A Three-Dimensional MOT of YO Towards Narrow-Line
CoolingbyAlejandra L. Collopy
B.S., Stanford University, 2010
M.S., University of Colorado, 2012

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
2018This thesis entitled:
A Three-Dimensional MOT of YO Towards Narrow-Line Cooling
written by Alejandra L. Collopy
has been approved for the Department of Physics

Jun YeEric Cornell

Date

The final copy of this thesis has been examined by the signatories, and we find that both thecontent and the form meet acceptable presentation standards of scholarly work in the above
mentioned discipline.

iii
Collopy, Alejandra L. (Ph.D., Physics)
A Three-Dimensional MOT of YO Towards Narrow-Line Cooling
Thesis directed by Jun Ye

Laser cooling and magneto-optical trapping of neutral atoms has been a driving force inphysics over the last few decades by providing an efficient method to produce cold and dense samples
of cold atoms. Polar molecules which can have strong, long-range dipolar interactions and possess
more rich internal structure promise a wide range of new physics and chemistry studies if they canbe controlled efficiently. Until recently, the only way to achieve sub-milliKelvin level temperatures inmolecules was to associate two precooled atomic species, which while very effective, has a firm boundon the chemical diversity accessible. While laser cooling of molecules relies on fortuitous molecularproperties, it will significantly increase the choices of species available for molecular cooling.
In this thesis I present the improved optical deceleration of the molecule yttrium monoxide(YO) and the loading of molecules into a 3-D magneto-optical trap (MOT). By making an improved
choice of repumping scheme from our groups’ previous work, our photon scattering rate has been
increased. By also improving our buffer gas cell source, we produce a much larger flux (∼2000 times
higher) of slowed molecules at 5 m/s to reach the trapping region. I have designed and implemented
3-D MOT field coils operating at 5 MHz, and demonstrated a successful operation of a 3-D MOT.
This is the first 3-D laser trapping of an oxide and the first of a molecule with an electronic stateintermediate to the main cycling transition states.
I have also performed a study of the transition from the ground state to the intermediate
electronic state, which has a narrower linewidth of ∼150 kHz, in contrast to the main cyclingtransition’s linewidth of 5 MHz. This transition is well suited to second-stage narrow line coolingafter loading molecules with the main MOT transition, which will allow direct laser cooling of amolecule to the 10 uK regime.

Dedication

For my family: past, present, and future

v

Acknowledgements

Words could never be enough, but I’ll give it a try. So many different people have gotten me
to where I am today, and I am truly grateful. Without your help, guidance, and commiseration
graduate school would have been a very different experience, and the work described herein could
never have come to be.
Firstly, I’d like to thank my advisor, Jun Ye. You have always been the optimist giving usconfidence that someday we actually would succeed at trapping molecules, even when the path forward was murky. You always teach us so much, from how to be an effective scientific communicator
to giving your invaluable perspective on how to solve the many problems that crop up in day to
day scientific advances and setbacks. Thank you for your resolve and your patience.
I’ve had the great fortune to work with many wonderful labmates over the years. In particular,
I’d like to thank Matt Hummon for being an excellent teacher, from how to assemble vacuum
chambers to optical alignments. Mark Yeo inducted me into the land of the frequency comb andlaser locking, without which the experiment couldn’t continue to exist. Bo Yan was forever cheerfuland helping to fix the many broken pieces of equipment that would otherwise bring us to a halt.
Yewei Wu tackled the problem of learning how the entire system works, and succeeded with flying
colors. It is in his hands that I confidently leave the future of our experiment. Thank you so muchfor your enthusiasm and humor. In the last couple of years I’ve gotten to work with two great
postdocs, Shiqian Ding and Ian Finneran. They are both very capable and anxious to push on to
new experimental frontiers. I can’t wait to see where it takes them. Our sister experiment, OH,
has been manned with two graduate students during the majority of my time here, Dave Reens andvi
Hao Wu. It’s been amazing sharing a lab, ideas, and molecule angst with you guys.
There are many others in JILA with whom I’ve had great problem solving discussions, interesting physics ideas, and most importantly, laughs. They’ve provided such great advice and support(in no particular order): Ed Marti, Michelle Miller, Cory Goldsmith, Yomay Shyur, Craig Benko,
Brian Lester, Bryce Bjork, Shimon Kolkowitz, Ben Spaun, Will Cairncross, Cathy Klauss, Hans
Green, Corey Keasling, J.R. Raith, James Fung-A-Fat.
I’d like to thank my family, Aria, Pam, and Paul Collopy for always loving, supporting,and being there for me. You were the first to instill an excitement for science in me and I’m soglad. I’m also very thankful for my soon-to-be family, Tom, Sherry, and Alexander who have sooverwhelmingly welcomed me.
Finally, I’d like to thank my fiance Andrew for hanging in there through the frustrations
and late nights and being there for all the joys and excitments. I can’t wait for our future adventures.

Contents

Chapter
1 Overview

1

1.1

Why cold molecules? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

1.2

Cooling process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.3

Overview of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42 Level structure and optical cycling transitions in YO

5

2.1

Level structure of YO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

2.2

Optical Cycling Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.3

Optical repumping of N"=2, v"=0 . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.4

N"=3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.5

Is a v"=3 repump necessary? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.6

Microwave mixing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.7

Decoupling the N"=1,v"=1 manifold . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

2.8

N"=0 optical repumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

3 Experimental apparatus

15

3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

3.2

Laser systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

3.3

Microwaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

3.4

In-vacuum shutter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

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3.5

Buffer gas cell overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

3.6

Detection systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

3.7

Light scatter reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

3.8

Coils and beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

4 (Mis)Adventures in buffer gas cell design and ablation chemistry

37

4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

4.2

Magic dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

4.3

Cell modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

4.4

Oxidizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

4.5

Yttrium metal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

4.6

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

5 Slowing molecules to trappable velocities

52

5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

5.2

Large cell modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

5.3

White light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

5.4

Optimizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

5.5

Helium flow rate dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

5.6

Optical repumping of N"=2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

5.7

Detection efficiency estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

5.8

Total gains realized . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

6 3D MOT coil design

63

6.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

6.2

Change to parallel configuration of the MOT coils . . . . . . . . . . . . . . . . . . . .

65

6.3

Impedance matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

6.4

Magnetic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

ix
6.5

Coil characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

6.6

Blackening methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

6.7

Heat link and mounting construction . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

6.8

Pound locking to resonance of coils . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

7 A three-dimensional molecular MOT of YO

79

7.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

7.2

Fundamentals of molecular MOTing . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

7.3

1D MOT reconfirmation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

7.4

3D MOT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

7.5

Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

7.6

Intensity dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

7.7

Overslowing for loading the MOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

8 690 nm Narrow-line transition: prospects for secondary cooling

97

8.1

Spectroscopy of the A02 ∆3/2 state . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

8.2

Mixing of the A02 ∆3/2 and A2 Π states . . . . . . . . . . . . . . . . . . . . . . . . . .

98

8.3

Narrow-line cooling on the X 2 Σ to A02 ∆3/2 transition . . . . . . . . . . . . . . . . . 100

8.4

Narrow-line MOT simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

8.5

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Appendix
A MOT coil layout and assembly

106

A.1 Coil design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
A.2 Coil assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
B Frequency calculation and locking for slowing and trapping

109

B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

x
B.2 Comb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
B.3 Raman Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
B.4 Toptica Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
B.5 v=1 Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
B.6 v=2 Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
C PMT characterization and transimpedance amplifier

114

D Data Acquisition

119

D.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
D.2 Acquisition devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
D.2.1 CCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
D.2.2 PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
D.2.3 Multi-channel scaler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
D.2.4 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
D.3 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
D.3.1 Digital Delay Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
D.3.2 PulseBlaster Timing Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
D.3.3 PulseBlaster breakout board . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
D.3.4 Function generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
D.3.5 Arduino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
D.3.6 Altbins box . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
D.4 Data acquisition modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

D.4.1 MCS acquisition modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
D.4.2 PulseBlaster acquisition modes . . . . . . . . . . . . . . . . . . . . . . . . . . 126
E Replacing Y2 O3 targets in the cell129

E.1 Epoxying targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

xi
E.2 Disassembling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
E.3 Reassembling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

Bibliography

132

xii

TablesTable
7.1

Fitted MOT lifetime for different MOT beam main cooling laser powers per beam . .

94

8.1

Identification of X 2 Σ to A02 ∆3/2 transitions . . . . . . . . . . . . . . . . . . . . . . .

97

8.2

Vibrational branching rates for various transitions of interest. . . . . . . . . . . . . .

99

Figures

Figure1.1

Cooling process schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

2.1

Relevant level structure of the YO molecule . . . . . . . . . . . . . . . . . . . . . . .

7

2.2

Choice of cycling transition for repumping N ”=2 either optically or with microwaves
at 46 GHz. Optical repumping uses the dashed-dotted orange arrow transition, while
microwave mixing uses the dashed-dotted green arrrows transitions. We only apply
one or the other, not both. We anticipate the largest unplugged leak at this point is
into N ”=0 and 2 of the v”=1 state via the A02 ∆3/2 state. . . . . . . . . . . . . . . .

2.3

10

(a)Proposed repumping scheme which decouples v"=1 from the main cycling transition, allowing for a maximum photon scattering rate of Γ/4. (b) The relevant
rotational and parity splittings in the A2 Π1/2 state. . . . . . . . . . . . . . . . . . . .

2.4

13

By applying an electric field to mix the parity levels in the A02 ∆3/2 state and addressing the 690 nm X 2 Σ to A02 ∆3/2 transition, we can pump molecules from the N ”=0level and allow them to rejoin the main cycling transition. This adaption would not
require any microwave coupling of states to provide closure. . . . . . . . . . . . . .

14

xiv
3.1

Schematic of the experimental apparatus. Molecules are produced at left via ablationof a precursor target inside the buffer gas cell. They propagate to the right whileinteracting with a counterpropagating slowing beam, until they reach the trapping
region. The trapping region contains the coils, three sets of counterpropagating MOT
beams, and can be imaged from either side by the CCD or PMT. . . . . . . . . . . .

3.2

16

Simulation of microwave intensity for 50 mW input power at horns in MOT region(circular region .38 meters along axis) for 23 GHz (upper) and 46 GHz (lower) microwaves. Color scale has units of mW/cm2 . Black rectangles indicate the volume
witin the hollow conductive cylinder of the Conflat nipples of the chamber. . . . . . .

3.3Electronics schematic for microwave system. This setup allows mixing of v”=0 and
1, N ”=0,1,2 in a variety of arrangements. . . . . . . . . . . . . . . . . . . . . . . . .

3.4

21

23

A schematic of our cryostat as viewed from above. Different colors indicate temperature of the constituent parts: all external vacuum/room boundaries are at room
temperature (purple), while a set of radiation shields are held at 30 Kelvin (blue)
and the cell itself along with the charcoal cryosorb are anchored to the 4 Kelvinstage(green). Helium is precooled to 4 K before entering the cell by going through alength off copper tubing soldered to a heat sink that is anchored to the 4 K stage.
YO is produced via ablation of a Y2 O3 ceramic target with a 532 nm 8 mJ pulse.
Rastering the ablation beam allows efficient use of the whole surface area of the target. 26

3.5

Image of cryostat chamber and cell from the front with the front copper radiation
shields removed. The helium precooling bobbin is visible in the upper left. On theleft side of the cell the brass ablation window mount is visible. . . . . . . . . . . . . .

3.6

28

Peak YO molecule production for different temperatures and flow rates . Temperature
variation was induced by shutting off the pulse tube while still producing molecules.

29

xv
3.7

Image of ablation window after having been in use for ∼2 weeks for helium flow rates
around 1 sccm. The most transparent locations suffer ∼25 percent attenuation, withdarker areas being even higher. This results in a reduction of YO molecules produced
over time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.8

30

PMT and CCD Imaging systems. Blue lenses are 2 inch diameter 150 mm focal length
lenses, while red are 1 inch diameter 75 mm lenses. The orange box indicates a color
filter used to remove all ∼650 nm scattered light from our vibrational repump lasers.
There is an image plane between the lens sets where the iris is placed for spatial
filtering. All lenses are installed outside the vacuum chamber. The achromatic lenspart numbers are Newport PAC086AR.14 for the two inch lenses and PAC046AR.14
for the 1 inch lenses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.9

32

CCD alignment confirmation: by placing a notched threaded rod in the MOT region
and imaging it with the CCD, we can confirm the CCD is imaging the desired region

32

3.10 CCD magnification calibration: the cross sectional average counts vs pixel value along
the edge of the 8-32 screw indicates the magnification of our imaging system. Thislabel refers to 2 ×2 binned pixels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

3.11 Imaging the unslowed molecule packet from 5-15 ms after ablation fire. Color axis indicates average CCD counts per 6×6 binned pixel, with 1 mm×1 mm square smoothing filter. (a) The vertical (transverse) MOT beam. (b)The NE/SW beam. (c)The
NW/SE beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

3.12 Scheme for combining v"=0,1, and 2 components for both MOT and slowing beams.

35

4.1

Left: Buffer gas cell well-coated with Y2 O3 nanopowder. Right: Cell with too much
nanopowder coating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2

38

Comparing the peak molecule number produced vs flow rate for the unpowdered andpowdered cell shows that the powder improves molecule number as well as allowing
operation at lower helium flow rates. . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

xvi
4.3

For a given flow rate, the YO produced is faster for the powdered cell than theunpowdered cell. However, the velocity of the powdered cell at low flow rates iscommensurate with the velocity of the unpowdered cell at higher flow rates. . . . . .

4.4

40

Velocity distribution for molecules produced from the old two-stage cell (left) andthe single stage cell (right). The two-stage cell data was taken at a helium flow of
5.5 sccm, while the single stage data was with a helium flow of 3 sccm. Velocity
sensitive detection is performed via LIF from a low-power probe beam at 45 degrees
with respect to the molecular beam axis with detuning chosen to detect a specificvelocity class.

4.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

Comparison of different YAG laser repetition rates. The signal detected is LIF by
unslowed molecules transiting the MOT region. The detection beam is 10 mW andorthogonal to the molecular trajectory with zero detuning. . . . . . . . . . . . . . . .

4.6Peak molecule signal (top) or peak time of arrival (bottom) for different flow rates
with the smaller bore (22 mm, blue trace) or larger bore (27 mm, red trace) cell. . .

4.7

43

Peak molecule signal (top) or peak time of arrival (bottom) for different flow rates
with a 2.1 mm front aperture (blue) or 3.1 mm aperture (red).

4.8

42

. . . . . . . . . . . .

44Comparison of behavior with same attempted MOT and slowing sequence with andwithout the diffuser installed in the cell for 0.5 and 1.5 sccm. On the right is a pictureof the diffuser plate which is placed between the He inlet and the rest of the buffer
gas cell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.9

45

Resulting number and velocity distributions of YO produced with 10 sccm of helium
buffer gas and varying levels of oxygen gas flowed into the cell. Counts are averagecounts over a 10 ms window in which the vast majority of molecules reached thedetection region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

xvii
4.10 Resulting number and velocity distributions of YO produced with 10 sccm of helium
buffer gas and varying flow levels of a 94% oxygen and 6% ozone gas mixture flowed
into the cell. Counts are average counts over a 10 ms window in which the vast
majority of molecules reached the detection region. . . . . . . . . . . . . . . . . . . .

47

4.11 Dependence on ablation lens position for Y metal and Y2 O3 targets. . . . . . . . . .

48

4.12 Comparison of Y metal + O2 with Y2 O3 ablation. . . . . . . . . . . . . . . . . . . .

49

4.13 Peak velocity of YO beam vs ablation lens position.

50

5.1

. . . . . . . . . . . . . . . . . .

Dependence on helium buffer gas flow rate of peak YO velocity produced from single
and two stage cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2

Molecule LIF during and after the slowing sequence (slowing ends at 21.5 ms) for
different repetition rates of the ablation laser. . . . . . . . . . . . . . . . . . . . . . .

5.3

53

54

By varying the assumed deceleration for slowing sequences designed to slow moleculesfrom 110 to 30 m/s (lasers chirped from resonance frequencies of 100 to 40 m/s) we
can determine our actual deceleration rate. These sequences used microwave remixing
of N 00 =2 levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.4

56

Average counts/second over a 12 ms time window occuring after slowing for slowing
sequences to 35 or 55 m/s (vs unslowed) for different flow rates (purple: 0.5 sccm,
green: 1.0 sccm, and orange: 1.5 sccm). These data were taken before the implementation of the in vacuum shutter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.5

57

Comparison of the effect of N ”=2 optical or microwave repumping in slowing on the
production of slowed molecules. The same length of vacuum chamber and appropriately optimized frequency chirp rates of the slowing lasers were used. . . . . . . . . .

5.6

59

Different chirp parameters yield different velocities of slowed molecules. The verticalaxis is the average count rate over a 17 ms window ending after slowing detected witha low power Doppler sensitive detection beam. These slowing sequences all utilized
optical repumping of N 00 =2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

xviii
6.1

The AC magnetic-field producing coils that provide the trapping gradients for our
MOT. The blackened copper C-clamps on the left provide the heat dissipation andstructural support for the bottom boards. Each board has coil traces on each side,
allowing for 4×7 windings on each half of the coils. The white blocks on the top right
are the high Q capacitors that tune the frequency of the resonant circuit. . . . . . . .

64

6.2

Series MOT coil configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

6.3

Parallel MOT coil configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

6.4

Low pass(a) and high pass (b) L-network configurations. . . . . . . . . . . . . . . . .

68

6.5

Π (a) and T (b) matching networks. . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

6.6

Predicted fields (green) and gradients (red) in the axial (left) and radial (right) dimenstions. Fields and gradients are calculated for 1 Amp drive through each coil andscale up linearly with amperage.

6.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71(a) Sqrt(ratio of power picked up to drive power) vs position in the axial direction. A
quadrupole field should show two linear lines with a cusp at the magnetic field zero.
(b) The white horizontal line indicates the expected magnetic field zero location inthis dimension with the magnetic pickup coil at the measured zero. The doubleheaded arrow indicates the direction of the motion of the micrometer. . . . . . . . .

6.8

72

(a) Sqrt(ratio of power picked up to drive power) vs position in the radial direction
along the molecule propagation direction. A quadrupole field should show two linear
lines with a cusp at the magnetic field zero. (b) The white horizontal line indicatesthe expected magnetic field zero location in this dimension with the magnetic pickup
coil at the measured zero. The double-headed arrow indicates the direction of the
motion of the micrometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

xix
6.9

(a) Sqrt(ratio of power picked up to drive power) vs position in the radial direction
orthogonal to the molecule propagation direction. A quadrupole field should show
two linear lines with a cusp at the magnetic field zero. (b) The white horizontal
line indicates the expected magnetic field zero location in this dimension with themagnetic pickup coil at the measured zero. The double-headed arrow indicates the
direction of the motion of the micrometer. . . . . . . . . . . . . . . . . . . . . . . . .

