A Chakraborty, CJH Rich, L Caldwell, HJ Williams, NJ Fitch, BE Sauer,
Matthew D Frye, Jeremy M Hutson, and MR Tarbutt. Collisions between ultracold molecules
and atoms in a magnetic trap. arXiv preprint arXiv:2101.01580, 2021.
[65] S Jurgilas, A Chakraborty, CJH Rich, BE Sauer, Matthew D Frye, Jeremy M Hutson, and
MR Tarbutt. Collisions in a dual-species magneto-optical trap of molecules and atoms. arXiv
preprint arXiv:2104.09990, 2021.
[66] Loı̈c Anderegg, Lawrence W Cheuk, Yicheng Bao, Sean Burchesky, Wolfgang Ketterle, KangKuen Ni, and John M Doyle. An optical tweezer array of ultracold molecules. Science,
365(6458):1156–1158, 2019.
[67] Lawrence W Cheuk, Loı̈c Anderegg, Yicheng Bao, Sean Burchesky, S Yu Scarlett, Wolfgang
Ketterle, Kang-Kuen Ni, and John M Doyle. Observation of collisions between two ultracold
ground-state caf molecules. Physical review letters, 125(4):043401, 2020.

112[68] Loı̈c Anderegg, Sean Burchesky, Yicheng Bao, Scarlett S Yu, Tijs Karman, Eunmi Chae,
Kang-Kuen Ni, Wolfgang Ketterle, and John M Doyle. Observation of microwave shieldingof ultracold molecules. arXiv preprint arXiv:2102.04365, 2021.
[69] Mark Yeo. The Laser Cooling and Magneto-Optical Trapping of the YO Molecule. PhD
thesis, Citeseer, 2015.
[70] Friedrich Hund.
Allgemeine quantenmechanik des atom-und molekelbaues.
Quantentheorie, pages 561–694. Springer, 1933.

In[71] John Michael Brown, John M Brown, and Alan Carrington. Rotational spectroscopy of
diatomic molecules. Cambridge University Press, 2003.
[72] JL Dunham. The energy levels of a rotating vibrator. Physical Review, 41(6):721, 1932.
[73] RF Curl Jr. The relationship between electron spin rotation coupling constants and g-tensor
components. Molecular Physics, 9(6):585–597, 1965.
[74] JM Brown, M Kaise, CML Kerr, and DJ Milton. A determination of fundamental zeemanparameters for the oh radical. Molecular Physics, 36(2):553–582, 1978.
[75] MR Tarbutt, BE Sauer, JJ Hudson, and EA Hinds. Design for a fountain of ybf molecules tomeasure the electron’s electric dipole moment. New Journal of Physics, 15(5):053034, 2013.
[76] EB Norrgard, DJ McCarron, MH Steinecker, MR Tarbutt, and D DeMille. Submillikelvin dipolar molecules in a radio-frequency magneto-optical trap. Physical review letters,
116(6):063004, 2016.
[77] Timothy C Steimle and Jeffrey E Shirley. A molecular beam-optical stark study of the a2π–x 2σ band system of yo. The Journal of chemical physics, 92(6):3292–3296, 1990.
[78] Carl L Chalek and James L Gole. Chemiluminescence spectra of sco and yo: Observation andanalysis of the a 2δ–x 2σ+ band system. The Journal of Chemical Physics, 65(7):2845–2859,
1976.
[79] A Bernard, R Bacis, and P Luc. Fourier transform spectroscopy: Extensive analysis of thea2ii-¿ x2e+ and b2e+-¿ x2e+ systems of yttrium oxide. The Astrophysical Journal, 227:338–
348, 1979.
[80] A Bernard and R Gravina. The emission spectrum of yttrium monoxide-new rotational andvibrational results on the a2pi-x2sigma+ system. The Astrophysical Journal Supplement
Series, 52:443–450, 1983.
[81] Timothy C Steimle and Yahya Al-Ramadin. Fine and hyperfine structure in the x2σ+ stateof gas-phase yttrium monoxide. Journal of molecular spectroscopy, 122(1):103–112, 1987.
[82] RD Suenram, FJ Lovas, GT Fraser, and K Matsumura. Pulsed-nozzle fourier-transformmicrowave spectroscopy of laser-vaporized metal oxides: Rotational spectra and electric dipole
moments of yo, lao, zro, and hfo. The Journal of chemical physics, 92(8):4724–4733, 1990.
[83] Benoit Simard, Andrew M James, Peter A Hackett, and Walter J Balfour. On the a 2δx2σ+(0, 0) band of yo. Journal of Molecular Spectroscopy, 154(2):455–457, 1992.

113[84] J Hoeft and T Törring. The microwave rotational spectrum of x 2σ+ yo. Chemical physics
letters, 215(4):367–370, 1993.
[85] RR Reddy, Y Nazeer Ahammed, K Rama Gopal, P Abdul Azeem, and S Anjaneyulu. Rkrv
potential energy curves, dissociation energies, γ-centroids and franck-condon factors of yo,
cro, bn, sco, sio and alo molecules. Astrophysics and space science, 262(2):223–240, 1998.
[86] JW-H Leung, Tongmei Ma, and ASC Cheung. Cavity ring down absorption spectroscopy ofthe b2σ+–x2σ+ transition of yo. Journal of Molecular Spectroscopy, 229(1):108–114, 2005.
[87] Deping Zhang, Qiang Zhang, Boxing Zhu, Jingwang Gu, Bingbing Suo, Yang Chen, andDongfeng Zhao. High-resolution electronic spectra of yttrium oxide (yo): The d 2 σ+–x 2
σ+ transition. The Journal of chemical physics, 146(11):114303, 2017.
[88] Chaoqun Zhang, Hannah Korslund, Yewei Wu, Shiqian Ding, and Lan Cheng. Towards accurate prediction for laser-coolable molecules: relativistic coupled-cluster calculations for yttrium monoxide and prospects for improving its laser cooling efficiencies. Physical Chemistry
Chemical Physics, 22(45):26167–26177, 2020.
[89] S Truppe, M Hambach, SM Skoff, NE Bulleid, JS Bumby, RJ Hendricks, EA Hinds, BE Sauer,
and MR Tarbutt. A buffer gas beam source for short, intense and slow molecular pulses.
Journal of Modern Optics, 65(5-6):648–656, 2018.
[90] Mark Yeo, Matthew T Hummon, Alejandra L Collopy, Bo Yan, Boerge Hemmerling, Eunmi
Chae, John M Doyle, and Jun Ye. Rotational state microwave mixing for laser cooling ofcomplex diatomic molecules. Physical review letters, 114(22):223003, 2015.
[91] Matthew T Hummon, Mark Yeo, Benjamin K Stuhl, Alejandra L Collopy, Yong Xia,
and Jun Ye. 2d magneto-optical trapping of diatomic molecules. Physical review letters,
110(14):143001, 2013.
[92] Hsin-I Lu, Julia Rasmussen, Matthew J Wright, Dave Patterson, and John M Doyle. A coldand slow molecular beam. Physical Chemistry Chemical Physics, 13(42):18986–18990, 2011.
[93] Frank Pobell. Matter and methods at low temperatures, volume 2. Springer, 2007.
[94] Nicholas R Hutzler, Maxwell F Parsons, Yulia V Gurevich, Paul W Hess, Elizabeth Petrik,
Ben Spaun, Amar C Vutha, David DeMille, Gerald Gabrielse, and John M Doyle. A cryogenic
beam of refractory, chemically reactive molecules with expansion cooling. Physical chemistrychemical physics, 13(42):18976–18985, 2011.
[95] JF Barry, ES Shuman, and D DeMille. A bright, slow cryogenic molecular beam source forfree radicals. Physical Chemistry Chemical Physics, 13(42):18936–18947, 2011.
[96] HC Hseuh, TS Chou, HA Worwetz, and HJ Halama. Cryosorption pumping of he by charcoal
and a compound cryopump design for tsta. Technical report, Brookhaven National Lab.,
Upton, NY (USA), 1979.
[97] Wesley C Campbell. Magnetic trapping of imidogen molecules. PhD thesis, Citeseer, 2008.
[98] Eunmi Chae. Laser Slowing of CaF Molecules and Progress Towards a Dual-MOT for Li and
CaF. 2016.