74

6.10 Copper heatlink and coil mounts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

6.11 Schematic diagram of MOT coil frequency lock. We maintain the drive of our coilson resonance by using a Pound lock. Sidebands to the drive are applied to the coil
1 MHz away, and the signal reflected from the coil is demodulated to DC, giving anerror signal we can feed into the loop filter. . . . . . . . . . . . . . . . . . . . . . . .

77

6.12 Frequency scanning MOT Pound lock error signal. . . . . . . . . . . . . . . . . . . .

78

7.1

Fundamentals of MOT operation: by driving with the correct polarization of lighton a transition with a differential magnetic moment between the lower and excitedstates, a magnetic field gradient in combination with red-detuned (δ) laser beams canprovide a restoring force to the magnetic field zero of the trap. Because the magnetic
fields produced by two anti-Helmholtz coils are a spherical quadrupole, the helicityof the axial laser beams must be the opposite of that of the radial laser beams. . . .

7.2

MOT types are described based on whether the trapping transition is from a lower
F 00 to a higher F 0 (type I, left) or a higher F 00 to a lower F 0 (type II, right). . . . . .

7.3

81

Phase for the Type II MOT operation refers to the delay between the polarization
switching of the MOT beams and the magnetic field oscillation of the MOT coils. . .

7.4

80

82

Differential signal (in phase minus 180 degrees out of phase) peak 1D MOT signal.
Horizontal axis is the DDS supplied offset phase between the MOT coil drive and the
Pockels cell drive. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

xx
7.5

Differential (in phase minus out of phase) signal of 1D MOT operation on unslowed
beam, for red detuning and blue detuning of all hyperfine components by 5 MHz. . .

84

7.6

timing diagram used for loading MOT . . . . . . . . . . . . . . . . . . . . . . . . . .

85

7.7

Differential (in phase minus out of phase) detection of MOT loaded at 20 G/cm RMS
magnetic field gradient via PMT (left ) or CCD (right). The CCD is exposed from30 to 50 ms after ablation fire, and processed with a Gaussian smoothing function
with sigma = 1 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.8

Differential (in phase-out of phase) PMT trace of MOT signal when using N 00 =3
optical repump in slowing (orange trace) and MOT or when not (green trace). . . . .

7.9

85

87

Dependence on the main cooling-laser components’ detuning for the MOT operatingwith 20 G/cm field gradient. Maximal loading is found at 9 MHz red detuning of all
hyperfine components in the laser addressing the v”=0, N”=1 level. . . . . . . . . . .

88

7.10 Differential LIF of MOT signal using the same slowing sequence but with varying
magnetic field gradients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

7.11 Differential LIF of MOT signal using the same slowing sequence (timing, detuningof slowing beams) and same mot beam detuning for each but with varying magnetic
field gradients. Images are smoothed with a gaussian filter with sigma = 1 mm. Color
scales are the same between images, with units of photon counts registered by the
CCD. Each image represents 80 experimental cycles of averaging, 40 at the correct
phase and 40 out of phase which are then subtracted. The vertical axis is the axial
direction of the trap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

7.12 Fitted gaussian standard deviations vs applied magnetic field gradient in the MOT
for both radial (blue) and axial (red) dimensions. Error bars indicate 95 percent
confidence interval of fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

xxi
7.13 MOT temperature characterization: Imaging the MOT cloud after some period offree expansion (a) and then measuring the gaussian width of the cloud in the axial
direction of the molecular cloud after allowing some amount of time of free flight,
the temperature of the cloud can be extracted (b). The CCD exposure time is
2 ms for each image. Color scale (total counts registered per pixel on the CCD) of
the expanded clouds is scaled up by a factor of 2 for greater visibility. Error bars
represent 95 percent confidence interval of the gaussian fits. (c) Depicts the LIF
recorded by the PMT for the same scenarios in (a). . . . . . . . . . . . . . . . . . . .

92

7.14 Using different powers for the main cooling transition in the MOT beams changes thenumber of molecules loaded but also affects the lifetime of the MOT. Powers statedare powers per MOT beam for N 00 =1, v 00 =0 light. . . . . . . . . . . . . . . . . . . .

94

7.15 Different amounts of slowing time and their effect on the slowed molecule distribution.
The sequence used for 5 m/s slowing is typically 0 extra added time (green), while
we find maximal MOT loading for the +12 ms (orange) slowing sequence. . . . . . .

96

8.1

Level structure for the narrow-line MOT . . . . . . . . . . . . . . . . . . . . . . . . . 100

8.2

Narrow-line MOT simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

A.1 PADS design for MOT coil boards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
B.1 Optical setup for the Raman laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

B.2 Optical setup for the Toptica laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
B.3 Optical setup for v=1 repump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
B.4 Optical setup for v=2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
C.1 Circuit schematic for PMT transimpedance amplifier. . . . . . . . . . . . . . . . . . . 115
C.2 Photons counted vs MOT beam laser power for different transimpedance amplifier
gains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

xxii
C.3 Signal to noise ratio, for same acquisition time, for different amplifier gains vs laser
beam powers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
C.4 Log-log plot of signal/noise vs signal for different transimpedance amplifier gains.
All are well fit with y=.5x +b function, implying a square root dependence on signal/noise on signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
C.5 Counts registered by MCS vs discriminator level for various PMT voltages and transimpedance amplifier gains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
D.1 GUI for interfacing with the CCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
D.2 GUI for interfacing with the TDS7104 scope . . . . . . . . . . . . . . . . . . . . . . . 122
D.3 GUI for interfacing with the Tegam function generator . . . . . . . . . . . . . . . . . 124
D.4 GUI for interfacing with the PulseBlaster timing card

. . . . . . . . . . . . . . . . . 126

E.1 vacuum chamber disassembly for target removal . . . . . . . . . . . . . . . . . . . . . 130
E.2 vacuum chamber disassembly for target removal . . . . . . . . . . . . . . . . . . . . . 131
E.3 vacuum chamber disassembly for target removal . . . . . . . . . . . . . . . . . . . . . 131

Chapter 1

Overview

1.1

Why cold molecules?
Cooling of molecules has far-flung applications, from tests of fundamental symmetries [1, 2, 3],

study of long range anisotropic interactions [4], to cold chemistry [5, 6]. The more complex structureof molecules as compared to atoms, though it provides a rich field of study, also makes difficult thecooling methods readily available to atoms. Indirect methods have so far produced the coldest
molecules, via magneto-association and adiabatic transfer [7]. Unfortunately, the number of species
that can be produced in this way is limited, and so we must look to direct cooling methods to support
a wider range of molecular species. Cold molecular beams can be produced via supersonic expansion[8] or from a cryogenic buffer gas beam source [9]. Such beams can be decelerated with techniquessuch as Stark deceleration [10, 11], Zeeman deceleration [12], or via centrifugal deceleration [13].
From a low velocity beam, a two photon process has been used to directly load a magnetic trap
[14].
For a long time, it was thought that laser cooling of molecules was impractical due to the large
number of states and therefore lasers required to implement an optical cycling transition capableof many photon scatters. However, in 2004 it was proposed [15] that a large class of molecules has
sufficently diagonal Franck-Condon factors to be amenable to laser cooling. The identified molecules
were diatomic hydrides or halides. In 2008 the first concrete proposal was made for a class of cyclingtransitions that through angular selection rules, avoids all dark states for molecules, enabling quasiclosed cycling and so the scattering of many photons [16]. It was also noted that these laser coolable

2
molecules could include diatomic carbides, oxides, or sulfides, suggesting that the potential chemical
diversity for laser-cooled molecules is quite large. In the intervening time, optical cycling has been
demonstrated in a number of diatomic species, leading to the demonstration of laser cooling in the
SrF molecule[17], radiation pressure slowing in SrF [18], CaF [19], and YO molecules [20]. This laid
the foundation for the realization of magneto-optical trapping in two dimensions of YO in 2013 [21]and in three dimensions for SrF in 2014 [22], followed by CaF in 2017 [23, 24]. The last few years
have been truly exciting on the cold molecule frontier! For polyatomic molecules which are similar
enough in structure to the identified diatomics, quasi-cycling transitions can also be realized. In
this way one dimensional Sisyphus [25] cooling has been performed on the SrOH molecule (which isisoelectronic to SrF). Additionally, it has been proposed that the optical bichromatic force [26] orultrafast stimulated slowing [27] can be used for molecular beam deceleration and cooling [28]. The
lowest temperature realized with these direct cooling techniques is so far that of the magneto-opticaltrap (MOT) followed by a sub-Doppler cooling stage of a blue [29, 30] or gray [31] optical molasses
with temperatures reaching the ∼50 µK level.
I have had the great privilege of working on this experiment from near its inception. Bybuilding up a buffer gas source and lasers to address the first three vibrational levels in YO, wewere able to demonstrate transverse Doppler cooling of YO to ∼10 mK. By further implementing
a 2-D quadrupole field coil resonant at 2 MHz, we showed that the magneto-optical effect worked
with our cycling transition in YO, and further reduced the transverse temperature to the 2 mKlevel [21]. Logistically, some experimental aspects are simplified by working with a molecular beam,
but in order to move forward to 3-D trapping we needed to implement deceleration of the molecules
produced by our buffer gas cell. We utilized the same cycling transition that allows for laser coolingto optically decelerate the molecules from production speeds of ∼70 m/s to less than 10 m/s, using
a combination of frequency chirping of the laser beams and white-light sidebands on the slowing
light [20].
In this thesis I present the first three dimensional MOT for YO. This is the beginning of the
expansion beyond fluorides to the wide range of species that laser cooling of molecules promises to3open. By improving our group’s earlier slowing results [20], and guided by principles of our 2D MOT
implementation [21], we designed and implemented a slowing and trapping sequence that yields
approximately 1000 molecules in our trap. Looking to the future, while a short-lived excited stateis desirable for quickly slowing a molecular beam, a viable option to decrease the final temperatureof the MOT is to use a narrower linewidth transition [32, 33]. Having recently implemented a MOT
for YO on the broad main cooling transition, we also identify a transition in YO that is amenable
to use in narrow-line cooling [34]. We anticipate that this transition will enable narrow line coolingto the Doppler temperature TD = ~γ/2/kB ≈ 5 µK where ~ is the reduced Planck constant, γ is the
linewidth of the transition, and kB Boltzmann’s constant. Our proposed scheme will only require
the addition of one laser to the broad cooling setup of the YO molecule.

1.2

Cooling process
The process to take YO from initial production temperatures down to the µK scale involves

a number of steps, as depicted in Figure 1.1. The initial temperature of YO after ablation is high(a)ablation
laser

(b)

(c)

(d)

YO

~1000K

YO beam~3.5K

red MOT
beams<10 mK~10 μK

slowinglaser

Y 2O 3He(e)orange MOT
beams

<1K

T:

Figure 1.1: Cooling process schematic. After production via ablation (a), YO molecules thermalize
with helium at 3.5 K in a cryogenic buffer gas cell (b). Upon exiting, the beam has velocity∼120 m/s. Longitudinal slowing produces molecules <5 m/s (c), loadable into a MOT. The orange
MOT will produce cold molecules less than ∼10 mK (d). Narrow line cooling can then be performedon the red transition (e). Steps (a) through (d) have been implemented experimentally, with (e)being our next planned step forward

both rotationally and translationally, whereas any optical cycling scheme requires a large numberof molecules in a single state. To meet this requirement, we utilize a cryogenic buffer gas cell [21]to produce cold YO molecules. The buffer gas cell is anchored to a 3.5 K cold plate and helium gas

4
is constantly flowed in to maintain a high density (∼1016 /cm−3 ) of helium in the cell. The helium
collisions with the cell walls cool the helium, and YO collisions with the helium buffer gas thenrotationally, vibrationally, and translationally cool the YO molecules. The net result is a beam of
YO molecules with forward velocity distribution peaked at 120 m/s with a 40 m/s full width at
half maximum. Longitudinal slowing of the YO beam is accomplished [20] with a frequency chirped
slowing beam, resulting in a population of YO molecules with speeds under 10 m/s, sufficiently slow
to load into our MOT. In the future, we plan to perform secondary laser cooling with a narrow-line
MOT, analagous to the methods demonstrated for several atomic species [33, 35, 36, 37, 38, 39, 40].

1.3

Overview of thesis
In order to provide an understanding of the YO molecule and how we can scatter many

photons with it, I detail the level structure and several different repumping schemes in Chapter 2.
In Chapter 3 I explain the nuts and bolts of the experimental apparatus that we use to produce,
decelerate, trap, and image molecules, including the laser, microwave, photon collection, cryogenic,
and vacuum systems. We systematically studied several characteristics of our buffer gas cell, suchas geometry, nanopowder coatings, the addition of oxidizers, and the ablation of Y metal insteadof Y2 O3 . These studies are detailed in Chapter 4. In the intervening years since our last slowing
publication [20] we have achieved a number of improvements to the slowing efficacy of our system.
Detailed in Chapter 5, these improvements range from transitioning our cell and laser systems toaccomodate a single-stage buffer gas cell rather than a two-stage cell, to changing the repumping
scheme used to decelerate the molecules, to changing the repetition rate of the experiment. Chapter
6 explains the design considerations, construction, impedance matching, and characterization of theAC magnetic field coils that make up our trap. Results of loading molecules into our trap are detailedin Chapter 7, where I explain the sequence we use for trapping and perform characterizations of theloaded molecules. Finally, our future goals are described in Chapter 8, where I analyze a transition
and a repumping scheme that we will use to perform narrow-line cooling in YO.

Chapter 2

Level structure and optical cycling transitions in YO

2.1

Level structure of YO
Developing an understanding of the level structure of YO is necessary for any effort to slow ortrap the molecules. This structure determines the frequencies of the lasers we use to interact withthe molecules, as well as determining the ability to scatter many photons and so exert a reasonable
force. The molecule YO has three electronic states that are of primary concern to us: the X 2 Σground state, the A2 Π excited state, and the A02 ∆ intermediate state, as shown in Figure 2.1(a). For
describing the angular momentum coupling in these states we follow the notation used by Brown
and Carrington [41]. When discussing a specific value of angular momentum, the factor of ~ isomitted. For the states we consider in YO, we have electronic spin S = 1/2 and nuclear spin I=
1/2. Only the Y atom has nuclear spin; the oxygen atom’s nuclear spin is zero. Electron orbital
angular momentum is labeled L, while rotational and total angular momenta are labeled R and F
respectively. Energy eigenstates of the molecule are frequently superposition states of R, and so
we use intermediate angular momenta to describe the states: J = F − I, and N = J − S = R + L.
Parity of states is indicated by (+) or (-). As well as possessing an array of rotational levels, eachstate also has a ladder of vibrational levels labeled with quantum number v.
We begin by considering the electronic ground state X 2 Σ. Because L is 0, there is no spinorbit coupling, and so the state can be described by Hund’s case (bβS ). The effective Hamiltonian

6
for this case that describes the coupling of momenta in this state is:
Heff = γS · N + bI · S + cIz Sz(2.1)

where γ = −9.2 MHZ, b = −763 MHz, and c = −28 MHz, representing the spin-rotation, Fermi
contact, and electron-nuclear spin dipolar interaction respectively [42]. The strong Fermi contact
interaction couples the electron and nuclear spin to form intermediate angular momentum G = I+S.
The total angular momentum is then formed by the additional coupling of N through the spinrotation interaction yielding F = G + N. We also note for Σ states, orbital angular momentum L
is zero and so N = R. For N >0, levels can be expressed as a superposition of J levels J=N ± 1/2(J=1/2 for N =0). In this state, the rotational splittings are giving by B × N × (N + 1) withrotational constant B.
The excited A2 Π1/2 and A02 ∆3/2 states are well described by Hund’s case (a). The rotational
states are labeled by angular momenta J and F, though the hyperfine interaction in these states issmall and is not resolvable via optical transitions with the X 2 Σ state. The quantum number Ω isgiven by the projection of L + S onto the internuclear axis. For Π states, L=1, while for ∆ states
L=2. So, for the A2 Π states, Ω is 1/2 or 3/2, and for A02 ∆ states Ω is 3/2 or 5/2. The value of Ω isindicated by the subscript on the molecular term symbol, e.g. A02 ∆3/2 has Ω =3/2. Additionally,
the two senses of projections of L onto the internuclear axis give rise to a pair of states with opposite
parity for each J level, called lambda doubling. In the A2 Π1/2 state, the lambda doubling term, p,
is 4.5072 GHz, indicating a splitting of 4.5 GHz for the opposite parity levels in the J = 1/2 level[43]. In the A02 ∆3/2 state, the lambda doubling is expected to be small, and has so far not beenmeasured. These states have rotational splittings given by B × J × (J + 1). Throughout this thesis
single primes (’) denote quantum numbers belonging to an excited state, whereas double primes (")
denote ground state levels.
The X 2 Σ to A2 Π1/2 transition (v”=0 to v 0 =0) is at 614 nm, as depicted in Figure 2.1(a).
While A2 Π1/2 primarily decays back to X 2 Σ, it has a ∼3×10−4 chance of decaying to A02 ∆3/2 [20].
As will be discussed in more detail in chapter 8 while the A02 ∆3/2 to X 2 Σ transition is nominally7electric dipole forbidden, it does in fact occur due to mixing of the nearby A2 Π3/2 state with theA02 ∆3/2 state [44]. This narrower transition has a wavelength of 690 nm, and linewidth 2π×160 kHz[34].

A2Π1/2 v'=0

49
nm

4
48
e- λ=623 GHz

v"=2
v"=1

X2Σ+

N"=0

3e

G"=1 F"=1,2,3

G"=0 F"=1 760 MHz

N"=1

nm

v"=0

G"=0 F"=2 760 MHz

N"=2

λ=6

2
q=

X2Σ+

λ=614 nmN"=1(-)
N"=0(+)

0 74

q=.9924

μs
nm

0
69

-1 ≈1

γ

λ=

X2Σ+

v"=0

N"=2(+)

q=.0

A' Δ3/2

J'=3/2(-) F'=1,2γ-1=33nsλ=614 nm2

G=I+S F=G+N(c)

46 GHzv'=1-4A2Π1/2 J'=1/2(+) F'=0,1(b)

q=.984

A2Π3/2(a)G"=1 F"=0,1,2
G"=0 F"=0 760 MHz
G"=1 F"=1

Figure 2.1: Relevant level structure of the YO molecule. (a) Electronic structure and ground state
rotational structure. Solid lines indicate the broad (orange) and narrow (maroon) transitions thatwill be used to make MOTs in YO. (b) Vibrational structure and repumping scheme. Solid lines
indicate lasers for first stage cooling (orange) and vibrational repumps (red). Dashed lines showspontaneous decays and are labeled with Franck-Condon factors. (c) Ground state rotational andhyperfine structure. For each G level, F ranges from |G − N | to |G + N |.