114[99] Loic Anderegg. Ultracold Molecules in Optical Arrays: From Laser Cooling to Molecular
Collisions. PhD thesis, 2020.
[100] RC Dye, RE Muenchausen, and NS Nogar. Laser ablation of y2o3 in an oxygen atmosphere.
Chemical physics letters, 181(6):531–536, 1991.
[101] Jack Ekin. Experimental techniques for low-temperature measurements: cryostat design,material properties and superconductor critical-current testing. Oxford university press, 2006.
[102] Christopher J Foot et al. Atomic physics, volume 7. Oxford University Press, 2005.
[103] DJ Wineland and H Dehmelt. Proposed 1014δν/ν laser fluorescence spectroscopy on tl+
mono-ion oscillator iii (side band cooling). Bull. Am. Phys. Soc, 20(4):637–637, 1975.
[104] Theodor W Hänsch and Arthur L Schawlow. Cooling of gases by laser radiation. Optics
Communications, 13(1):68–69, 1975.
[105] David J Wineland and Wayne M Itano. Laser cooling of atoms. Physical Review A, 20(4):1521,
1979.
[106] William D Phillips and Harold Metcalf. Laser deceleration of an atomic beam. PhysicalReview Letters, 48(9):596, 1982.
[107] John V Prodan and William D Phillips. Chirping the light—fantastic? recent nbs atom
cooling experiments. Progress in quantum electronics, 8(3-4):231–235, 1984.
[108] Maurice Petzold, Paul Kaebert, Philipp Gersema, Mirco Siercke, and Silke Ospelkaus. A
zeeman slower for diatomic molecules. New Journal of Physics, 20(4):042001, 2018.
[109] Maurice Petzold, Paul Kaebert, Philipp Gersema, Timo Poll, Niklas Reinhardt, Mirco Siercke,
and Silke Ospelkaus. Type-ii zeeman slowing: Characterization and comparison to conventional radiative beam-slowing schemes. Physical Review A, 98(6):063408, 2018.
[110] Qian Liang, Wenhao Bu, Yuhe Zhang, Tao Chen, and Bo Yan. A general zeeman slower for
type-ii transitions and polar molecules. arXiv preprint arXiv:1906.10797, 2019.
[111] Graham P Greve, Baochen Wu, and James K Thompson. Laser cooling with adiabatic transfer
on a raman transition. New Journal of Physics, 21(7):073045, 2019.
[112] John P Bartolotta, Matthew A Norcia, Julia RK Cline, James K Thompson, and Murray J
Holland. Laser cooling by sawtooth-wave adiabatic passage. Physical Review A, 98(2):023404,
2018.
[113] John P Bartolotta, Jarrod T Reilly, and Murray J Holland. Speeding up particle slowing
using shortcuts to adiabaticity. Physical Review A, 102(4):043107, 2020.
[114] Alejandra Louise Collopy. A three-dimensional mot of yo towards narrow-line cooling. Ph.
D. Thesis, 2018.
[115] EL Raab, M Prentiss, Alex Cable, Steven Chu, and David E Pritchard. Trapping of neutral
sodium atoms with radiation pressure. Physical Review Letters, 59(23):2631, 1987.