2.2

Optical Cycling Transition
The transition we leverage as a cycling transition in YO is at 614 nm from X 2 Σ, N ”=1 to

A2 Π1/2 , J 0 =1/2, as shown in Figure 2.1(a). We have demonstrated optical cycling using this coolingtransition as a one and two dimensional MOT [21], and for molecular beam slowing [20]. Decays torotational levels other than N ”=1 are forbidden by parity and angular momentum selection rules.
We address vibrational branching by repumping the v”=1 level directly to the A2 Π1/2 , v 0 =0 level
using 648 nm light (Figure 2.1(b)). The v”=2 level is repumped using a two step process, firstexciting it to A2 Π1/2 , v 0 =1 at 649 nm, which predominantly decays to the v”=1 level, and thenallowing the v”=1 repump light to take the molecule back to the v”=0 level. Molecules that decay

8
to X 2 Σ via A02 ∆3/2 end in the N ”=0 or 2 levels because of parity and angular momentum selection
rules. To maintain cycling, we apply microwave mixing resonant with the N ”=0↔N ”=1 and the
N ”=1↔N ”=2 rotational transitions, depicted as gray arrows in Figure 2.1(c). In total, we estimatethat the setup yields a closed cycling transition up to the ∼ 10−6 level of enclosure, sufficient toslow and trap a subset of the molecules. Our largest unplugged leaks at this stage will likely be to
the v”=1, N ”=0,2 levels.
The G”=1: F ”=1,2 levels are subject to Zeeman splitting in an applied magnetic field, thus
allowing us to not only Doppler cool on the X 2 Σ state to A2 Π1/2 state transition, but to also
implement a MOT. For this transition, the greater multiplicity of states in the ground state meansthat coherent dark states can form [45], limiting the total number of photons which can be scattered.
In our setup, we avoid this issue by switching our laser polarization at a rate approximately equal
to the transition linewidth, eliminating long-lasting dark states. Type-II MOTs like ours, which
operate from F ” to F 0 = F ” − 1, tend to have weaker trapping forces and be larger than their typeI counterparts, which operate from F ” to F 0 = F ”+1. The final sizes tend to be on the order of 1 mm
[46]. We anticipate the final temperature of the orange MOT to be on the order of 500 µK [47, 24],even though the rapid polarization and magnetic field switching in our system should help to negate
the weakness of the type-II MOT [48] This is larger than the Doppler temperature TD = 110µK,
but so far type-II MOTs do not reach the Doppler limit [49, 22]. It has been theorized that the final
temperature of type-II MOTs is limited by competition between Doppler and sub-Dopper effects[50].
To achieve our goal of slowing and trapping a large number of YO molecules, we would liketo exert large slowing and trapping forces. This requires a laser cooling scheme that can rapidly
cycle photons in our molecule, and so we must pay careful attention to the photon scattering ratethat we can achieve. The maximum scattering rate that can be realized while exciting an opticaltransition is determined by the steady state population of the excited state divided by the total
number of states that are coupled (either optically or with microwaves, in our instantiation) to theexcited state. In a case where only one lower and one excited state are involved that have equal

9degeneracy, this reduces to Γ/2, where Γ is the natural linewidth of the transition. For the X 2 Σ state
to A2 Π1/2 state transition, Γ is equal to 2π×5 MHz. In YO, the excited state A2 Π1/2 , J’=1/2 (+)
has a degeneracy of 4 (F’=0 or 1). The ground states which can be optically connected to theexcited state are X 2 Σ v”=0, N ”=0,1, or 2 and v”=1, N ”=1, which have allowed values of F of
0,1|1,0,1,2|2,1,2,3|1,0,1,2, respectively, giving degeneracies of 4|12|20|12, using the same orderingof states. In all of our previous work[21, 20], all of these states were coupled to the excited state,indicating a maximum possible scattering rate of Γ×4/52, or Γ/13. Later in this chapter are detailed
a number of other possiblities for increasing the scattering rate.

2.3

Optical repumping of N"=2, v"=0Endeavouring to realize a larger photon scattering rate in YO, we experimented with modify-

ing the choice of repumping scheme described in the previous section. By using microwaves to remix
only N ”=0 and 1 levels in v”=0, and optically repumping the N ”=2 level through the negative
parity level in the A2 Π1 state, J 0 =1/2 level which then decays to N ”=0,2, we can increase thescattering rate on our main cycling transition. This is diagramatically shown in figure 2.2. Becauseof the change in the number of states connected to the same excited state, the scattering rate isincreased by ∼60 percent with this choice of rempumping scheme, from Γ/13 to Γ/8. As will be
discussed in more detail in Chapter 5, implementing this scheme dramatically increased our optical
deceleration rate and the number of molecules slowed to trappable velocities.

J'=5/2(+)
J'=3/2(-) v'=0
v'=0
J'=1/2(+)
v'=0

(a)

2

A Π1/2

N"=2

3e-4

nm
61
4

m

nm

N"=0(+)

N"=0(+)v"=1

X 2Σ +v"=0

N"=1(-)v"=2

N"=1
23 GHzN"=2(+)

N"=1(-)

46 GHz

9n
64

8
64

J'=3/2(-)

N"=1(-)

G"=0 F"=2 760 MHz
G"=1 F"=1,2,3

A'2Δ3/2

N"=3(-)

G=I+S F=G+N

J'=1/2(+)
v'=1

v'=0

N"=2(+)

10

(b)

N"=0

X 2Σ +

G"=0

F"=1 760 MHz

G"=1 F"=0,1,2
G"=0 F"=0 760 MHz
G"=1 F"=1

Figure 2.2: Choice of cycling transition for repumping N ”=2 either optically or with microwaves
at 46 GHz. Optical repumping uses the dashed-dotted orange arrow transition, while microwave
mixing uses the dashed-dotted green arrrows transitions. We only apply one or the other, not both.
We anticipate the largest unplugged leak at this point is into N ”=0 and 2 of the v”=1 state via theA02 ∆3/2 state.

2.4

N"=3
In case of unintended excitation to an unplanned excited state leading to leakage to excitedrotational levels in the ground state, we implemented a laser pumping out the N ”=3 population
via the A2 Π1/2 state, J 0 =5/2 level. This has no effect on the main cycling transition rate as it isconnecting to a different excited state. Molecules can either decay back to N ”=3, or they can decay
to N ”=1 where they can rejoin the normal cycling transition. This frequency is 9.775 GHz fromthe N ” = 2 repump, and so is obtained by sending the N ” = 2 light through an EOM. The effectsof this repump laser on our MOT operation are detailed in Chapter 7.

2.5

Is a v"=3 repump necessary?
Based on the estimated Franck-Condon factors (vibrational overlap integrals) of 2×10−6 [34]between the A2 Π1/2 v”=0 state and the X 2 Σ v”=3 state, we would not anticipate a significant
amount of leakage to v”=3 or higher vibrational states within the number of photon scatters required

11
for slowing and trapping. While monitoring the MOT signal, we did apply a laser throughout the
expected frequency range to see if a v”=3 to v 0 =2 repump would increase the number or the lifetimeof our MOT, but we did not see an effect. This also suggests that we do not have a substantial
initial population in v”=3. We further confirmed this hypothesis by failing to detect in-buffer-gascell absorption on that transition. While it is possible that we missed the correct location of thetransition, our estimates suggest we know the frequency to within 100 MHz and we traced out∼1 GHz in each case. We conclude that v”=3 is not affecting our experiment at this point in time,
though we have the laser on hand if we ever wish to experiment with it again.

2.6

Microwave mixing
Just as with our optical cycling and our need to prevent polarization dark states when exciting

on a F ” >F 0 transition, we need to consider a similar issue when using microwave mixing. Withcircularly polarized light, as in our MOT beams, it is straightforward to realize that σ + light cannot
drive a ∆ F = 0 or -1 transition, and likewise that σ − polarized light will not drive a ∆ F = 0
or +1 transition. So, one of the streched F ” states will always be unaddressable. Likewise, withlinearly polarized light, there can always be a superposition state that will be unaddressable to thelight for F ” >F 0 .
Similarly, when driving microwave transitions we have to be conscientious of the F number ofstates that we are driving to and from. In our best slowing scheme so far realized (using microwave
mixing of N ”=0 and 1 and optical addressing of N ”=1 and 2) we note that we are relying on driving
N ”=0 to N ”=1, where the F goal is greater than the F start . In our less optimal configuration (See
Chapter 5 for further details), where we use microwaves to mix N ”=0,1,2, and optically address
only N ”=1, we find we may have difficulty. For the N ”=2 to 1 microwave pumping, we are reliant
on pumping to a Fgoal less than Fstart , and so can be susceptible to issues arising from polarization
dark states. This can be ameliorated by rapidly switching between microwave horns of orthogonal
polarization or introducing a varying phase shift between horns of orthogonal polarization. While
we have preliminarily tried rapid switching between two 46 GHz horns of orthogonal polarization

12
during the slowing sequence, we have not yet found an improvement. This may not be currently alimiting factor. However, when we work towards a narrow-line MOT for YO on the X 2 Σ state to
A02 ∆3/2 state transition, depending on the choice of microwave mixing scheme we will want to bediligent about carefully addressing all possible states. The details of our plans for the narrow-line
transition are laid out in Chapter 8.

2.7

Decoupling the N"=1,v"=1 manifold
In the interest of increasing the photon scattering rate even higher, there are other laser

schemes we can consider. By removing the laser exciting the N ”=1, v”=1 manifold to the excitedJ 0 =3/2 (+) level, we could further increase the photon scattering rate, akin to the gain realized by
the optical repumping of N ”=2. This modified repumping scheme is depicted in Figure 2.3. The
scheme would reduce the maximum realizable scattering rate even further, from Γ/8 with N ”=2
optically repumped to Γ/5. The difference in frequency between the current transition to J 0 =1/2
and the one to J 0 =3/2 is only 27.916 GHz, within the tuning range of the laser. In order for thisscheme to be effective, it is necessary to have the N ”=3 to J 0 =5/2 repump that was discussed
earlier in the chapter in use, so as to recycle molecules that end up in N ”=3 after being repumped
through the J 0 =3/2 level.

(a)
A 2Π

J'=5/2(+)
J'=3/2(-) v'=0
v'=0
J'=1/2(+) J'=3/2(+)
1/2
v'=0
v'=0

13

(b)
J'=5/2(+)

J'=1/2(+)
v'=1

13.564 GHz
9n64

J'=5/2(-)

m

61

nm

4n

m

648

A2Π1/2
N"=1(-)v"=2

N"=2(+)

N"=3(-)

N"=1(-)v"=1

N"=1(-)
N"=0(+)v"=0

46.528 GHz

v'=0

J'=3/2(-)
J'=3/2(+)

9.030 GHz
27.916 GHz

X 2Σ +

J'=1/2(+)
J'=1/2(-)

4.515 GHz

Figure 2.3: (a)Proposed repumping scheme which decouples v"=1 from the main cycling transition,
allowing for a maximum photon scattering rate of Γ/4. (b) The relevant rotational and parity
splittings in the A2 Π1/2 state.

2.8

N"=0 optical repumping
Going even further along the path of increasing the photon scatter rate, another possibility

we are considering in the near future is to remove the microwaves completely from the slowing
and broad MOT implementation. In order to do this we would need to resolve the leak via theA02 ∆3/2 state to the N ”=0 and 2 levels in a different manner than we currently are. A possible way
to achieve this, depicted in Figure 2.4, is to maintain the optical repump of N ”=2 to the J 0 =3/2
level of the A2 Π/2 state, which would then pump that population to the N ”=0 level. The additionof a 690 nm laser (which will eventually be used for the narrow-line cooling) will bring the N ”=0
population to the A02 ∆3/2 state. Without further change, this wouldn’t allow the molecules to rejoin
the cycling transition. However, the parity splitting in the A02 ∆3/2 state is relatively small (known
to be less than the Doppler broadened linewidth inside the buffer gas cell, ∼60 MHz [34]). So, anapplied electric field on the order of tens of Volts per centimeter will be enough to mix the opposite
parity states and allow decay from the A02 ∆3/2 state to the N ”=1 level and rejoin the main cycling

14
transition.

J'=1/2(+)
v'=0

J'=5/2(+)
J'=3/2(-) v'=0
J'=3/2(+)
v'=0
v'=0

A2Π1/2A'2Δ3/2
J'=3/2(-)
J'=3/2(+)

v'=0

0n

69
m

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

N"=3(-)

N"=1(-)v"=1

X 2Σ +

Figure 2.4: By applying an electric field to mix the parity levels in the A02 ∆3/2 state and addressing
the 690 nm X 2 Σ to A02 ∆3/2 transition, we can pump molecules from the N ”=0 level and allow themto rejoin the main cycling transition. This adaption would not require any microwave coupling ofstates to provide closure

It is possible that the small electric field would have other unforeseen consequences on theoperation of the MOT. However, it will be straightforward to install electric field plates in the MOT
region, though somewhat more difficult to install them along the entire slowing length. Anotheroption would be to utilize microwave mixing during the slowing time, then switch off the microwaves
and use the N ”=0 to A02 ∆3/2 state optical repumping only in the MOT region. If used without
the decoupling of v”=1 discussed in the previous section, the decoupling of the N ”=0 manifold
will bring our maximum possible scattering rate from Γ/8 to Γ/7. If used in combination with theaforementioned decoupling, it will bring the maximum scattering rate from Γ/5 to Γ/4. As will
be discussed more thoroughly in Chapter 5, since a 60 percent change in scatter rate yielded a 20
times gain in slowed molecule signal, these various cycling transition schema are exciting potential
experimental directions for improving slowed and trapped molecule number.

Chapter 3

Experimental apparatus

3.1

Introduction
In this chapter I describe various components that are important parts of our experimental

apparatus. An overhead diagramatic view of our vacuum chamber is shown in Figure 3.1. Molecules
are produced in a single-stage cyrogenic buffer-gas cell, after which they are optically decelerated
and loaded into our MOT in the octagonal chamber. I give an overview of our laser systems, ourmicrowave system (which is used to maintain optical cycling of YO molecules), the imaging systems,
the vacuum setup, the buffer gas cell, and the MOT. The cell is described in more detail in Chapter
4, and specifics of the MOT coil are given in Chapter 6.
The vacuum system is pumped out by three 300 L/s turbomolecular pumps, one on the crossdirectly outside the cell, one at the six inch cube along the slowing region, and one above the MOT.
The MOT region turbo is an Agilent TwisTorr 304, which has a high compression ratio even forlight gasses such as helium. In comparison with the non-high compression-ratio turbo we had on
the chamber previously, our MOT region vacuum pressure went down by a factor of three when
the He buffer gas is on. The other turbos are Varian V300s, which are not optimized for lighter
gasses, though replacing them is a potential improvement that could be implemented in the future.
We have two ion gauges on the system, one located at cell region and one near the slowing laser
beam entrance window. With no buffer gas helium flow, our MOT region reaches a pressure of
9×10−10 Torr, while the cryostat region reaches 2×10−8 Torr.

v=

microwave
horns

CCD

0

1;

ablation
laser

N=

N=
1;

v=
1,
2

16

N=1;v=1,2

116 cmv= 0; N=1,2,3

shutter

PMT

Figure 3.1: Schematic of the experimental apparatus. Molecules are produced at left via ablationof a precursor target inside the buffer gas cell. They propagate to the right while interacting witha counterpropagating slowing beam, until they reach the trapping region. The trapping region
contains the coils, three sets of counterpropagating MOT beams, and can be imaged from eitherside by the CCD or PMT.

17

3.2

Laser systems
In order to address the various necessary optical transitions in the YO molecule, we have anumber of laser systems. Additionally, because we frequency chirp the light for slowing and keep
fixed frequency beams for the MOT, we find that having two separate 614 nm systems addressing
the main cooling transition to be helpful. Currently, all of our frequency stabilization is done bylocking our lasers to a home-built erbium octave-spanning frequency comb, though in the future wewill need to stabilize a 690 nm diode for addressing the X 2 Σ to A02 ∆3/2 narrow-line transition.
Because this transition is only 13 GHz away from the 689 nm transition used by the Strontium
clock experiment in our group, we will be able to use an EOM offset lock to their laser. The detailsof our laser frequency locking schema are described in more detail in Appendix B.
We have three systems we use for producing 614 nm light in our experiment. A Sirah Mattise
dye laser produces around 400 mW of N ”=2 optical repumper utilized for slowing. We use Rhodamine 610 dye mixed into ethylene glycol as the gain medium for the laser (at a concentrationof 0.57 grams per liter). A 1228 nm seed is Raman amplified and doubled using an MPB Communications system with a home built ECDL (external cavity diode laser) as the seed to produce
the slowing main cooling transition light. The doubled output can be up to 1 Watt with 25 mW
fiber coupled seed power. The seed laser diode is from Innolume, part number GC-1230-TO-200. A
Toptica SHG system produces N ”=1 light for the MOT beams, yielding approximately 750 mW.
After frequency manipulation and combination of beams, this yields about 100 mW of v”=0 lightfor slowing and for the MOT, and about 40 mW of N ”=2 in the slowing beam.
We generate repump light at 648 and 649 nm with home-built ECDLs in the Littrow configuration. Since these master lasers only produce around 20 mW, we use the master lasers for v”=1
and 2 to each injection lock two slave diodes, one each for the G”=0 and 1 components. Theseslave diodes are not AR-coated (Thorlabs part number HL6385DG), so the cavity is the diode itself.
The temperature and current have to be set appropriately for the slaves to follow the mode of theseed. To produce the ∼770 MHz offset between the G”=0 and G”=1 manifold, we use a single pass

18
AOM. Because the G”=1 manifold covers a range of about 15 MHz, we apply a modulation to thefrequency of the AOM. The frequency modulation has a span of 15 MHz and a rate of 1 kHz in orderto address the entire level manifold. In order to monitor the injection locks, we use both an optical
spectrum analyzer (OSA) and a 10 MHz resolution wavemeter. In order to maintain injection lockwith the hyperfine scanning, we feed-forward the current on the second slaves to facilitate theirability to stay injection locked. The output power of each slave laser is on the order of 120 mW.
After combination of the G”=0 and 1 beams, the power is split for use in slowing or the MOT
and AOMs are used to correctly place the frequencies. The light is then coupled into polarization
maintaining fibers and coupled over to the experimental table. Typically at this point the power
levels at the output of the fibers is 15 mW, which are then each coupled into a tapered amplifier(TA) (either Eagleyard EYP-TP-0650-00259-2007-CM502 or Sacher TPA-0650-0250). The outputsof the TAs are fiber coupled once again to maintain ease of alignment, and are combined with otherslowing or MOT components. The beams then pass through the Pockel’s cells which switch theincident light between orthogonal linear polarizations(Conoptics 350-160-01) at a rate of ∼5 MHz.
In order to prevent competition between the different hyperfine frequencies seeded into the sameTA, which potentially causes fluctuations of the power splitting between the modes, we are planningto modify our systems to have only a single hyperfine component per TA.
In order to have our optical frequency comb be a useful ruler to lock our laser frequencies to,
we require a stable microwave source. The lab shares a Wenzl oscillator, which is locked to a 10 MHz
signal that is stabilized by a cesium reference in the building. By stabilizing both the repetition
rate (approximately 100 MHz) and the carrier offset frequency to these known RF frequencies, theoptical frequency of all comb teeth are stabilized. In order to lock the carrier offset frequency, weneed to obtain a heterodyne beat between doubled light from the 2100 nm end of the comb withfrequency 2fco + 2n0 frep and locking it to the undoubled 1050 nm end with frequency fco + n1 frep .
Thus, in order to self reference the comb, we require sufficient power in both ends of the broadened
comb spectrum. In order to lock our other lasers to the comb, we also require power at 1228, 1296,
and 1298 nm. We double the ∼1297 nm section of the spectrum with a periodically poled lithium

19
niobate crystal that has 1.5 nm of bandwidth in order to lock the 648 and 649 nm repumps. The
undoubled 1228 nm comb light is used to directly lock the Raman seed laser. We use a optical
bandpass filter to isolate the comb light around 1228 nm to produce a beatnote with the Raman
seed. In order to allow amplification of all of the RF beatnotes, we use a 10 MHz bandpass filter
around the offset lock frequency, and then use frequency-to-voltage converters to establish a voltage
error signal. This error signal is the input to our loop filters, which servo the laser currents tostabilize the laser frequency. In this way, we frequency lock all the lasers needed for slowing andorange MOT operation. More extensive information on the comb and its spectrum, as well as laser
locking, has been previously detailed in Mark Yeo’s thesis [51].

3.3

Microwaves
As described more fully in Chapter 2, in order to maintain optical cycling, we need to recovermolecules that end up in the N ”=0 or 2 levels after decaying through the A02 ∆3/2 state. We
accomplish this by coupling microwaves at 23 GHz (resonant with the N ”=0↔1 transition) or at
46 GHz (resonant with the N ”=1↔2 transition) into the chamber. We couple the microwaves in to
the chamber at several locations: into the 6 inch cube along the slowing region, and into the MOT
region behind the MOT retroreflect mirrors or behind the slowing input mirror to get microwaves
in the MOT region for trapping. In order to prevent attenuation of the microwaves, we use large
dielectric coated mirrors and Delrin plastic holders for waveplates so as to avoid reflections fromany small metallic constraints (other than limitations of the chamber itself). The microwave horns
themselves are all 20 dBi gain waveguide coupled horns, where the i refers to isotropic, indicating
the gain along the primary axis compared to a fully isotropic antenna radiation pattern. The partnumber for the 23 GHz horns is Sage Millimeter SAR-2013-42-S2, while the 46 GHz horns are
SAR-2013-22-S2.
The majority of the slowing region is composed of 2-3/4" Conflat parts with an inner diameterof 1.5 inches (about 3.8 cm) and our microwave wavelengths are 1.3 cm and 0.65 cm for 23 GHz and
46 GHz. Because these lengths are on a similar scale, we have to consider whether our microwaves

20
can be coupled sufficiently well to the chamber or if they will likely have dead zones at the MOT
location or along the slowing region. In order to achieve a Rabi frequency of about 1 MHz for our
4.5 Debye rotational transition dipole moment molecules, we require an electric field strength ofapproximately 60 Volts/meter, or 1 mW/cm2 intensity of our microwaves. Using COMSOL, oursetup of microwave horns, 2-3/4" nipple, and open MOT region can be simulated (though the entire
MOT region chamber is not used). Doing so for the MOT region for 23 and 46 GHz yields the results
seen in Figure 3.2. From this simulation, we find that for both 23 and 46 GHz microwaves, butparticularly for 23 GHz there is a "dead" zone at the MOT region due to spreading of the wavefronts
after the 2-3/4" conflat nipple. This simulation led us to install 2 Watt microwave amplifiers for
the MOT region, rather than using the 50 mW output we previously had.

21

Figure 3.2: Simulation of microwave intensity for 50 mW input power at horns in MOT region(circular region .38 meters along axis) for 23 GHz (upper) and 46 GHz (lower) microwaves. Color
scale has units of mW/cm2 . Black rectangles indicate the volume witin the hollow conductive
cylinder of the Conflat nipples of the chamber.

As mentioned in Chapter 2, there is a potential for polarization dark states to form whenrelying on larger N ”start to smaller N ”goal microwave repumping. We have the ability to rapidly
switch between two horns in the MOT region for 46 GHz, which can be aligned to different polarizations to break up polarization dark states. While we have not yet determined if this capability isnecessary, it could resolve an issue when doing narrow line cooling as described in Chapter 8, due
to the different planned microwave mixing scheme.

22
The circuit schematic for our microwave system is laid out in Figure 3.3. In order to switch
between microwave remixing of v”=0 rotational states or v”=1 rotational states, we utilize an Analog
Devices 9959 evaluation board to produce the appropriate sideband frequency, which is then mixed
with the 12 GHz unmodulated signal. In order to only have the appropriate (first lower) sideband
address the experiment, we utilize a bandpass filter spanning from 11.375 to 11.725 GHz (Miteq
FLT-105449). The signal is amplified with an Avatek AWT-18057 42 dB gain amplifier, and thendoubled to 23 GHz with a Marki Microwave D95190 doubler. All of the remaining amplifiers at
23 GHz are New Millenium AMT-05-25-23 with 13 dB gain, with the exception of a 2 Watt output
amplifier directly before the MOT region horn (Fairview microwave SPA-265-33-01-K ). The fourway power dividers are Krytar 7020265 matched-line directional dividers, which have only 2.3 dB
total insertion loss and good power matching between the different outputs. In order to mix thev”=1 N ”=1,2 manifolds at 46 GHz, as the v”=0, N ”=2 repumping is done optically, we use two
synchronized switches to simultaneously switch between v”=1 and v”=0 sideband frequencies fromthe DDS while directing what will be the 46 GHz signal to a terminator or to the horns. We usually
perform this switching at 1 MHz. Because the isolation of these switches is only 20 dB, we havea second higher isolation (40 dB), but slower, switch to ensure that no 46 GHz resonant with thev”=0, N ”=1↔2 transition is entering the chamber. For example, we will regularly have no 46 GHz
radiation during the slowing but then turn it on during the MOT to remix v”=1 N ”=2 populationthat may have accumulated as decay from the A02 ∆3/2 state. The last stage is doubling to 46 GHz
with a set of Marki Microwave ADA-2050 CMV active doublers, before coupling to the chamber. In
order to prevent polarization dark states, we have the capability of switching at 100 kHz between
a low-power and high-power MOT region horn which are aligned to the chamber with orthogonal
polarizations.

23

term

16
dBm

synchronizedswitches

16dBm

4-way power divider

33
dBm

A
DDS B

x2

16
dBm

Bandpass

13
dBm

atten

12 GHz

12
dBm

term

x2
16
dBm

term

x2
16
dBm

4-way power divider

x2

33
dBm

16
dBm

term

Figure 3.3: Electronics schematic for microwave system. This setup allows mixing of v”=0 and 1,
N ”=0,1,2 in a variety of arrangements.

3.4

In-vacuum shutter
In order to reduce the effect of collisions from helium on the YO molecules during slowing and

MOT operation and to lower the MOT region vacuum pressure despite having a continuuous flowof helium buffer gas, we have a shutter installed in the vacuum chamber along the slowing region. It
is installed 28 cm downstream of the buffer gas cell directly after the 2-3/4" Conflat cross on which
the cell region turbo is mounted. It is located before the gate valve so the shutter can be modified
or replaced without breaking the MOT region side of the vacuum chamber. Unfortunately, after acouple months of use, the in-vacuum shutter starts to stick and will not open or close fully, and so24
needs replacement. The shutter is installed upstream of our gate valve so that we do not have torebake the MOT region of the chamber every time the shutter is replaced.
The shutter itself is a Vincent Associates Uniblitz shutter. This company offers a vacuum
compatible version of their shutters where the drive coil is potted in epoxy. The shutter is mounted
within two Conflat 2-3/4" to 6" adapters. The wires for the shutter drive and a thermistor connection go through a feedthrough mounted on the preceding 2-3/4" cross. In order to prevent
overheating of the shutter, the drive coil is heat sunk to the mount with copper blocks. This allows
running of the shutter full-time while reaching only 40 degrees Celsius. Without this heatsinking,the experiment would have to be run at a lower repetition rate in order to prevent overheating of
the shutter.
As will be referred to in greater detail in Chapter 5, we find that the reduction in heliumpressure also helps reduce loss of slowed molecules due to background helium collisions.

3.5

Buffer gas cell overview
Further detail of the buffer gas cell we use to produce YO is given in Chapter 4, though here

I give a cursory overview. As shown in Figure 3.4, the cell consists of a copper block anchored tothe "4 K" level of a two-stage pulse tube cryocooler (Cryomech PT410). The "40 K" stage of thepulse tube has radiation shielding anchored to it in order to reduce the heat load on the "4 K"stage. In actuality, these stages reach temperatures of approximately 3.5 Kelvin and 30 Kelvinafter cooldown. The system takes approximately four hours to cool down from room temperature
to its lowest level, with the chamber already pumped out. The radiation shields at 3.5 Kelvin arecovered with coconut charcoal that is epoxied to the copper with Stycast 2850FT, an epoxy that isthermally expansion matched to copper from cryogenic to room temperatures. This charcoal allows
for effective cryopumping of the helium buffer gas, which would otherwise build up and adversely
affect the vacuum and cold molecule production. The buffer gas cell has a window on one sidethrough which the ablation laser enters. The helium inlet is made of 1/8" copper tubing, and enters
the back of the buffer gas cell, where the helium then passes through a diffuser plate. There is25
a helium "bobbin" to precool helium before entering the cell so that it does not enter the cell atroom temperatuere. We find that leaks in the gas manifold manifest as ice plugs in the helium
inlet line, which cause pressure buildup after the mass flow controller (Alicat MG-20sccm-D15M,
5IN,Gas:He) and cessation of molecule production. Since Swagelok only has so many reconnect
cycles while remaining vacuum tight, it is important to carefully check for leaks after changes to
the gas manifold. We typically use helium flow rates in the range of 0.5-5 sccm (standard cubic
centimeters per minute). When the helium reaches the cell, it thermalizes to 3.5 Kelvin. Ablated
molecules from the Y2 O3 target then thermalize translationally, vibrationally, and rotationally withthe cold helium before exiting the cell as a molecular beam.

26
radiation shields

30 Kelvin
3.5 Kelvin
He in

diffuser plateroom temperature
Y 2 O3aperture

To MOT region

flow controller

He precoolingbobbinwindows

ablation lens
532 nmablation beam

Figure 3.4: A schematic of our cryostat as viewed from above. Different colors indicate temperatureof the constituent parts: all external vacuum/room boundaries are at room temperature (purple),while a set of radiation shields are held at 30 Kelvin (blue) and the cell itself along with the charcoal
cryosorb are anchored to the 4 Kelvin stage(green). Helium is precooled to 4 K before entering thecell by going through a length off copper tubing soldered to a heat sink that is anchored to the 4 Kstage. YO is produced via ablation of a Y2 O3 ceramic target with a 532 nm 8 mJ pulse. Rastering
the ablation beam allows efficient use of the whole surface area of the target.

We found that a completely sealed 40 K shield (except for the molecule beam exit aperture)
did not allow helium gas to be efficiently pumped out from between the shields. By punchingholes in the 40 K shield to increase the pumping efficiency, we improved molecule production
by about 50 percent, despite an increased temperature of the cell due to less effective radiation
shielding. These two extra holes (1" diameter each) dramatically improved pump out speed atroom temperature as well, reducing our down time due to ablation target changes, etc. In the
future, modifying the radiation shield (perhaps by doing a chevron design) will improve conductancewithout increasing blackbody radiation impinging on 4 K stage and allow a lower cell temperature.

27
Since it is not clear if we have the maximum possible production of YO molecules, time spent
improving the local gas pressure directly outside of the cell may be worthwhile.

28

Figure 3.5: Image of cryostat chamber and cell from the front with the front copper radiation shields
removed. The helium precooling bobbin is visible in the upper left. On the left side of the cell thebrass ablation window mount is visible.

29
We can measure the dependence of molecule production on temperature, as shown in Figure
3.6, by turning on and off the pulse tube while still acquiring data. The temperature of the cellis read out from a Lakeshore temperature diode installed directly underneath the cell. Molecule
production increases strongly with lower temperature, with the effect being more steep with respect
to temperature for 2.5 sccm as opposed to 5 sccm. At some point in the future, it could beinteresting to try further cooling the cell with a 1 K pot as in Reference [52] in order to see how
the trend continues. However, since we are using microwaves to mix N ”=0 and 1, if the onlychange is shifting the produced rotational distribution lower, we will not see a further improvement
in molecule number. On the other hand, if the molecule number increase is due to improved
thermalization of the YO molecules with the helium buffer gas, we may see an improvement at evenlower temperatures.

1.8E+06

4.0E+06

1.6E+06
1.4E+06
1.2E+06

3.0E+06
2.5E+06

1.0E+06

2.0E+06

8.0E+05

1.5E+06

6.0E+05

1.0E+06

4.0E+05

5.0E+05

2.0E+05
0.0E+00

Counts/s

Counts/s

3.5E+06

5 sccm
2.5 sccm

2

3

4

5
Temperature (K)

6

7

8

0.0E+00

Figure 3.6: Peak YO molecule production for different temperatures and flow rates . Temperature
variation was induced by shutting off the pulse tube while still producing molecules.

We find that the ablation window of the cell becomes blackened with extended use. This

30
effect is due to deposition of various ablation products on the window followed by localized heating
as the ablation laser passes through the window. A used window showing this effect is pictured
in Figure 3.7. Our replacement schedule of the window is dependent on buffer gas flow rate, butneeds to be quite frequent (about once a week) when running at less than or equal to 1 sccm . The
procedure to replace the ablation side window and Y2 O3 targets is described in Appendix E

Figure 3.7: Image of ablation window after having been in use for ∼2 weeks for helium flow rates
around 1 sccm. The most transparent locations suffer ∼25 percent attenuation, with darker areas
being even higher. This results in a reduction of YO molecules produced over time.

We have tried using a "snorkel" to move the ablation beam window further from the ablation
plume. This seemed to reduce the rate of blackening of the window, but also reduces our ability toraster the YAG laser to ablate different parts of the Y2 O3 targets.

3.6

Detection systems
In order to detect the laser induced fluorescence of the YO molecules in the trap region, we

have two separate imaging systems. For spatially resolved detection of our molecules, we use thedata from a charge coupled device (CCD) camera offloaded directly to a desktop computer. Our
CCD is an Apogee Alta U47, which has a quantum efficiency of 93% at our detection wavelength of
614 nm. The camera has a 1024×1024 pixel array, each of which has a 13×13 µm area. While the31
CCD can offload all pixels individually, it can also bin pixels on chip before offloading. We typicallyuse this capability to bin 6×6 pixels on chip in order to improve readout times.
For time resolved light detection, we use a red-enhanced photomultiplier tube (PMT) (Hamamatsu R10699). The PMT current spikes go through a transimpedance amplifier and are countedwith a SRS430 multichannel scaler (MCS). We find that saturation of current spikes in the time
domain occurs at 1.7×107 counts per second (limited by the transimpedance amplifier). At thisphoton count rate there is a high probability of succesive pulses overlapping each other, and sobeing under-counted by the MCS. To avoid the saturation regime of the PMT/MCS system we use
careful alignment of the MOT and slowing laser beams and copper blackening in the chamber, but
could potentially switch to current accumulation mode if the light scatter were too high. However,in order to reduce photon shot noise it is in our interest to keep the light background as low as possible. The characterization of the PMT transimpedance amplifier is discussed further in Appendix
C.
In our system, both the PMT and CCD imaging systems are similar, and located on opposite
sides of the MOT chamber orthogonal to the molecular beam. The lens setup is depicted in Figure
3.8. The color filter (Edmund Optics 84-118) is a fluorescence filter centered at 607 nm with 32 nm
bandwidth.
While our vacuum chamber is open to air, we align our MOT coils with respect to our chamberby placing a threaded rod in the center of the MOT coils, with a notch at the center between thetwo boards. By shining our horizontal MOT beams while centered through the chamber windows,
we can confirm that they are well aligned to the threaded rod and thus the MOT coils.

32

150 mm

150 mm

150 mm

75 mm

75 mm

75 mm

Figure 3.8: PMT and CCD Imaging systems. Blue lenses are 2 inch diameter 150 mm focal length
lenses, while red are 1 inch diameter 75 mm lenses. The orange box indicates a color filter used toremove all ∼650 nm scattered light from our vibrational repump lasers. There is an image plane
between the lens sets where the iris is placed for spatial filtering. All lenses are installed outside thevacuum chamber. The achromatic lens part numbers are Newport PAC086AR.14 for the two inch
lenses and PAC046AR.14 for the 1 inch lenses.

Figure 3.9: CCD alignment confirmation: by placing a notched threaded rod in the MOT region
and imaging it with the CCD, we can confirm the CCD is imaging the desired region

We utilize this illuminated threaded rod to confirm our imaging system alignments as well.
Additionally, by imaging the 8-32 rod with the CCD, we can determine where the MOT region is

33
on the CCD and determine the absolute magnification. Figure 3.9 shows the resulting CCD image,confirming that the CCD is properly aligned to the MOT region. By averaging horizontally acrossthe white box region in Figure 3.9, we calibrate the thread distance to pixel size, as shown in Figure
3.10. Since the threaded rod is 32 threads per inch, we determine that our imaging is 102.6 pixels
per mm, corresponding to a total image area of 1 cm by 1 cm, and a system magnification of 1.3.

Figure 3.10: CCD magnification calibration: the cross sectional average counts vs pixel value along
the edge of the 8-32 screw indicates the magnification of our imaging system. This label refers to 2
×2 binned pixels.

As a final calibration check to confirm the positioning of our MOT beams, we can also utilize
the MOT beams and the CCD to image the unslowed molecular packet. The results of this test
are depicted in Figure 3.11. For this measurement, the desired beam was left on the whole time,
and the CCD was exposed from 5 to 15 ms after ablation fire, thus containing the majority of themolecular packet. In panel (a) the transverse beam was used and so the laser detuning was set to
0 m/s. Panels (b) and (c) use the MOT beams that are at 45 degrees with respect to the molecules,
and so the laser beam detuning was set to be resonant with 110 m/s molecules. In these images, themolecules are traveling from right to left, and gravity points downward. As a note, these images are
not from the most recent alignment, and so should not necessarily line up with the screw imaged
in Figure 3.9.