115[116] Kyle N Jarvis, JA Devlin, TE Wall, BE Sauer, and MR Tarbutt. Blue-detuned magnetooptical trap. Physical review letters, 120(8):083201, 2018.
[117] Matthew Harvey and Andrew James Murray. Cold atom trap with zero residual magnetic
field: The ac magneto-optical trap. Physical review letters, 101(17):173201, 2008.
[118] MR Tarbutt and TC Steimle. Modeling magneto-optical trapping of caf molecules. PhysicalReview A, 92(5):053401, 2015.
[119] Anne Cournol, Pierre Pillet, Hans Lignier, and Daniel Comparat. Bichromatic magnetooptical trapping for j→ j, j- 1 configurations. Physical Review A, 93(5):053423, 2016.
[120] John F Barry. Laser cooling and slowing of a diatomic molecule. Technical report, YALE
UNIV NEW HAVEN CT, 2013.
[121] EB Norrgard, N Sitaraman, JF Barry, DJ McCarron, MH Steinecker, and D DeMille. Invacuum scattered light reduction with black cupric oxide surfaces for sensitive fluorescence
detection. Review of Scientific Instruments, 87(5):053119, 2016.
[122] ED Erikson, DD Berger, and BA Frazier. A comparison of the outgassing characteristics
of several solar absorbing coatings. Journal of Vacuum Science & Technology A: Vacuum,
Surfaces, and Films, 3(3):1711–1714, 1985.
[123] Sheldon M Smith and Richard V Howitt. Survey of material for an infrared-opaque coating. In Infrared, adaptive, and synthetic aperture optical systems, volume 643, pages 53–62.
International Society for Optics and Photonics, 1986.
[124] Paul J Kuzmenko, Daniel M Behne, T Casserly, W Boardman, D Upadhyaya, K Boinapally,
M Gupta, and Y Cao. Hard infrared black coating with very low outgassing. In Advanced
Optical and Mechanical Technologies in Telescopes and Instrumentation, volume 7018, page701852. International Society for Optics and Photonics, 2008.
[125] Bastian Engeser. A novel surface trapping apparatus for ultracold cesium atoms: and theinvestigation of an Efimov resonance. na, 2006.
[126] Hamamatsu Photonics K.K. Photomultiplier tubes basics and applications. download fromvendor site, 2007. 2007.
[127] HJ Williams, S Truppe, M Hambach, L Caldwell, NJ Fitch, EA Hinds, BE Sauer, and
MR Tarbutt. Characteristics of a magneto-optical trap of molecules. New Journal of Physics,
19(11):113035, 2017.
[128] JA Devlin and MR Tarbutt. Three-dimensional doppler, polarization-gradient, and magnetooptical forces for atoms and molecules with dark states.
New Journal of Physics,
18(12):123017, 2016.
[129] MR Tarbutt. Magneto-optical trapping forces for atoms and molecules with complex levelstructures. New Journal of Physics, 17(1):015007, 2015.
[130] K Liu and JM Parson. Laser fluorescence detection of nascent product state distributions inreactions of sc and y with o2, no, and so2. The Journal of Chemical Physics, 67(5):1814–1828,
1977.

116
[131] DJ McCarron, EB Norrgard, MH Steinecker, and D DeMille. Improved magneto–opticaltrapping of a diatomic molecule. New Journal of Physics, 17(3):035014, 2015.
[132] Wolfgang Petrich, Michael H Anderson, Jason R Ensher, and Eric A Cornell. Behavior ofatoms in a compressed magneto-optical trap. JOSA B, 11(8):1332–1335, 1994.
[133] Paul D Lett, Richard N Watts, Christoph I Westbrook, William D Phillips, Phillip L Gould,
and Harold J Metcalf. Observation of atoms laser cooled below the doppler limit. Physicalreview letters, 61(2):169, 1988.
[134] Jean Dalibard and Claude Cohen-Tannoudji. Laser cooling below the doppler limit by polarization gradients: simple theoretical models. JOSA B, 6(11):2023–2045, 1989.
[135] J Dalibard, C Salomon, A Aspect, E Arimondo, R Kaiser, N Vansteenkiste, and C CohenTannoudji. New schemes in laser cooling. Atomic Physics XI, page 199, 1989.
[136] Matthias Weidemüller, Tilman Esslinger, Maxim A Ol’shanii, Andreas Hemmerich, andTheodor W Hänsch. A novel scheme for efficient cooling below the photon recoil limit.
EPL (Europhysics Letters), 27(2):109, 1994.
[137] Andrew T Grier, Igor Ferrier-Barbut, Benno S Rem, Marion Delehaye, Lev Khaykovich,Frédéric Chevy, and Christophe Salomon. λ-enhanced sub-doppler cooling of lithium atoms
in d 1 gray molasses. Physical Review A, 87(6):063411, 2013.
[138] JA Devlin and MR Tarbutt. Laser cooling and magneto-optical trapping of molecules analyzed
using optical bloch equations and the fokker-planck-kramers equation. Physical Review A,
98(6):063415, 2018.
[139] J Lim, JR Almond, MA Trigatzis, JA Devlin, NJ Fitch, BE Sauer, MR Tarbutt, andEA Hinds. Laser cooled ybf molecules for measuring the electron’s electric dipole moment.
Physical review letters, 120(12):123201, 2018.
[140] Ivan Kozyryev, Louis Baum, Kyle Matsuda, Benjamin L Augenbraun, Loic Anderegg, Alexander P Sedlack, and John M Doyle. Sisyphus laser cooling of a polyatomic molecule. Physicalreview letters, 118(17):173201, 2017.
[141] B Sheehy, SQ Shang, P Van Der Straten, S Hatamian, and H Metcalf. Magnetic-field-induced
laser cooling below the doppler limit. Physical review letters, 64(8):858, 1990.
[142] Olivier Emile, Robin Kaiser, Christoph Gerz, Hartmut Wallis, Alain Aspect, and Claude
Cohen-Tannoudji. Magnetically assisted sisyphus effect. Journal de Physique II, 3(12):1709–
1733, 1993.
[143] Edward S Shuman, John F Barry, and David DeMille. Laser cooling of a diatomic molecule.
Nature, 467(7317):820–823, 2010.
[144] Matthew H Steinecker, Daniel J McCarron, Yuqi Zhu, and David DeMille. Improved radiofrequency magneto-optical trap of srf molecules. ChemPhysChem, 17(22):3664–3669, 2016.
[145] LR Liu, JD Hood, Yichao Yu, JT Zhang, NR Hutzler, Till Rosenband, and K-K Ni. Building
one molecule from a reservoir of two atoms. Science, 360(6391):900–903, 2018.