(a)

(b)

(c)

34

counts

15
5
-5

-15
Figure 3.11: Imaging the unslowed molecule packet from 5-15 ms after ablation fire. Color axis
indicates average CCD counts per 6×6 binned pixel, with 1 mm×1 mm square smoothing filter. (a)The vertical (transverse) MOT beam. (b)The NE/SW beam. (c)The NW/SE beam.

3.7

Light scatter reduction
Because we want to minimize the amount of light scatter at 614 nm detected by both our

CCD and our PMT, we take steps to reduce light scatter in the chamber. In order to make vacuum
compatible light baffles, we use the copper oxide blackening method described in Reference [53],which gives copper sheet metal a matte black finish. We have blackened cylinders in all the MOT
beam vacuum nipples (which are themselves used to move the windows further away from the MOT
region to prevent excess scatter), as well as modified 6 inch copper gaskets for the top and bottomof the 6-inch main octagonal chamber. We also have a blackened copper octagon to prevent scatterwithin the MOT chamber itself. As shown in Chapter 6, we also use the copper oxide blackening
on the MOT coil traces to further reduce light scatter.
The MOT windows are anti-reflection (AR) coated to prevent scattering of our main coolingtransition (614 nm) light. Because the 648 and 649 nm scattered light is blocked out by the bandpass color filter in the detection system, we do not have to worry about the scatter due to therepump beams. Light is coupled in and out of the chamber using homemade window vacuum ports,
constructed by epoxying (Epotek 353ND) N-BK7 AR coated windows to KF to CF adapters.. We
experimented also with fused silica windows, which have better birefringence properties, but they

35
ended up introducing a lot of light scatter. We determined the cause was that after a bake the AR
coating shifted so that the amount of reflection at 614 nm was quite significant. Because N-BK7 ismore closely expansion matched to the stainless steel of the vacuum chamber, it also means thatthe windows are less prone to cracking under the thermal cycling of bakes.
As a final step to reduce scatter, we also use irises for all of our MOT beams (typically set toabout 13 mm diameter) on both the input and the retroreflected beam paths.

3.8

Coils and beams
In order to preserve as much laser power as possible, we rely on a combination of long-passdichroics (Thorlabs DMLP638) which transmit repump light and reflect v”=0 light, and polarizing
beam combiners for both the slowing and the MOT beams, as depicted in Figure 3.12. This
necessitates that in the MOT region, our G”=0 and G”=1 components of v”=0 have opposite
polarizations. For MOT operation, this is not an issue, as all the MOT force comes from the G”=1
manifold, with G”=0 acting as a repump.

AOM

v"=0

G"=0
G"=
1

λ/2

v"=2
From TAs

v"=1

λ/2

dichroics
PBS

To experiment

Pockel's cell

Figure 3.12: Scheme for combining v"=0,1, and 2 components for both MOT and slowing beams.

Looking forward, we can use a similar method for introducing 690 nm light to our chamber
for narrow-line cooling, by using another dichroic mirror which passes 690 nm and reflects 648 or
649 nm light. With this dichroic mirror, the 690 nm light can be combined with a vibrational
repump, and then combined with the other components in the same way.

36
After combination of all components and passing through the Pockel’s cell, light for the MOTthen goes through quarter and half wave plates in order to circularly polarize the light before going
into the chamber. In correspondence with the magnetic field gradient being of the opposite signfor the axial compared to the radial direction, the vertical laser beams have orthogonal (opposite
handedness) polarization to the two horizontal beams. The MOT beams are aligned to the centerof the vacuum chamber. The slowing beam is gently focused with a 100 cm focal length lens inorder to have better spatial overlap with the molecular beam exiting the buffer gas cell. Focusingof the slowing beam also made the slowing beam alignment more robust in our experiment. Since
we need N ”=2 repumping for both slowing and the MOT, N ”=2 is always repumped through theslowing beam, so as not to need yet another 614 nm laser system.
Our magnetic field gradients for MOT operation are produced with an in-vacuum set of AC
anti-Helmholtz MOT coils, which are resonant at 4.75 MHz, and are capable of producing a 20 G/cm
field gradient with 50 Watts drive. Further description of the MOT coil design and construction
is in Chapter 6. In addition to the main MOT coils, we also have external (DC) magnetic fieldcancellation coils positioned outside of the vacuum chamber. The currents of these Helmholtz coils
are set to zero out the earth’s magnetic field and residual magnetization of the chamber. However,
we have not yet found the external field cancellation coils to improve the MOT operation.

Chapter 4(Mis)Adventures in buffer gas cell design and ablation chemistry

4.1

Introduction
As ever in experimental physics, we would love to have a higher number and density of our

species of interest. Molecular sources produce lower yields than the ovens that are found in alkali
atom experiments [54, 9], which in combination with the lower photon scattering rates available
makes the goal of trapping a large number of molecules more difficult. So, we asked ourselves why
not produce more molecules? Those working with fluorides, such as CaF, have found an improvement
in molecule yield by ablating a metallic target in the presence of SF6 [55, 31]. Researchers at theImperial College, London have a specially designed cell that helped improve molecule production
and reduced the width of the molecular packet in the time domain [56]. Some understanding andguiding principles to the mechanisms of buffer gas cells are understood [9], but the parameter spaceis large and far from fully characterized, especially with regards to production of varying kinds ofmolecules and in-cell chemical reactions. So, we spent some effort attempting to improve upon our
initial molecular distribution and yield from our buffer gas cell implementation. Overall, we foundthat adding various oxidizers to our buffer gas cell did not improve the production of YO, and neither
did using a metallic Yttrium precursor (with or without oxidizers). We did, however, learn a helpful
trick in our system regarding the powdering of our cell with a Y2 O3 nanopowder, which resulted
in a significant gain in the number of YO molecules. We also performed some characterizations on
how different aspects of the cell geometry affected molecule production.

38

4.2

Magic dust
Perhaps due to collisions with helium after the YO exits the cell, we have regularly foundimproved slowing with lower buffer gas flow rates, in spite of larger molecule yields at similar
velocities for higher helium flow rates. So, we endeavoured to produce more molecules for these low
helium flows (less than 2 sccm). We found that a coating on the inside of the buffer gas cell of Y2 O3nanopowder helped improve yield at low buffer gas flow rates. However, we also found that too
much nanopowder coating is also detrimental. The cell is coated by mixing the nanopowder, whichhas particulate size less than 50 nm (Sigma Aldrich 544892), with isopropanol and then brushing
onto the intrior cell surfaces. After drying, the coating stays adhered to the copper, though is easily
rubbed off with contact. Images of the coated and overcoated cell are shown in Figure 4.1. We
found no adverse effect on vacuum pressure due to the coating of the cell. Since the ablation laser
itself only hits the Y2 O3 target, and not the dust, it is possible that some other kind of nanopowder
would also suffice to yield this improvement or perhaps be even more influential.

Figure 4.1: Left: Buffer gas cell well-coated with Y2 O3 nanopowder. Right: Cell with too much
nanopowder coating.

The variation of the peak signal size for different helium rates for the powdered and unpowdered cell is shown in Figure 4.2. From this, we find that the nanopowder in the cell not only

39
increases the molecule number, but also allows for the system to be run at a lower helium flow rate.
This is a win on both accounts for us.

Figure 4.2: Comparing the peak molecule number produced vs flow rate for the unpowdered andpowdered cell shows that the powder improves molecule number as well as allowing operation atlower helium flow rates.

The other thing that needs to be verified is that the molecules are not arriving too quickly
using the powdered cell, the results of which are shown in Figure 4.3. We find that for a given flow
rate, the cell with nanopowder produces molecules that arrive in the detection region in about half
the time of the unpowdered cell. However, when running at a lower flow rate such as 1 sccm, themolecules’ velocity is similar to the 5 to 10 sccm range we had been using for the unpowdered cell,and so the velocity is not a concern. We find in both cases that the peak time for molecules exiting
the cell is 2-2.5 ms.

40

Figure 4.3: For a given flow rate, the YO produced is faster for the powdered cell than the unpowdered cell. However, the velocity of the powdered cell at low flow rates is commensurate with thevelocity of the unpowdered cell at higher flow rates.

We did not discover the usefulness of the nanopowder coating until after the oxidizer tests
described in the remainder of this chapter, so it could be nice to go back and repeat with thedust coating and see if we achieve different results with different molecule production methods.
Additionally, this implies that the absolute number for the following studies is low because we wereusing a clean cell instead of a coated one for the tests.

4.3

Cell modifications
One of the largest modifications made since our most recent published work [20] is the tran-

sition from using a two-stage buffer gas cell to a single-stage cell. This made the molecules we
produced faster, but we produced many more of them, as shown in Figure 4.4. However, we havenever experimented with different mesh sizes, different spacings of the second stage from the first,
and so on. This suggests that there is a possibility of a modified two-stage cell still being effective
for us, but with the much larger number produced with our single-stage compared to our two-stage
we moved forward with the single-stage buffer gas cell.

41

Figure 4.4: Velocity distribution for molecules produced from the old two-stage cell (left) and thesingle stage cell (right). The two-stage cell data was taken at a helium flow of 5.5 sccm, while thesingle stage data was with a helium flow of 3 sccm. Velocity sensitive detection is performed via LIF
from a low-power probe beam at 45 degrees with respect to the molecular beam axis with detuningchosen to detect a specific velocity class.

While in the past we used a repetition rate of 10 Hz in our experiment for fast data acquisition,
we find that the buffer gas cell does not behave similarly across different YAG laser repetition rates.
As shown in Figure 4.5, the distribution of molecule arrival times of the unslowed beam varies bothin timing and in beam brightness. While the total number increases by a factor of 6 with the reduced
repetition rate of 1.4 Hz, the peak time-of-arrival also shifts earlier. This time shift corresponds toa peak velocity produced by the cell of 120 m/s instead of the 105 m/s produced by a 10 Hz rate.

counts/sec x105

42

1.4 Hz
10 Hz

Figure 4.5: Comparison of different YAG laser repetition rates. The signal detected is LIF by
unslowed molecules transiting the MOT region. The detection beam is 10 mW and orthogonal tothe molecular trajectory with zero detuning.

We have also experimented with a couple of different cell main bore sizes– 22 mm diameterand 27 mm diameter, as shown in Figure 4.6. The number is significantly (about a factor of 2)
improved for the smaller bore cell, despite the slightly faster molecules that are produced. So, we
now have the smaller bore size cell installed, though we have not yet tried even smaller bore sizes
due to the slow experimental turn-around of trying various cell geometries. It would definitely beinteresting to try even smaller bores if time permits to see if the trend of more molecules withdecreasing interior cell size continues.

Smaller bore

Peak Signal (X105 count/sec)

16

43

Larger bore

12

8

4

0

0

4

8

12

16

He Flow Rate (SCCM)

Peak Arrival Time (ms)21
Smaller bore

Larger bore

18

15

12

9

0

4

8

11

15

He Flow Rate (SCCM)

Figure 4.6: Peak molecule signal (top) or peak time of arrival (bottom) for different flow rates withthe smaller bore (22 mm, blue trace) or larger bore (27 mm, red trace) cell.

As shown in Figure 4.7, varying the size of the front aperture of the cell does not increase
the number of total molecules that can be produced, but improved the number at a given flow
rate, allowing for running of the cell with a smaller helium load. The average initial velocity of themolecules is also modestly increased for a given helium flow rate. We have not yet attempted evensmaller front apertures, though it is possible it would continue to improve molecule production at

44
low helium flow rates.

Peak Signal (X105 count/sec)

20

15

10

5
2.2 mm aperture
00

4

3.1 mm aperture

8

12

16

He Flow Rate (SCCM)

Peak Arrival Time (ms)21
2.2 mm aperture

3.1 mm aperture

18

15

12

9

0

4

8

11

15

He Flow Rate (SCCM)

Figure 4.7: Peak molecule signal (top) or peak time of arrival (bottom) for different flow rates witha 2.1 mm front aperture (blue) or 3.1 mm aperture (red).

Following the lead of the Doyle group at Harvard [57], we also installed a diffusion plate at
the rear of our buffer gas cell. This plate prevents helium from directly entering the cell from thefill line by requiring a few collisions with the plate and the back of the cell before entering themain volume. Interestingly, the number of slowed molecules improved with the diffuser, as shown in45
Figure 4.8, while the initial number was relatively unchanged. This is possibly because the diffuser
plate prevents helium from directly leaving the cell and colliding with the molecules during theslowing time, or that it improves thermalization of the helium with the cell.
1.5 sccm with diffuser
1.5 sccm no diffuser.5 sccm with diffuser.5 sccm no diffuser

fluorescence (arb. u.)

12

8

4

0
10

20

30

time after ablation (ms)40

Figure 4.8: Comparison of behavior with same attempted MOT and slowing sequence with andwithout the diffuser installed in the cell for 0.5 and 1.5 sccm. On the right is a picture of the
diffuser plate which is placed between the He inlet and the rest of the buffer gas cell.

4.4

Oxidizers
At room temperatures, it has been shown that production of YO via ablation of a Y2 O3 target

is increased by the presence of oxygen [58]. In order to test the theory in our system that adding
an oxidizing gas along with the helium in the buffer gas cell would improve production of YO, it
was necessary to modify the cell to accomodate an extra gas fill line. We modified the back plateof the cell to hold another fill line that punched through the diffuser plate. We utilized an Ultem
spacer between the line and the cell to prevent icing, as well as attaching a resistive heater to the
supplemental gas line to prevent clogging due to gas freezing in the line. We then flowed (controlled
by another mass flow controller) in various flow rates of oxygen into the cell to see how it affected

46

counts/second x10 4

YO production, as shown in Figure 4.9

no O2
0.1 sccm O2
0.2 sccm O2
0.5 sccm O2

4

2

0

90

100

110

120

velocity (m/s)

130

Figure 4.9: Resulting number and velocity distributions of YO produced with 10 sccm of helium
buffer gas and varying levels of oxygen gas flowed into the cell. Counts are average counts over a
10 ms window in which the vast majority of molecules reached the detection region.

Small amounts of oxygen (less than 0.1 sccm) do not adversely affect the production of YO,
but also do not improve the molecule production. For larger oxygen flow, we find that the productionof YO is actually greatly diminished.
Similarly, we used an ozone generator to turn the oxygen into a oxygen/ozone mixture before
flowing it into the cell with results as shown in Figure 4.10. The generator when running at maximum
ozone production could convert 6 percent by weight of the gas to ozone.

47

no O2+O3
0.1 sccm O2+O3
0.2 sccm O2+O3
0.5 sccm O2+O3

average counts/second x10

4

4

2

0

90

100

110

120

130

speed (m/s)
Figure 4.10: Resulting number and velocity distributions of YO produced with 10 sccm of helium
buffer gas and varying flow levels of a 94% oxygen and 6% ozone gas mixture flowed into the cell.
Counts are average counts over a 10 ms window in which the vast majority of molecules reached
the detection region.

To our frustration, ozone also did not improve the number of YO that we were producing. We
repeated these experiments for a range of helium buffer gas flows, from around 1.5 to 15 sccm, andsaw similar trends throughout: added oxidizers only decreased the production of YO. This trend
also held when using N2 O as the supplemental gas.

48

4.5

Yttrium metal

Peak signal (106 counts/sec)

7

Y metalY2O3 ceramic

6
5
4
3
2
1
0
215

220

225

230

235

240

245

250

Lens position from target (mm)Figure 4.11: Dependence on ablation lens position for Y metal and Y2 O3 targets.

By placing both a Y2 O3 and a Y metal target into the cell, we also compared the productionof YO. We ensured that the different targets had their faces at the same distance from the albation
lens. For this comparison, we used 5 sccm of He for both cases, with an additional 0.25 sccm of O2
gas for the metal ablation. We used a 7 mJ, 532 nm ablation pulse with a collimated beam widthof 4.7 mm. The beam was then focused with a 300 mm focal length lens onto the target. In orderto characterize the different targets, we scanned out the peak YO molecular signal by adjusting theablation lens distance from the chamber, yielding the traces shown in Figure 4.11. Here we findthat the dependence on ablation lens position is more sensitive for Y metal ablation as opposed toY2 O3 ceramic ablation. Additionally, the optimal distance of the lens with respect to the cell isfarther for metallic targets than ceramic. Unfortunately, we do not know where the absolute focusof the laser was at this time with respect to the ablation lens.

49

Y metalY2O3 ceramic

Figure 4.12: Comparison of Y metal + O2 with Y2 O3 ablation.

By placing the ablation lens at the distance with the peak molecular yield for the respective
target, we find the results as seen in Figure 4.12. Though the total integrated signal is approximately
1.8 times higher for the Y metal ablation, we find that the arrival time is much earlier as well. This
arrival time corresponds to a YO beam of 300 m/s for Y metal ablation, compared to the more
typical 120 m/s we find from Y2 O3 ceramic ablation. So, while ablation of yttrium metal allows formore total molecules to be produced, extending the chamber and our lasers’ chirp range in order
to slow molecules to rest from 300 m/s would be technically challenging. Additionally, because oftransverse divergence and the longer time needed to slow from higher velocity, it is likely that the
total number of slowed molecules could not be improved by switching to metallic targets. In order todetermine whether the velocity difference between the targets is intrinsic to the different materials
involved or due to the change in lens position, we also performed a cross check of peak molecule
velocity with respect to ablation lens position for the two targets, as shown in Figure 4.13. For thismeasurement, we extrapolated the velocity from the known cell-to-detection region distance andassumed a constant cell exit time of 2.5 ms, which we find does not tend to vary greatly. Here wefind that for ablation lens distances less than∼235 mm to the target, there is a not a large change

50
in peak beam velocity upon changing target materials. For larger lens-target distances, the peak
speed created by the Y metal target is larger than that for the ceramic target.

400

Y metalY2O3 ceramic

Peak velocity (m/s)

350
300
250
200
150
100
215

220

225

230

235

240

245

250

Ablation lens distance to cell (mm)Figure 4.13: Peak velocity of YO beam vs ablation lens position.

4.6

Conclusion
While we found that adding oxidizers to our buffer gas cell in hopes of improving YO produc-tion was fruitless, we did gain some insight into cell modifications that were helpful. By removing
the second stage from our buffer gas cell we greatly increased the number of YO produced from ourcell, though with the tradeoff that the mean velocity was increased to ∼120 m/s. We found that asmaller bore size of the buffer gas cell improved the number of molecules produced. A smaller front
aperture of the cell did not improve maximum number, but it did allow for running the system atlower helium flow rates, which will help keep vacuum pressures down. A diffuser plate installed at
the rear of the cell between the helium line entry and the main volume of the cell improved ourability to slow molecules (though did not change initial numbers). Lastly, we found that coating
the buffer gas cell with Y2 O3 nanopowder improved the production of molecules, particularly for51
low buffer gas flow rates.

Chapter 5

Slowing molecules to trappable velocities

5.1

Introduction
In order to improve our signal to noise ratio when looking for a MOT signal, as well as

to produce a larger MOT, we invested time in improving our slowed molecule signal above ourfirst proof-of-principle demonstration [20]. In 2014 when we first realized the slowing of molecules
to below 10 m/s, we wanted a molecular source that produced molecules as slow as possible, tominimize the technical difficulty of the slowing process itself. At that time, the original unslowed
packet contained approximately 7000 molecules reaching the detection region [51], of which 0.1
percent could be slowed to velocities less than 10 m/s [20]. While this signal was large enoughto definitively confirm that our slowing was succesful, the number was not large enough to be
encouraging for loading into a MOT. The laser system was set up such that the slowing lasers
addressing the molecules could have their frequency chirped from resonance with 65 m/s molecules
to 35 m/s (a frequency chirp range of 48 MHz for the main cooling transition), and relied on whitelight sidebands applied by EOMs and the Pockel’s cell to interact with molecules beyond that range.

5.2

Large cell modifications
While for our initial demonstration of slowing we wanted to start with as slow of a molecularsource as possible, for advancing our system we wanted to increase the total number of molecules.
Because of this, we switched from a two-stage buffer gas cell as in References [20, 52] to a single stage
cell. The second stage of the buffer gas cell is ‘leaky’ and so has a lower helium density, allowing

53
the molecules to have a couple more collisions with cold helium and reducing the forward boosting
seen with a higher density of molecules. This reduces the velocity spread and initial velocity of thebeam of molecules produced at the expense of molecule number. In our case, we found that thetradeoff was more favorable to have an increased amount of slowing necessary but to start with more
molecules, as mentioned in Chapter 4. Removal of the second stage increased the peak molecularvelocity from around 70 m/s to 120 m/s, while also increasing the velocity dependence on helium
flow rate, allowing for more optimization options for slowing and trapping. This effect is shown in
Figure 5.1. The removal of the second stage also increased the initial molecular number of YO by
about a factor of 400.

peak velocity (m/s)

140

120

single stage
two stage

100

80

60

0

2

4

6

8

flow rate (sccm)
Figure 5.1: Dependence on helium buffer gas flow rate of peak YO velocity produced from single
and two stage cells.

In order to slow molecules with the increased initial velocity, it was necessary to modify
our laser system to have an extended frequency chirp range. In the process, we also changed ourfrequency locking scheme. While in the past we chirped the entire frequency comb to pull themain slowing and repump lasers, and then compensated the detection laser to stay fixed, we havetransitioned to a method where the comb stays fixed. Since the MOT beams need to be fixed in54
fluorescence (arb. u.)

10

1.4 Hz
10 Hz
6

2

10

20

30

40

time after ablation (ms)Figure 5.2: Molecule LIF during and after the slowing sequence (slowing ends at 21.5 ms) for
different repetition rates of the ablation laser.

frequency, this relegated all frequency chirping to AOMs associated with the slowing lasers, insteadof putting strain on the laser frequency locks by having all master laser frequencies chirping. Moredetails of the current frequency locking scheme are detailed in Appendix B. Our expanded chirp
capability now lets lasers continually address molecules from 120 m/s to 5 m/s in the slowing beam
while providing enough power to properly seed the tapered amplifiers for the repumps and to seed
the Raman laser for the main slowing transition.
Another straightforward but critical improvement in our system was to reduce the experimental (YAG fire) repetition rate from 10 Hz to around 1 Hz. With the slowing beam on, thischange shows an even larger increase of molecular signal than the unslowed improvement describedin Chapter 4. The slowing beam itself adds a few hundred mW of heat load onto the cell during
operation, perhaps increasing the importance of cell rethermalization between YAG pulses. This
also points to a potential further improvement by reducing the temperature of the cell or increasing
the cooling of the cell after an ablation pulse. Being able to increase the experimental repetition
rate, even without an increase in molecular signal, would still improve averaging time.

55

5.3

White light
In the past we had electro-optic modulators (EOMs) installed in the slowing beam to apply

sidebands at 10 MHz to the main slowing transition and to the repumps. Currently, however, we find
we have improved slowing without the white-light modulation and instead more finely optimizing
the rate at which we chirp the frequency of the slowing lasers. Even without the EOMs, we do still
have sidebands due to the Pockels cell polarization switching (5 MHz) and the hyperfine components
in the slowing beam (14 MHz). There is a larger hyperfine splitting that is also adressed, but at
760 MHz detuning, these components are too far away to affect one another. We have varied theslowing Pockel’s cell chopping rate between 1.5 and 5 MHz, and have not seen a degradation inslow molecule signal within this frequency range. Of course, no Pockels cell polarization switchingwhatsoever is deleterious to the slowing.

5.4

Optimizations
To produce a large enough flux of slowed molecules to work towards implementing our MOT,

we underwent a number of optimizations to our slowing vacuum system, lasers, and timing sequences.

56
35400 m/s2
6000 m/s2
7000 m/s2

2.5

counts/s (x104)

2
1.5
1
0.5
0
-0.5

0

10

20

30

40

50

60

time after ablation (ms)Figure 5.3: By varying the assumed deceleration for slowing sequences designed to slow moleculesfrom 110 to 30 m/s (lasers chirped from resonance frequencies of 100 to 40 m/s) we can determine
our actual deceleration rate. These sequences used microwave remixing of N 00 =2 levels.

To ensure that we had enough power in all the appropriate lasers and microwaves to effectour best slowing, we tried varying the powers in different components. The most critical is the v 00 =0
laser, yet we still found no reduction in slow molecule signal for an intermediate slowing sequence(slowing to 50 m/s) up to a reduction of 50% in power. The v 00 =1 repump laser power could be
reduced by a factor of 3 before showing any change. The v 00 =2 repump required a drop in powerof a factor of 5 before it began to lose efficacy. The microwave power being delivered to the horns
had to be reduced by 30 dB before the molecules produced by this intermediate slowing sequencedegraded.

5.5

Helium flow rate dependence
Before installing an in-vacuum shutter we found that slowing to low velocities could betterbe accomplished with low helium buffer gas flow rates, despite lesser initial molecule number at low
flow rates. As shown in Figure 5.4, although 1.5 sccm starts with many more molecules at 100 m/s,
for slowing to or below 35 m/s we found that 0.5 sccm produced a greater flux of slow molecules.

57

average counts/s (x104)

10

1.5 sccm
1.0 sccm
0.5 sccm

8

unslowed

6

slowing to 55 m/s
420

slowing to 35 m/s
0

20

40

60

80

100

120

velocity (m/s)

Figure 5.4: Average counts/second over a 12 ms time window occuring after slowing for slowing
sequences to 35 or 55 m/s (vs unslowed) for different flow rates (purple: 0.5 sccm, green: 1.0 sccm,
and orange: 1.5 sccm). These data were taken before the implementation of the in vacuum shutter.

A possible explanation for this phenomenon is that the vacuum pressure in the slowing region
due to the constant helium flow being supplied to the cell is too high. We note that the space inthe slowing region is fairly constrained directly outside the cell, and so allowing for larger expansion
volume or more cryopumping could help. In addition to reducing the vacuum pressure after the
shutter, we find that the shutter also prevents unnecessary heating of the cell, which itself decreases
molecule production, as mentioned in Chapter 4. Finally, the shutter should prevent line-of-sighthelium from chasing down the slow YO molecules and interfering with the MOT. As will be discussed
in Chapter 7, we find that the now installed in-vacuum shutter allows for similar sized MOTs to beloaded for different flow rates, instead of falling off swiftly with increased helium buffer gas flow.

5.6

Optical repumping of N"=2
As discussed in Chapter 2, we have a variety of options for plugging leaks in our molecules’

cycling transition. One of the changes implemented that had a large effect on our ability to slow

58
molecules from production speeds to trappable velocities was to modify the way we repumped
molecules that fell into the X 2 Σ state N 00 =2, v 00 =0 level. Following this change, it was necessary
to reoptimize our slowing timing sequences. The new optimized deceleration (frequency chirp) rate
was congruent with the 60 percent change in number of states coupled /scattering rate for the new
optical cycling transition. The optimal deceleration rate for our slowing timing sequences changed
from 5500 m/s2 to 8000 m/s2 , an increase of 60 percent. This implies a photon scattering rateincrease from approximately 9.2×105 per second to 1.3×106 per second. The photon recoil velocityof YO on the 614 nm cooling transition is 6 mm/s.
By integrating the slowed molecule LIF signal for the optical versus the microwave repumpingof the N 00 =2 level, we find that the optical repumping yields a 19× larger flux of slowed molecules.
This is a larger effect than we would assume based on the reduced divergence of the molecularbeam. The mechanism by which the improvement is so great is not yet determined, but may be due
to ‘dead’ spots along the slowing region for microwaves, whereas the N 00 =2 optical beam can bevery well overlapped with the laser slowing beam. The other possibility, as mentioned in Chapter
2, is the difficulty of using microwaves to pump states with larger F to smaller F , as the potential
for polarization dark states arises. While we have done some experimenting with rapid switching
between microwave horns at different polarizations to see if that improves the utility of microwave
repumping of N 00 =2, the results have been inconclusive.

59

slowing to 5 m/s
microwave repumping

LIF (arb. u)

2

optical repumping

1

0
20

30

40

50

time after ablation (ms)60

Figure 5.5: Comparison of the effect of N ”=2 optical or microwave repumping in slowing on the
production of slowed molecules. The same length of vacuum chamber and appropriately optimized
frequency chirp rates of the slowing lasers were used.

By choosing different frequency chirp endpoints and slowing timings, we can slow our molecules
to our choice of velocity, as shown in Figure 5.6. Timing sequences are determined by using the
known propagation distance from the cell to the detection region, assuming a deceleration rate (typically around 6000-8000 m/s2 ) and frequency chirping the lasers from the initial frequency minus
10 m/s to the goal frequency plus 10 m/s. Since multiple hyperfine components are addresssed
and the Pockel’s cell adds sidebands at 5 MHz, the slowing lasers can interact with molecules ina range around their resonance frequency. Timings are designed such that the peak of the desired
slow molecules arrive in the detection region immediately after the slowing shuts off, to minimize
the effects of transverse divergence.

60

18
unslowed
chirp 100-60 m/s
chirp 100-30 m/s
chirp 100-20 m/s

Counts/s x104

14
10
6
2
20

40

60

80

Speed (m/s)

100

120

140

Figure 5.6: Different chirp parameters yield different velocities of slowed molecules. The verticalaxis is the average count rate over a 17 ms window ending after slowing detected with a low power
Doppler sensitive detection beam. These slowing sequences all utilized optical repumping of N 00 =2.

5.7

Detection efficiency estimates
In order to turn the fluorescence collected by our PMT or CCD into a total molecule number,

we have to determine the total detection efficiency of our imaging systems. The only thing differing
between our CCD and PMT systems is the quantum efficiencies of the sensors themselves, which
are 93 percent for the CCD and 20 percent for our PMT at our detection wavelength of 614 nm.
The part numbers and details of the collection system are discussed more thoroughly in Chapter
3. The collection systems both have a color filter which has 97 percent transmission for 614 nm
light, and four anti-reflection coated lenses which each have a transmission of 99.8 percent. The
vacuum windows are uncoated, and so have a transmission of 96 percent per interface. We havea geometric solid angle efficiency determined by the size of the first lens and its distance from the
MOT region, which for a 2 inch lens 6 inches away is a factor of 1/144. Finally, there is likely
an imperfectness factor for the solid angle estimation (not all photons that hit the first lens will

61
make it to the detector, which is probably of order unity. As a conservative estimate, I will here
assume that it is one, giving a worst case molecule number. All these factors multiplied together
appropriately yield a photon detection efficiency of 0.58 and 0.12 percent for the CCD and PMT
respectively.
For determining the number of molecules transiting through the detection region with theunslowed beam, we use a full power zero detuned orthogonal beam, and assume that our photon
scattering rate is 1×106 per second (previously determined by shutting off the v”=1 repump andmeasuring the time constant of loss into v”=1). The transit time through the detection beam
for a unslowed molecule moving at 120 m/s is 83 µs, meaning each photon has time to scatter
83 photons. Integrating the counts registered on the CCD or those measured by the PMT gavevery similar number estimates after applying the appropriate correction factor, 1.2×106 or 1.3×106
unslowed molecules transiting the detection region respectively for the CCD and PMT.
For detecting slowed molecules we use a low power probe beam at 45 degrees with respect tothe molecular propagation direction. In order to avoid velocity confusion, we shut off the 760 MHz
component in the laser beam, so as to avoid attributing faster molecules to the slow molecule signal.
Because of the number of states involved, each time a photon is cycled, there is then a 1/12 chanceof falling into the unaddressed state. So, each molecule can scatter on average 12 photons before
going dark. The transit time through the detection region for a slow molecule is more than 1 ms,
which is plenty of time to scatter all 12 photons. By integrating the PMT signal after slowing andassuming 12 photons are scattered by each molecule, we estimate that 5.3×104 molecules are slowed
to approximately 5 m/s.

5.8

Total gains realized
For production of 5 m/s molecules in the MOT region, we have realized a total change insignal of a factor of 7500 (53000 molecules slowed vs 7). If we define a slowing efficiency as thenumber of slowed molecules divided by the number of initial unslowed molecules detected in thetrap region, we can also compare this metric of our current system to that in 2014. From the62unslowed molecular signal, we estimate a flux of approximately 1.3×106 molecules transiting thedetection region for a typical molecular pulse on a good day. This indicates a slowing efficiency of
4 percent for our current system taking molecules from 120 m/s to 5 m/s. In contrast, with our old
slowing we realized an efficiency of 0.1 percent [20] from 70 m/s to less than 10 m/s. This level of
improvement is significant, and was critical for being able to detect and improve our MOT signal,
which is detailed in Chapter 7.
While there are likely still further gains to be made in the system, especially in molecule
production, the level of slowing actualized here is sufficient for us to load our MOT with several
hundred molecules, as will be more comprehensively described in Chapter 7. The largest improvements found were by switching from a repetition rate of 10 Hz to 1 Hz (11×), changing from a
2-stage buffer gas cell to a single stage cell (400×, though at a faster velocity and so requiring moreslowing), and switching from microwave to optical repumping of the N ”=2 manifold (19×). Allother improvements to the slowing were of order unity.

Chapter 6

3D MOT coil design

6.1

Introduction
MOT trapping force calculations [21] indicate that we need a magnetic field gradient of about

10 Gauss per cm in the trapping region (approximately 1.5 cm large) in order to effectively load
molecules into our MOT. Additionally, in order to not decrease our photon scattering rate due tomagnetic sublevel dark states in the ground state, we need to be switching the magnetic fields on
the order of the scattering rate (a few MHz). The current and voltage requirements for out of
vacuum coils would be enormous do to their required size, and so we have designed and constructedvacuum compatible MOT coils that can yield the required fields and field switching. The current
set of in-vacuum coils (before they were blackened to reduce light scatter) are shown in Figure 6.1.

64

Figure 6.1: The AC magnetic-field producing coils that provide the trapping gradients for our MOT.
The blackened copper C-clamps on the left provide the heat dissipation and structural support forthe bottom boards. Each board has coil traces on each side, allowing for 4×7 windings on each halfof the coils. The white blocks on the top right are the high Q capacitors that tune the frequency of
the resonant circuit.

While we initially made MOT coils out of copper coated alumina that could be machinedin house, the current MOT coils are on an amorphous aluminum nitride substrate, as the aluminum nitride has a higher thermal conductivity (170 Watts/(meter×Kelvin)) as opposed to alumina (25 Watts/(meter×Kelvin)). In addition, the thicker copper should result in less effect due

65
to skin depth, more surface area due to thicker traces, as well as reduction of rough edges dueto the difficulty of cutting the thin copper. However, the thicker copper also necessitates more
spacing between traces, as smaller cutting tools cannot manage the process. Wider gaps between
traces also mean we must make the inner diameter somewhat smaller to accomplish the same fields.
Additionally, AlN is much harder than alumina, so the cutting must be done with diamond tools,
making the fabrication of the coils more difficult. The magnetic field coils currently installed in thechamber were fabricated by REMTEC. The PADs layout schematic of the coils are displayed andexplained in Appendix A
There are a number of design considerations that went into the making of the coils. To make alarge AC field at 5 MHz, we decided to go with a LC resonant tank circuit, as that is an efficient way
to produce reasonably large AC currents. These resonant circuits also build up a large voltage, andso the components need to be high voltage compatible. Because the coil is in a vacuum chamber,
we both want to avoid dissipating more power in them than necessary (and so wanting a low loss
circuit) as well to have good thermal connection to the outside to prevent overheating. As the coils
are close to the MOT beams, we also have to consider ways in which to minimize the scattered lightoff of them, which is detrimental to our signal-to-noise. Within this chapter I detail some of theconsiderations regarding impedance matching, the expected magnetic field gradients, the assembly,
and the circuitry for making sure the coils are always being driven on resonance.

6.2

Change to parallel configuration of the MOT coils
Up until September 2015, we were running the coils in a series configuration, as shown in

Figure 6.2.

66

coil 1
Impedance
Matching

coil 2
C_tuneFigure 6.2: Series MOT coil configuration.

While this configuration has the benefit of knowing that the same current is necessarily going
through both coils, due to the resonant buildup of voltage between the capacitor and inductors,
and dropping half of that voltage over each coil, we were applying an electric field of approximately
450 V/cm between the two halves of the trap. While this would eventually cause problems due tomixing of levels in the A2 Π state, thus causing leakage into N ”=0 and 2 in the v”=1 state, themore pressing issue is actually the shifting of the N ”=0,1,2 levels in the v”=0 state with respect
to each other. The shift of the transition in the quadratic regime between two states of opposite
parity is given by:∆U =p(µ × E)2 + (energyfield-free )2 − energyfield-free(6.1)

The electric dipole moment of YO in the Σ state is 4.5 Debye. With our applied electric field, wewere then causing a frequency shift of ∼880 MHz on the N ”=0↔N"=1 transition. Given that our
Rabi rate is about 25 MHz [20], this means we are unable to bring our molecules back to N ”=1 tocontinue optical cycling (except during the small amount of time during the 5 MHz switching that
we are applying the microwaves at resonance).
In order to address this issue, we rewired the coils in a parallel configuration, as depicted in
Figure 6.3.

67

coil 1coil 2

Impedance
Matching
C_tuneFigure 6.3: Parallel MOT coil configuration.