117[146] David Reens, Hao Wu, Tim Langen, and Jun Ye. Controlling spin flips of molecules in anelectromagnetic trap. Physical Review A, 96(6):063420, 2017.
[147] Rudolf Grimm, Matthias Weidemüller, and Yurii B Ovchinnikov. Optical dipole traps forneutral atoms. In Advances in atomic, molecular, and optical physics, volume 42, pages
95–170. Elsevier, 2000.
[148] Andrey Kobyakov, Michael Sauer, and Dipak Chowdhury. Stimulated brillouin scattering in
optical fibers. Advances in optics and photonics, 2(1):1–59, 2010.
[149] Richard G Smith. Optical power handling capacity of low loss optical fibers as determinedby stimulated raman and brillouin scattering. Applied optics, 11(11):2489–2494, 1972.
[150] Nelson Darkwah Oppong. TOWARDS A DEGENERATE FERMI GAS OF STRONTIUM-IN
AD OPTICAL LATTICE. PhD thesis, ETH Zurich, Switzerland.
[151] A Mazurenko, Sebastian Blatt, F Huber, MF Parsons, CS Chiu, G Ji, D Greif, and Markus
Greiner. Implementation of a stable, high-power optical lattice for quantum gas microscopy.
Review of Scientific Instruments, 90(3):033101, 2019.
[152] TA Savard, KM O’hara, and JE Thomas. Laser-noise-induced heating in far-off resonanceoptical traps. Physical Review A, 56(2):R1095, 1997.
[153] G Janik, W Nagourney, and H Dehmelt. Doppler-free optical spectroscopy on the ba+ monoion oscillator. JOSA B, 2(8):1251–1257, 1985.
[154] Sara Rosi, Alessia Burchianti, Stefano Conclave, Devang S Naik, Giacomo Roati, Chiara
Fort, and Francesco Minardi. λ-enhanced grey molasses on the d 2 transition of rubidium-87
atoms. Scientific reports, 8(1):1–9, 2018.
[155] D Rio Fernandes, Franz Sievers, Norman Kretzschmar, Saijun Wu, Christophe Salomon, andFrédéric Chevy. Sub-doppler laser cooling of fermionic 40k atoms in three-dimensional grayoptical molasses. EPL (Europhysics Letters), 100(6):63001, 2012.
[156] A Kastberg, William D Phillips, SL Rolston, RJC Spreeuw, and PS Jessen. Adiabatic coolingof cesium to 700 nk in an optical lattice. Physical review letters, 74(9):1542, 1995.
[157] Jian Chen, J Greg Story, Jeffrey J Tollett, and Randall G Hulet. Adiabatic cooling of atoms
by an intense standing wave. Physical review letters, 69(9):1344, 1992.
[158] SR Wilkinson, CF Bharucha, KW Madison, Qian Niu, and MG Raizen. Observation of
atomic wannier-stark ladders in an accelerating optical potential. Physical review letters,
76(24):4512, 1996.
[159] Coherent. Mephisto lasers – ultra-low noise and narrow linewidth. download from vendor
site, 2019. 2019.
[160] MA Ali, J Moghaddasi, and SA Ahmed. Temperature effects in rhodamine b dyes andimprovement in cw dye laser performance. Laser Chemistry, 11(1):31–38, 1991.
[161] John P Bartolotta and Murray J Holland. Sawtooth-wave adiabatic passage in a magnetooptical trap. Physical Review A, 101(5):053434, 2020.