This design should greatly reduce the electric field we are applying across the coils. With
this design, the apparent resistance at resonance for the un-impedance matched circuit (given by
the Smith chart function of the network analyzer) is 6 ohms, which is consistent with the 24 ohms
we saw in the series configuration. In order to get the 2 Amps necessary to produce our desiredmagnetic fields, we will still need to drive the circuit at ∼24 Watts. Impedance matching was again
achievable with a toroidal transformer, and yielded a -45 dB dip in reflection at resonance. The
loaded quality factor Q is 39, again consistent with the impedance of 6 Ohms, the reduction inapparent L of a factor of 4 from the change from the series to parallel configuration, and the factorof 2 between loaded and unloaded Q.

6.3

Impedance matching
The RF amplifier used to drive our coils has a source impedance of 50 ohms, so for maximal

power transfer it is necessary to impedance match the coils to appear as if they were 50 ohms to
the generator. There are a few different methods to try and accomplish this. What we used forthe 2D MOT was a wound toroidal transformer, adjusted to maximize the dip in reflection at theresonant frequency. For the current coils, I was also able to achieve good impedance matching witha toroidal transformer in our set up with very careful winding. The Smith chart from the network
analyzer of the impedance matched circuit read 50 ohms at resonance and we achieved a -45 dB dip

68
in reflection for the impedance matched circuit, indicating very good power transfer.
While we currently use the wrapped toroidal transformer, there are other methods of matching
the impedance. It is possible to match the load (purely resistive for our LC tank circuit at resonance)
to the source using a matching network designed to operate at the resonance frequency. The simplest
network possible is an L network made of two elements, with three elements there are Π and T
networks. In Figure 6.4 are depicted the two possible L network configurations, as a low pass or ahigh pass LC filter.

(a)

(b)
Cmatch

LmatchCmatchRload

LmatchRload

Figure 6.4: Low pass(a) and high pass (b) L-network configurations.

For both configurations, the values of the elements required are straightforward to calculate.
The design "Q" (not the same as the quality factor) is given byQ=p
Rsource /Rload − 1(6.2)

Then, the reactance of the series leg is given by:
Xseries = Q × Rsource(6.3)

While the reactance of the parallel leg is:
Xparallel = Rload /Q(6.4)

For the series configuration board, from the network analyzer we find that our impedance atresonance is 23 ohms. So, our design Q is 1.08. For an L-network configuration, this means we

69
can use a low pass configuration with 1300 pF and 1700 nH, or use a high pass configuration with
600 pF and 780 nH. I found that either configuration worked in approximately the same way, sochoosing whichever components are easier should be fine. I decided on the low pass configuration,
and wound the inductor by hand using an appropriate toroidal core, as none of the bulk ones instock in that size range allowed for ∼1 Amp of current. With this form of impedance matching,
we have a -13 dB dip in reflection, meaning 95 percent of the power is coupled into the MOT coils.
The MOT coils were tested in this configuration with high RF power input, and were able to run
with 30 Watts of power, and the board temperature rose to 85 ◦ C in air. By using the L-matching
network, the perceived loaded quality factor Q will necessarily be smaller than the Q of the tankcircuit alone, a.k.a. the unloaded Q which we know to be
Qunloaded = ω × L/R ,(6.5)

Qloaded = Qunloaded /(1 + κ) = Qunloaded /2 ,(6.6)

while the loaded Q is

where κ is the coupling parameter. For critical coupling (maximal power transfer) κ is equal to 1
and Qloaded = Qunloaded /2 [59].
Other options for impedance matching include 3 element matching networks, called Π or T
networks, again according to their shape. These are depicted in figure 6.5. In each case, X1 and X3
will be one type (inductor or capacitor) while X2 will be the other type. Both Π and T networks are
configured by choosing a virtual resistance in the middle that is larger (T network) or smaller (Πnetwork) than both the source and the load. Then, you make two L type networks, one matching
the source to the virtual resistance, the other matching the load, and combine the two. This seemed
to frequently require difficult values of circuit components, at least for the parameters of our coils.

(a)

70

(b)

X1

X2
X1

X3

Rload

X3
X2

Rload

Figure 6.5: Π (a) and T (b) matching networks.

6.4

Magnetic fields
In order to design the coils, we calculate the expected magnetic field due to a set of coils. The

boards we use are double sided PCBs. The design we currently have requires 4 layers of coils (twoboards) 7 traces wide for each side of the MOT. The coils are 1.2 mm away from each other radially,
with an inner diameter of 1.9 cm, z spacing of 1.5 mm, and the large z spacing between halves ofthe MOT of 2.3 cm. The inner radius and the z spacing between halves are large in an attempt
to reduce light scatter from the MOT beams, while the 1.2 mm trace to trace spacing is as small
as can be efficiently cut for our PCB material. The small z spacing is determined by the thicknessof the boards from which we cut the coils. The current coils are clad in .008" copper (ie 205 µm
thick) on an aluminum nitride substrate. The skin depth of copper at 5 MHz is approximately 35µm, so we should not be limited by the cladding thickness for the resistance of the coils.
In Figure 6.6 are plotted the anticipated magnetic fields and gradients in both axial and radial
directions due to the coils, assuming that 1 Amp of current is supplied through each coil. The values
are calculated numerically using the Biot-Savart law, and assuming that each spiral was a single
circle, with Matlab.

(a)

(b)

Magnetic Field (axial)

14

5

12

71
Magnetic Field (radial)4

B [gauss]

B [gauss]

10
8
6

3
2

4
1

2
0
0

5

10

15

0
0

20

5

z from center of MOT [mm]

(c)

15

20

(d)
Magnetic Field Gradient (axial)

15

6

dB/dr [gauss/cm]

10dB/dz [gauss/cm]

10r [mm]

5
0
-5
-10

4
2
0
-2
-4

0

5

10

15

z from center of MOT [mm]20Magnetic field gradient (radial)

0

5

10

15

20

r [mm]

Figure 6.6: Predicted fields (green) and gradients (red) in the axial (left) and radial (right) dimenstions. Fields and gradients are calculated for 1 Amp drive through each coil and scale up linearlywith amperage.

6.5

Coil characterization
By driving the coils with a network analyzer on resonance and moving a small pick up coilwith a micrometer, we can trace out the magnitude of the magnetic field energy density. The squareroot of the power ratio picked up then yields a value proportional to the magnetic field strength asa function of position, as can be seen for the axial direction in Figure 6.7.

72

Figure 6.7: (a) Sqrt(ratio of power picked up to drive power) vs position in the axial direction.
A quadrupole field should show two linear lines with a cusp at the magnetic field zero. (b) The
white horizontal line indicates the expected magnetic field zero location in this dimension with themagnetic pickup coil at the measured zero. The double-headed arrow indicates the direction of the
motion of the micrometer.

Similarly, we can perform the same measurement in both radial directions, that parallel to themolecular beam as shown in Figure 6.8 and transverse to the molecular beam as shown in Figure
6.9.

73

Figure 6.8: (a) Sqrt(ratio of power picked up to drive power) vs position in the radial direction along
the molecule propagation direction. A quadrupole field should show two linear lines with a cusp
at the magnetic field zero. (b) The white horizontal line indicates the expected magnetic field zero
location in this dimension with the magnetic pickup coil at the measured zero. The double-headed
arrow indicates the direction of the motion of the micrometer.

74

Figure 6.9: (a) Sqrt(ratio of power picked up to drive power) vs position in the radial direction
orthogonal to the molecule propagation direction. A quadrupole field should show two linear lines
with a cusp at the magnetic field zero. (b) The white horizontal line indicates the expected magnetic
field zero location in this dimension with the magnetic pickup coil at the measured zero. The doubleheaded arrow indicates the direction of the motion of the micrometer.
Together, these AC pickup measurements confirm the uniformity of the magnetic field gradientnear the trap center and that the coil is behaving as needed.

6.6Blackening methods
Because of the laser light in the MOT region from the slowing laser beam and the MOT beams

themselves, we wish to have the coils be blackened in some way to reduce light scatter. Because
we use fluorescence detection on the same transition as our main cooling transition, we cannot
completely avoid signal contamination by light scatter, though an orange color filter does blockout the light from the repumps. The components of the board, the substrate and the copper traces
themselves present different issues with regards to blackening. Initially we attempted blackening the75
coils with the black paint made by Ball Aerospace known as Ball Black or Vac Cote. While it gives
a very nice matte black coating, we found that Ball Black is not high voltage compatible (causing
arcing between different parts of the board), probably due to a small amount of conductivity ofthe paint. Confirming this hypothesis is the fact that the measured quality factor Q of the circuit
dropped after painting.
In contrast to the failed Ball Black coating, the copper oxide blackening method layed out inappendix G.2 of John Barry’s thesis ([53]) achieves blackness of the copper without impinging on
the electrical qualities of the circuit. The method involves bringing a sodium hydroxide and sodium
chlorite solution to boiling and immersing the copper to be blackened for a couple of minutes toachieve a copper(II) oxide coating on all exposed copper surfaces. This procedure yields a very
matte black surface on copper, but does not affect the color of other surfaces. This means thatwhile we can blacken the copper, we do not as yet have a method to blacken the ceramic substrate.
However, we anticipate that the copper would be the biggest issue as far as light scatter is concerned.

6.7

Heat link and mounting construction
In order to not have water cooling inside our vacuum chamber, we have a large solid copper

heatlink that connects to a high voltage, high amperage, copper vacuum feed-through (Lesker
EFT0313753). The outside vacuum end we attach to a chilled water pipe to allow heat transfer.
The mounting and in vacuum section of the heatlink is shown in Figure 6.10. The design leaves room
for all MOT beams, the longitudinal slowing beam, and side access for PMT and CCD viewing.

76

Figure 6.10: Copper heatlink and coil mounts.

In September 2015, we modified the copper electric feedthrough that is our heatlink out of
vacuum. Hans bored out the center for us to accommodate a water line going in through the middle
and out along the edges and out through a tee in order to get chilled water closer to the coils.
Additionally, by cutting some distance off of the feedthrough, the cooling power delivered to thecoils was improved. By using a combination of water and ethylene glycol in a chiller, we can run
the chiller at -30 degrees C. This then allows the coil to be run at 100 percent duty cycle with 50
Watts input power, with the boards reaching a temperature of 55 degrees C in vacuum. We also
can modulate the power of the coils such that they are at low power while waiting for the next
experimental cycle, and then full power for loading and trapping. In this way, we can maintainthe temperature of the coils at room temperature.The pH of the water/glycol mixture needs to bemonitored, as the inhibitor used to prevent corrosion stop being effective after 6 months or so.
Further notes on the assembly of the coils are given in Appendix A.

77

6.8

Pound locking to resonance of coils
Because the resonance frequency of the coils can drift with variation of temperature, we are

currently locking the drive signal to the center of the resonance using the Pound technique [60].
How we achieve this is depicted in the diagram in Figure 6.11.

DDS 0

To
EOMs

Ch 0 10 MHz full scale
Ch 1 9.9 MHz full scale
Ch 2 1 MHz 1/8 scale
Ch 3 1 MHz full scale(145 deg phase offset)

-3 dB
DDS 1

Ref clockRI+20 dB
11 MHz LP-7dB+52 dB

Ch 1 5 MHz full scale~65 MHz

Func gen(scanning)L

Ch 0 5 MHz full scale(with phase offset)

VCO

Voltage offset
and summer

50 ohmSine to TTL
comparator

dir
coup

Pockel’s
cell

B
Loop
filter

30 kHz LP

L

I
R

A

D

+20 dB+20 dB

1.9 MHz LP

1.4 MHz LP

CPower detector

MOT

Figure 6.11: Schematic diagram of MOT coil frequency lock. We maintain the drive of our coils on
resonance by using a Pound lock. Sidebands to the drive are applied to the coil 1 MHz away, andthe signal reflected from the coil is demodulated to DC, giving an error signal we can feed into theloop filter.

By scanning the drive frequency over resonance, we trace out the error signal as shown in
Figure 6.12. The center downward crossing is the resonance of the coils at 5 MHz, while the two

78
upwards crossings are the plus and minus 1 MHz points. One trace is the voltage being applied by
the scan, while the other is the lock error signal (while unlocked).

(a) full scale(b) zoom in

Figure 6.12: Frequency scanning MOT Pound lock error signal.

The VCO driving the clock of DDS 1 is a minicircuits ZX95-100, which has a tuning of
3.6 MHz/V, so we determine that this scan is sweeping out 4.3 MHz/ms for the VCO and .33MHz/ms
for the MOT drive frequency. Zooming in on the resonance zero crossing and extracting a slope, wefind that the conversion from error signal to MOT frequency error is 0.1 kHz/mV.
Finally, when the servo loop is closed, the error signal tells us our maximum frequency excursion and so phase error. We found that the error signal had maximum excursions of ±5 mV, whichcorresponds to frequency excursions of ∼0.5 kHz. From the calculated transfer function and the Q
for these coils of 70, this indicates that we have a maximum phase error of .02 rads, which should
be well below our needed stability.
With the specifics of the MOT coil design and installation discussed, I can proceed to cover
the experimental implementation of our MOT in Chapter 7.

Chapter 7

A three-dimensional molecular MOT of YO

7.1

Overview
In this chapter I will discuss some of the considerations that go in place for implementing amolecular MOT on a type II cooling transition. Finally, I present our implementation of the MOT
in three-dimensions along with some preliminary analysis of our system.

7.2

Fundamentals of molecular MOTing
As described in Chapter 2, the first step towards laser cooling is a sufficiently closed andrapidlycycling addressable transition in the molecule. While Doppler laser cooling can produce
slowing of molecules, in order to actually trap them we require a location-dependent force, in
addition to the velocity-dependent force given by the laser cooling. This is achievable by applying
a magnetic field gradient and using a transition with a differential magnetic g-factor between the
ground and excited state, such that the detuning of the transition with respect to the laser beams
has a position dependence. In this case, the center of the trap will be where the magnetic field iszero. The mechanism of this is diagramatically depicted in Figure 7.1.

80

m=+1

F' = 1

m=0
m=-1

δ

σ-

F" = 0X
Figure 7.1: Fundamentals of MOT operation: by driving with the correct polarization of light on
a transition with a differential magnetic moment between the lower and excited states, a magnetic
field gradient in combination with red-detuned (δ) laser beams can provide a restoring force to themagnetic field zero of the trap. Because the magnetic fields produced by two anti-Helmholtz coils
are a spherical quadrupole, the helicity of the axial laser beams must be the opposite of that of theradial laser beams.

Because of the strategy used to maintain rotational closure by exciting from a higher to alower rotational level, the transitions used for molecular MOTing end up being from a larger F 0 ’
to a smaller F 0 , complicating the simple picture in Figure 7.1 somewhat [16]. While most atomic
MOTs are conducted on a transition like the one in Figure 7.2 (a), where F 0 ’ is smaller than F 0 , a
few others [46] and molecular MOTs are conducted on transitions as shown in part (b). It is clear
to see that while the Type I MOTs allow the atom or molecule to return to a laser-addressable
state upon decay to the ground state, we find that there is the possiblity in type II MOTs to decay
to states that are only addressable by the anti-trapping MOT beam, which is detrimental to thecooling process.

81

mf'=1

mf'=0

mf'=0
mf'=-1

mf"=1
mf"=0
mf"=0

mf"=-1x,Bx,B

Figure 7.2: MOT types are described based on whether the trapping transition is from a lower F 00
to a higher F 0 (type I, left) or a higher F 00 to a lower F 0 (type II, right).

In order to avoid pumping light into these polarization dark states from which they are
either unaddressable or only addressable by the wrong laser beam, we choose to rapidly switch
the polarization of our MOT beams with a fast voltage-variable waveplate, or Pockels cell. Of
course, if we do only that, we find that we are switching between a trapping configuration of the
MOT and a fully anti-trapping one. To resolve this, we simultaneously switch the magnetic field
gradient with the in-vacuum magnetic field coils discussed in Chapter 6, allowing for resolving
the polarization dark states while always maintaining a trapping configuration. This means that
we have a certain phase ambiguity that must be determine in the experiment in the relative drive
between the switching signal that goes to the Pockel’s cell and the AC magnetic field that is applied,
as shown in Figure 7.3. While the appropriate delay is theoretically determinable to within 180
degrees in advance, because of cable length and electrical delays, we find it more straightforward todetermine the appropriate phase offset experimentally.

φMOT

82

σ+

σ-

B
Figure 7.3: Phase for the Type II MOT operation refers to the delay between the polarization
switching of the MOT beams and the magnetic field oscillation of the MOT coils.

Our group previously implemented a MOT in one and two dimensions utilizing a baseballcoil allowing for a 2D quadrupole magnetic field spanning about 10 cm, which resonated at 2 MHz.
This allowed us to demonstrate Doppler cooling and MOT action in the directions transverse to themolecular beam [21]. This gave us the knowledge that the type II MOT was suitable for use in ourmolecule, and gave confidence when moving towards the 3D implementation described here.

7.3

1D MOT reconfirmation
In an alternative method to our group’s one and two-dimensional MOT implementations

with a baseball field coil [21], we can use the anti-Helmholtz 3D magnetic field coils and apply only
the MOT laser beam in the axial (perpendicular to molecular beam) direction. This allowed for
optimization of the correct phase offset between the field coils and the polarization chopping in ourcurrent system, with a larger signal than initially achieved when searching for our 3D MOT, as
shown in Figure 7.4. The phase offset for the 1D MOT is of course the same one that optimizes the
3D MOT.

peak differential signal (counts/sec)

83
104

5x103

0

phase offset (degrees)-5x103-104

Figure 7.4: Differential signal (in phase minus 180 degrees out of phase) peak 1D MOT signal.
Horizontal axis is the DDS supplied offset phase between the MOT coil drive and the Pockels celldrive.

When operating at the optimal phase, we observe the molecular beam as it is compressed or
anticompressed into the field of view of the PMT, as shown in Figure 7.5. The 1D MOT signal size
is approximately 1 percent of the unperturbed signal. While this 1D MOT implementation is not a
step forward scientifically, as we had demonstrated the 1D MOT previously, it confirmed that our
3D MOT coils were working and gave us confidence while working on trapping of the molecularbeam. We do not consider it surprising that the 1D MOT effect is assymetric with regards todetuning, as we have previously noted that the detuning dependence is quite complicated due tothe closely spaced hyperfine levels in YO [21].

84

red detuned
blue detuned

counts/sec

10000

5000

0

-5000

5

10

15

20

25

30

35

time [ms]Figure 7.5: Differential (in phase minus out of phase) signal of 1D MOT operation on unslowed
beam, for red detuning and blue detuning of all hyperfine components by 5 MHz.