118[162] Alejandra L Collopy, Matthew T Hummon, Mark Yeo, Bo Yan, and Jun Ye. Prospects for anarrow line mot in yo. New Journal of Physics, 17(5):055008, 2015.

Appendix A

YO Molecular Structures and Spectroscopy

In this appendix, we show all the spectroscopies we’ve taken in the past few years. We
modulated the detection beam frequency at kHz and collect the fluorescence by photon multipliertube(PMT). The detection beam is perpendicular to the molecular beam to reduce the Doppler
shift. The YO energy level have been shown in Figure 2.3 and the relevant constants have beendetailed in [69, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88].

A.1

X 2 Σ+ → A2 Π1/2 Transition(v=0)

0

0

0

Figure A.1: X 2 Σ+ N=0(+) G=F=0→ A2 Π1/2 J =1/2(-) F =0,1 spectroscopy. F =0 and 1 arewithin the linewidth.
X 2 Σ+ → A2 Π1/2 is the main cycling transition for slowing, trapping and cooling. We choose0

X 2 Σ+ N=1(-)→ A2 Π1/2 J =1/2(+) as our main cycling transition to prevent the rotational leak0

age [54]. X 2 Σ+ N=2(+)→ A2 Π1/2 J =3/2(-) is chosen to decouple N=2 from cycling transition.

120

0

0

Figure A.2: X 2 Σ+ N=1(-)→ A2 Π1/2 J =1/2(+) spectroscopy. (a). G=0→ F =0,1. (b). G=1→00
F =0,1. The left peak is G=1, F=0→ F =0,1

0

0Figure A.3: X 2 Σ+ N=1(-)→ A2 Π1/2 J =3/2(+) spectroscopy. G=0→ F =1,2

0

0Figure A.4: X 2 Σ+ N=2(+)→ A2 Π1/2 J =3/2(-) spectroscopy. G=0→ F =1,2

121

0

0

Figure A.5: X 2 Σ+ N=2(+)→ A2 Π1/2 J =5/2(-) spectroscopy. G=0→ F =2,3

0

0Figure A.6: X 2 Σ+ N=3(-)→ A2 Π1/2 J =5/2(+) spectroscopy. G=0→ F =2,3

122

A.2

0

X 2 Σ+ → A 2 ∆3/2 Transition
0

Based on the initial calculation [78] and proposal [162], the A 2 ∆3/2 has a narrow linewidth0which can be used for further cooling. Therefore, we first determined the linewidth of A 2 ∆3/2 bymeasuring the decay of the light induced fluorescence after switching off the laser light. We assume
the fluorescence to decay exponentially and extract the lifetime to be 23(2) µs. The linewidthis 2π×6.9(6) kHz, much narrower than the previous calculation(2π×160 kHz). Our measurement
matches the most recent calculation [88]. This narrow linewidth can be used for narrowline coolingand SWAP cooling [111, 112, 161].

00Figure A.7: A 2 ∆3/2 J = 3/2(−) lifetime. The decay lifetime from the exponential fit is 23(2) µs.

123

0

0

0

Figure A.8: X 2 Σ+ N = 0(+) → A 2 ∆3/2 J = 3/2(−) spectroscopy. (a). N=G=F=0→ F =1. (b).
0
N=0 G=F=1→ F =2.

Appendix B

Dye Lasers - How to Make it Happy

B.1

Why Dye Laser
Our main cooling transition X 2 Σ+ → A2 Π1/2 is 614 nm. There is not any high power laser

diode or amplifier system available at 614 nm. To generate high power at 614 nm, people need toamplify at 1228 nm and then double the frequency to get 614 nm. We have four different systems
in our lab and each generates 1 watts of 614 nm laser, they are Raman fiber amplifier, solid statelaser employing second harmonic generation, dye laser and SFG laser. The first three lasers arevery expensive and each of them takes more than $150k. The last SFG laser was purchased very
recently from Precilasers at a much lower price. Currently we’re testing its performance.
Raman fiber amplifier(MPB-Communications) takes a 20 mW 1228 nm seed from a homebuilt ECDL, then amplify to ∼10 W in a P2 O5 doped fiber pumped by a ytterbium fiber laser.
Then, the 1228 nm light is frequency doubled to generate 1 W of 614 nm light. The entire system
is fiber coupled and very robust in the experiment. This system generates the beams for slowing.
Another way is to amplify the 1228 nm light with tapered amplifier and then get 1228 nm
light frequency doubled by a nonlinear crystal in a cavity. We bought an entire setup including seed,tapered amplifier, doubling crystal from Toptica photonics and it worked robustly. Currently it
provides the beams for trapping and cooling. However, the tuning range of these lasers are typicallylimited to hundreds of GHz, which is too narrow to perform any broad tuning for spectroscopy
measurement. A dye laser normally has a much broader tuning range than these two laser systems.

125

B.2

Sirah Matisse DR 2 Laser
A dye laser uses an organic dye as the lasing medium. Compared to other lasers, dye laser

offers exceptional tuning wavelength that is typically tens or even hundreds of nanometers. We
use Rhodamine B mixed in ethylene glycol with a concentration of 0.57 g/L. It takes at least one
hour for the dye to fully dissolve in the solvent. The dye is cooled to ∼15◦ C to lower the pumping
threshold and increase the output power [160]. The cold temperature also changes the viscosity ofthe ethylene glycol and extend the shelf life. The dye runs through a slit nozzle at a pressure close
to 15 bar, beyond which the turbulence introduces bubbles into the dye making the laser unstable.

Figure B.1: A simplified optical layout of Sirah Dye laser. PM: Pump mirror(reflect and focus
pump to dye jet). DJ: Thin slit dye jet. FM: Folding mirror(Bow-tie cavity mirror). SR: Rhombus
crystal to displace the beam. TM: Tuning mirror(Big mirror used for slow feedback). Thin E: Thin
etalon(A bandpass filter. A step motor controls the horizontal tilt angle of the etalon that control
the transmission wavelength. Piezo E: Thick etalon(Thick etalon selects a single longitudinal mode
from the spectral range that is determined by the configuration of output coupler, birefringencefilter, and thin etalon. It’s locked to the intensity maximum). TGG: Terbium-Gallium-Garnet
plate(Act as Faraday-rotator under a strong magnetic field. The combination of M2 and the
TGG plate forms an optical diode supporting lasing in counter clockwise direction). M3: A small
mirror used for fast feedback. M2: Out of plane mirror(This mirror transmits some light forlocking the thick etalon and also forms an optical diode together with TGG plates). OC: Optical
coupler(Transmits part of the beam and reflects the rest back into the ring cavity. The beampolarization is horizontal). BiFi: Birefringence filter(Coarse band pass filter). Image credit: Sirah.

The simplified layout of all optics is shown in Figure C.1. The laser is pumped by a 7 W of
532 nm light from a Coherent Verdi V-10, shown in green. The pump needs to be aligned parallelto the ring cavity and the polarization should be linear to match the lasing cavity. The ring cavity
enables the lasing and the single frequency operation is achieved together with filters. The gainof Rhodamine B in ethylene glycol is tens of nm wide. The mirror sets and coating first limit the

126lasing range to ∼60 THz. Then, the birefringence filters narrow the range down to ∼200 GHz. The
free spectral range(FSR) of thin etalon, thick etalon and cavity are 250 GHz, 20 GHz and 160 MHz
respectively. The single mode operation is maintained by locking the thick etalon to the maximum
transmission of the longitudinal cavity mode. An optical diode is used to avoid lasing in bothclockwise and counter clockwise directions. The beam propagating in clockwise direction suffers
more loss at each brewster surfaces. In addition, the thick etalon is slightly tilted to suppress lasingin the clockwise direction. For normal operation, only M1(next to OC, not shown in the figure) andM3 should be tuned to optimize the laser output. If the ring cavity is pretty tilted, TM, M1 andM3 should be walked to make the cavity parallel to the baseplate. This is achieved by putting caps
on FM1, FM2 and then adjust TM, M1, M3 to overlap the fluorescence spots propagating in both
directions. After the rough alignment, we should remove the caps and adjust M1(or M3) to see thelasing behaviour. If the cavity is still tilted with respect to the baseplate, the thick etalon requires
an out of cavity alignment. The entire process is documented in the manual. It is worth mentioningthat although the ring cavity has an optical diode rejecting lasing in unwanted direction, an opticalisolator should still be installed outside the cavity to prevent any reflection from entering the cavity.
We observed that the reflection from the angled fiber tip affects the stability of the laser.

Appendix C

Magnetic CoilThe first generation of in-vacuum magnetic coil was described previously [114]. In the new
design, we made the following changes:(1) We increased the coil aperture by ∼30%. This allows a larger MOT beam for trapping
more molecules in our setup .
(2) To maintain similar Q factor and magnetic field gradient(∼10 gauss/(cm·A)), we increased
the number of turns to 12 on each coil.
(3) An extra layer of copper is placed on the edge of the board to provide a better thermal
conductance between boards.

Figure C.1: Calculated coil performances. Two pairs of coils are used(four coil total), coil pairs are
separated by ∼30 mm. The new coils provide better homogeneity based on the geometry.

128

129

130
The detailed drawings of new coil are shown above. There are two types of designs: innerand outter board. Care must be taken when assembling the coils. Two different pairs of coils are
first assembled together to form the half of the entire assembly. A metal wire is used to connect
the two board through the via. A hot plate is required for this process due to the high thermal
conductance of the board. In order to avoid the unwanted shorting and arcing, a Kapton film issandwiched between the coils. At the edge of the coils, an indium foil is sandwiched between coils
to increase the thermal conductance at the joint. To mount the coil inside the chamber, we firstmachined the copper into a horseshoe shape. Each half of the coil assembly is mounted on thishorseshoe copper and then attached to the copper cold fingers, as shown in Figure 5.2 (c). Thisconfiguration ensures the coil center is well overlapped with the center of the vacuum chamber. The
top and bottom coil pairs are then connected outside the vacuum chamber, allowing both series
and parallel connections. The only drawback of this configuration is the limited access due to thepresence of cold fingers and electric feedthroughs, leaving a CF 2.75” vacuum flange on each side.
This is undesired if a large pumping conductance or the collection efficiency is needed. Therefore,
we came up with the second mounting scheme where all coils are installed on the single side of theflange, as shown in Figure 5.2 (d). In this configuration, the bottom coils are still mounted on thehorseshoe copper but the top coils are supported by C-shape copper connectors. The C-shape isdesigned to leave the connectors away from the detection region. It is worth mentioning that thecenter of the current MOT coils is offsetted compared to the geometric center of the chamber. Thisis due to the mismeasurement of the copper finger length. Currently, we shift the center of the
MOT by providing imbalanced currents into the coils. This should be fixed in the future since an
imbalance field gradient would result in an asymmetric MOT shape.

Appendix D

Compression Timing Diagram

Figure D.1: Timing sequence for optimized compression of molecular clouds.

We repeat the GMC-MOT cycle three times after the initial 5 ms MOT hold pulse, as shownin Figure D.1. The GMC pulse is always set at 2 ms, and the MOT pulse follows 2 ms, 1 ms,
and 1 ms. The decreasing MOT pulse duration accounts for the shrinking cloud after previous
compression cycles. This timing sequence reduces the trapping volume by a factor of 10.

ProQuest Number: 28546441
INFORMATION TO ALL USERS
The quality and completeness of this reproduction is dependent on the quality
and completeness of the copy made available to ProQuest.

Distributed by ProQuest LLC ( 2021 ).
Copyright of the Dissertation is held by the Author unless otherwise noted.

This work may be used in accordance with the terms of the Creative Commons licenseor other rights statement, as indicated in the copyright statement or in the metadata
associated with this work. Unless otherwise specified in the copyright statement
or the metadata, all rights are reserved by the copyright holder.

This work is protected against unauthorized copying under Title 17,
United States Code and other applicable copyright laws.

Microform Edition where available © ProQuest LLC. No reproduction or digitizationof the Microform Edition is authorized without permission of ProQuest LLC.

ProQuest LLC
789 East Eisenhower Parkway
P.O. Box 1346
Ann Arbor, MI 48106 - 1346 USA