7.4

3D MOT
The timing sequence used to load the MOT is shown in Figure 7.6. A slowing sequence isperformed that creates a large flux of 5 m/s molecules, and then the slowing beam is held on fora longer period of time. As will be mentioned later on in the chapter, this allows molecules to be
slowed to ∼0 m/s. Since the frequency is no longer chirped during this last 12 ms, the slowing lasers
remain relatively far detuned from at rest molecules (32 MHz) and so only weakly interact withthe molecules during this time. The in-vacuum shutter shuts after the molecules pass, in order toprevent line-of-sight helium collisions from the cell (the buffer gas flow is continuous) and to prevent
heating of the buffer gas cell due to the various lasers in the slowing beam.

85

ablationslowing

100 m/s

chirp vel. center

20 m/sin-vacuum shutter

0

4

6 8

18.5

40

time (ms)Figure 7.6: timing diagram used for loading MOT

The signal obtained from loading the MOT is shown in Figure 7.7. In order to improve
clarity and prevent confusion due to slow but untrapped molecules transiting the detection region,
the MOT data is shown as a correct phase signal minus a 180 degrees out of phase signal.

2

1 cm

1

1.5
1

0.5

0.5

counts per pixel

differential counts/sec (X105)

1.5

2.5

0

0
20

30

40

50

60

70

time after ablation [ms]

80

1 cm

Figure 7.7: Differential (in phase minus out of phase) detection of MOT loaded at 20 G/cm RMS
magnetic field gradient via PMT (left ) or CCD (right). The CCD is exposed from 30 to 50 ms
after ablation fire, and processed with a Gaussian smoothing function with sigma = 1 mm.

We estimate that the photon scattering rate of moleules in the MOT by assuming a saturation
parameter of 1 and our known detuning. This yields an estimated photon scattering rate of 650×103
per second. We plan to measure the scattering rate in the near future, but this estimate and the

86imaging system efficiencies discussed in Chapter 5 indicate that our peak molecule number loaded in
the MOT is ∼2000 molecules. As mentioned in Chapter 5, this is a conservative estimate assumingthat there are no inefficiencies in collection of photons within our lens’ solid angle.
We have also implemented optical repumping of N 00 =3 via the J 0 = 5/2 level of the A2 Π3/2 ,which can then decay only back to N 00 =1 to rejoin the cycling transition or directly back to N 00 =3
due to angular momentum selection rules. We put this laser component (with an applied 770 MHz
splitting) in the slowing beam and then kept it on during the MOT. Its effect on the MOT signal
is shown in Figure 7.8. We see that the total signal is increased by about 30 percent, but with nosignificant effect on lifetime. We believe then that this repump is not so much plugging a large leakchannel, but rather incorporating molecules that exited the buffer gas cell in the N 00 =3 state andbringing them into the main cycling transition.

87

with N"=3 repump
x104

without N"=3 repump

Figure 7.8: Differential (in phase-out of phase) PMT trace of MOT signal when using N 00 =3 optical
repump in slowing (orange trace) and MOT or when not (green trace).

7.5

Characterization
We can vary the detuning of the cooling lasers in the MOT beams and observe the effecton the MOT, as shown in Figure 7.9. All traces use the same slowing sequence and magnetic
field gradient of 20 G/cm RMS. Under these circumstances, we find that the best loading occurs
for 9 MHz red detuning of all hyperfine sideband of the v 00 =0, N 00 =1 laser from their respective
resonance. We have not yet experimented substantially with controlling the detuning of the different
hyperfine components seperately from each other. We note that the range of detunings over whichsome MOT effect is visible is actually fairly large, greater than 20 MHz. Blue detunings do notallow loading of the MOT, however.

x104

88

3 MHz
6 MHz
9 MHz
12 MHz16 MHzFigure 7.9: Dependence on the main cooling-laser components’ detuning for the MOT operatingwith 20 G/cm field gradient. Maximal loading is found at 9 MHz red detuning of all hyperfine
components in the laser addressing the v”=0, N”=1 level.

By varying the magnetic field gradient applied to the trapping coils, we find different efficiencies of loading of the MOT, though not a clear change in trap lifetime. A comparison of thedifferential (in phase - out of phase) MOT signal observed by the PMT at these varying RMS
magnetic field gradients is shown in Figure 7.10. This comparison was taken with a MOT laser
red-detuning of 6.2 MHz for all hyperfine components, and 25 mW of v 00 =0 laser light per MOT
beam. Here we can see that the number loaded into the MOT improves for RMS field gradients up
to about 18.5 G/cm, after which the improvement levels off.

89

5.4 G/cm
7.6 G/cm
9.7 G/cm
13.0 G/cm
16.6 G/cm
18.5 G/cm
20.4 G/cm

Figure 7.10: Differential LIF of MOT signal using the same slowing sequence but with varying
magnetic field gradients.

Similarly, we can observe the spatial distribution of the molecules in the MOT for thesedifferent field gradients as well, as shown in Figure 7.11. These images were taken with the CCD
exposing from 30 to 50 ms after the ablation fire.

5.4 Gauss/cm

90
1.5

13.0 Gauss/cm

1.5

1

1

1

0.5

0.5

0.5

0

0

0

1.5

18.5 Gauss/cm

1.5

20.4 Gauss/cm

1.5

counts

1 cm

9.7 Gauss/cm

counts

16.6 Gauss/cm

1.5

1

1

1

0.5

0.5

0.5

0

0

0

1 cm

Figure 7.11: Differential LIF of MOT signal using the same slowing sequence (timing, detuning ofslowing beams) and same mot beam detuning for each but with varying magnetic field gradients.
Images are smoothed with a gaussian filter with sigma = 1 mm. Color scales are the same between
images, with units of photon counts registered by the CCD. Each image represents 80 experimental
cycles of averaging, 40 at the correct phase and 40 out of phase which are then subtracted. The
vertical axis is the axial direction of the trap.

While some compression is visibly by eye from the CCD images, we can also be more quantitative. By performing a gaussian fit to the unsmoothed data, we determine the size in the radial(left/right) and axial (up/down) dimensions of the trap, as shown in Figure 7.12. We can see thatthe ratio between the radial and axial size is approximately a factor of two as expected for field
gradients less than 10 G/cm, but oddly for higher gradients the ratio settles to a ratio of approximately 1.2. The fitted trap size does not get smaller for field gradients above 12 G/cm, though as
noted previously the total number loaded is still larger for higher field gradients. We also find thatthe overall size is quite high, suggesting that we are suffering from heating of some kind.

91
8

radialaxial

fitted sigma (mm)

7
6
5
4
3
2
1
0

4

6

8

10

12

14

16

18

20

field gradient (Gauss/cm)
Figure 7.12: Fitted gaussian standard deviations vs applied magnetic field gradient in the MOT for
both radial (blue) and axial (red) dimensions. Error bars indicate 95 percent confidence interval offit.

Before we tried increasing the magnetic field gradient above 13 G/cm, we did attempt apreliminary temperature measurement at 13 G/cm via release and reimage as shown in Figure 7.13.
By plotting the expansion time squared and the width squared of the reimaged trap against eachother, we are able to extract a temperature of 11 mK (0–33 mK), which is indeed quite high comparedto the temperature we would expect of ∼1 mK. We will revisit the temperature measurement after
implementing some further changes to the trap.

no release(a)image 35-37 ms

0.2
0.15

image 37-39 ms

92

0.1

0.1

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02

0

0

0.1
0.05

(b)

[width (mm)]2

0

100
50
0
0

5

10

15

20

25

30

35

40

[free expansion time (ms)]2

differential LIF (arb. u.)(c)no release
image 35-37 ms
image 37-39 ms

10

5

0
20

30

40

50

60

70

80

time after ablation [ms]Figure 7.13: MOT temperature characterization: Imaging the MOT cloud after some period offree expansion (a) and then measuring the gaussian width of the cloud in the axial direction of
the molecular cloud after allowing some amount of time of free flight, the temperature of the cloud
can be extracted (b). The CCD exposure time is 2 ms for each image. Color scale (total counts
registered per pixel on the CCD) of the expanded clouds is scaled up by a factor of 2 for greater
visibility. Error bars represent 95 percent confidence interval of the gaussian fits. (c) Depicts the
LIF recorded by the PMT for the same scenarios in (a).

93
At this time, there are a number of things that could be contributing to heating of themolecules. The first is that we are possibly switching the magnetic fields and polarization of the
MOT too quickly, such that the (unavoidable) sidebands from the Pockels cell are heating some
hyperfine components while cooling others, due to the small (14 MHz) zero-field hyperfine splitting
within the G00 =1 manifold. In order to bring the sidebands further in (while still switching rapidly
enough to avoid polarization dark states) we are currently adapting the coils to have better heatsinking and lower resonance frequency, perhaps around 1.5-2 MHz. During the adaptation, we will
also increase the inner radius of the magnetic field coils and the spacing between coils in order tofurther reduce scattering of laser light in the chamber. Another possible source of heating is if theresistances of the two different halves of the MOT coil are slightly different, then the magnetic fieldzero (trap center) will be switching back and forth between two different positions at the rate of
the coil switching. With our current electrical configuration this uncertainty is unavoidable, but inthe future the two coil halves could be driven by two different phase locked sources and the current
going into each can be confirmed to be equal, preventing any heating from the oscillation of themagnetic field zero.
From the temperature and the initial size of the MOT before expansion, we can also estimate
the trapping frequency. Using the equipartition theorem in only the axial direction, we achieve an
estimate of 30 Hz, which while not fast is within a factor of 2 of that realized by the Doyle groupat Harvard for their initial implementation of a CaF RF MOT [24], though clearly the error bars
on our data need to be improved before any firm conclusions may be drawn.

7.6

Intensity dependence
While endeavouring to load more molecules into our MOT, we found an interesting interrela-tion between the power of the main cooling beams and the lifetime of the MOT. These results areshown in Figure 7.14.

94

counts/second x105

26 mW
12.5 mW
6 mW
2.5 mW
0.8 mW

Figure 7.14: Using different powers for the main cooling transition in the MOT beams changes thenumber of molecules loaded but also affects the lifetime of the MOT. Powers stated are powers per
MOT beam for N 00 =1, v 00 =0 light.

Not only is there a optimum power for loading of ∼12.5 mW per beam, we can also quantify
the effect of the MOT beam power on the lifetime. We perform this characterization by fitting the
MOT signal after 30 ms to an exponential decay. The results of these fits are outlined in Table 7.1.

Table 7.1: Fitted MOT lifetime for different MOT beam main cooling laser powers per beamPower (mW)

Lifetime (ms)

95% fit confidence interval (ms)

26

11.1

9.3-13.6

12.5

12.3

11.4-13.4

6

14.9

13.9-16.0

2.5

17.8

16.2-19.8

0.8

13.8

10.8-18.8

95
The general trend of increased lifetime with lower MOT beam power may be providing aclue as to the short lifetime of our MOT. It suggests that the lifetime is dependent on the photon
scattering rate. This would normally suggest a leak to a dark state, though we have alreadyinvestigated the possibility of loss into N 00 =3 and v 00 =3, and believe that they are not the limiting
factor. Additionally, we hypothesize that the lower MOT beam powers may be yielding a lower
temperature of the trap, which we plan to investigate experimentally in the near future. Because
the loaded molecule signal is highest for 12.5 mW per beam, we usually operate at that power forother characterizations in order to reduce data acquisition time.

7.7

Overslowing for loading the MOT
While working on optimizing the MOT signal, we found that the slowing sequence which

maximizes the flux of molecules at 5 m/s is not in fact the one that maximizes loading of molecules
into the MOT, despite our initial expectation that trappable velocities should be ± 5-10 m/s. In
fact, adding 12 ms of slowing light without frequency chirping to the end of the optimal 5 m/s
slowing timing sequence is the best sequence we have found for MOT loading. In order to better
understand this, we performed a low powered Doppler sensitive detection of the molecules after
various slowing sequences, as shown in Figure 7.15. This measurement occurs for 10 ms after theend of the slowing, and represents the average counts/sec for different velocities within this timeinterval.

average counts/second x104

96
2.5extra 12 ms
extra 7 ms
extra 4 ms
extra 0 ms

2
1.5
1
0.5
0
-0.5
-25

-20

-15

-10

-5

0

5

10

15

20

25

velocity [m/s]

Figure 7.15: Different amounts of slowing time and their effect on the slowed molecule distribution.
The sequence used for 5 m/s slowing is typically 0 extra added time (green), while we find maximal
MOT loading for the +12 ms (orange) slowing sequence.

Ideally we would have a large flux of molecules slowed to zero velocity at the center of thetrap when the slowing shuts off, so it is sensible that the largest MOT signal comes from a slowing
sequence that yields molecules at rest in the MOT region at the shut-off of slowing. It is however
somewhat surprising that the 5 m/s slowing sequence plus an extra 10 ms wasn’t even better for
MOT loading as the molecular distribution is seemingly higher for all slow velocities for an extra
7 ms of slowing than for an extra 12 ms. We are still working to improve our understanding of theefficacy of this timing sequence for loading molecules into the MOT.
While there are clearly improvements to be made to our MOT, we also feel that current number
and lifetime are sufficient to make forward progress. The next step on the horizon experimentally is
implementing further cooling on the narrow-line transition in our molecule. Narrow-line cooling will
yield colder temperatures and is in some ways experimentally more straightforward to implement,
as will be discussed in Chapter 8.

Chapter 8

690 nm Narrow-line transition: prospects for secondary cooling

8.1

Spectroscopy of the A02 ∆3/2 state
In order to characterize the properties of a second stage red MOT on the X 2 Σ to A02 ∆3/2

transition, we first need an estimate of the linewidth of the transition. We acquire this estimate
by comparing the absorption strength of the red transition to that of the known orange transition.
To that end, we have identified the N ”=0,1,2:G”=1 to A02 ∆3/2 transitions using absorption spectroscopy in our cryogenic buffer gas cell, as shown in Table 8.1, in agreement with previous work
[61].

Table 8.1: Identification of X 2 Σ to A02 ∆3/2 transitions
Transition

Frequency (THz)

N"=0, G"=1 → A02 ∆3/2 (-)

434.70310

N"=1, G"=1 → A02 ∆3/2 (+)

434.67989

N"=2, G"=1 → A02 ∆3/2 (-)

434.63333

The energy splitting between N ”=0→ A02 ∆3/2 and N ”=2 → A02 ∆3/2 is N ”(N ” + 1)B, with
N ” = 2, where B is the rotational constant for the X 2 Σ state. Evaluating this yields B = 11.6
GHz, which agrees with the known rotational splitting [44]. By comparison of the absorption on
the N ”=1 → A02 ∆3/2 transition with the N ”=1 →A2 Π1/2 transition and the known lifetime of
the A2 Π1/2 being 33 ns [62], we estimate that the lifetime of the A02 ∆3/2 state is τ =425 ns. We

98note that the N ” = 0,2 to A02 ∆3/2 transitions address a different parity level than the N ”=1 to
A02 ∆3/2 transition, but we do not find a different value of B, indicating that the parity splitting of
the A02 ∆3/2 state is smaller than the Doppler broadened linewidth of ∼60 MHz inside the cell.

8.2

Mixing of the A02 ∆3/2 and A2 Π states
In addition to performing an absorption measurement, we also calculate a lifetime estimate.

While electric dipole forbidden, the decay from the A02 ∆3/2 state is almost entirely due to mixing
with the A2 Π3/2 state, on the order of 3.5% [44]. The molecular potential can be approximatedusing the Rydberg-Klein-Rees (RKR) [63] method for the states of interest. The curves for the X 2 Σ
and A2 Π states can be corroborated with previous work [64]. After using a finite difference method
to determine the wavefunctions to evaluate the vibrational overlap integrals and the hv| 1/r2 |v 0 i
integrals we use the procedure outlined by Chalek and Gole [44] to compose the Hamiltonian including the electronic, rotational, vibrational, spin orbit, and coriolis operators. By diagonalizing
this Hamiltonian for J=3/2, we express the A02 ∆3/2 eigenstate in terms of the Born-Oppenheimer
states, the first few terms of which are:EΨ∆3/2 ,v0 =0 ≈ 0.9865 ∆3/2 , v 0 = 0 − 0.1582 Π3/2 , v 0 = 0−0.0369 Π3/2 , v 0 = 1 + 0.0176 Π1/2 , v 0 = 0 + ...

These coefficients squared indicate the mixing of the A02 ∆3/2 ,v 0 =0 state with other states,with the largest being a 2.5% mixing with the A2 Π3/2 , v 0 =0 state. Summing over the various BornOppenheimer states and their associated Franck-Condon factors yields estimates for the vibrational
branching ratios for the A02 ∆3/2 to X 2 Σ transition. These and other state branching ratios arecompiled in Table 8.2.

99
Table 8.2: Vibrational branching rates for various transitions of interest.
qv1 v2

State 1

State 2v1v2

qv1 v2

0.9924

A2 Π

1/2

X2Σ

1

0

0.00761

0.0074

A2 Π

1/2

X2Σ

1

1

0.975202

2.4×10−4

A2 Π1/2

X2Σ

1

2

0.0164X2Σ

0

3

2×10−6A2 Π1/2

X2Σ

1

3

7.8×10−4

A2 Π3/2

A02 ∆3/2

000.9078A02 ∆3/2

X2Σ

0

0

0.9422

A2 Π

3/2

A02 ∆

0.0860

A02 ∆

3/2

X2Σ

0

1

0.0568

3/2

A02 ∆

0

2

0.0011

0

3

<10−4

v1

State 1

State 2

A2 Π

1/2

X2Σ

1/2

X2Σ

0

A2 Π1/2

X2Σ

A2 Π1/2

A2 Π

A2 Π

A2 Π3/2

0

3/2

0

v2
0

1

3/2

0

2

0.0059

A02 ∆

3/2

X2Σ

A02 ∆3/2

03

3.3×10−4

A02 ∆3/2

X2Σ

Using 2.5% mixing and the known ∼30 ns lifetime of the A2 Π3/2 state [62], we estimate thelifetime of the A02 ∆3/2 state as 1200 ns. These two estimates of the lifetime of the A02 ∆3/2 state,
425 ns from the absorption measurement and 120 ns from calculation are of similar order and give
us a starting point for further calculations. From here on, we use an intermediate estimate of τ =1 µs, yielding a linewidth of γ = 2π×160 kHz.

100

Narrow-line cooling on the X 2 Σ to A02 ∆3/2 transition

8.3

A2Π1/2 v'=0

(a)

(b)

J'=1/2(+)

A'2Δ3/2

A'2Δ3/2

δ0J'=3/2(-)

J'=3/2(-)

mf'=2
mf'=1

F'=1,2g=1/5,3/10

v'=0

σ+

mf'=1
mf'=0 mf'=0
mf'=-1
mf'=-1
mf'=-2σ-G"=0,F"=0
N"=2(+)

mf"=0

X2Σ+

mf"=1

N"=0(+)

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

X2Σ+

v"=1

N"=0(+)

v"=0

mf"=0
g=1

G"=1,F"=1xmf"=-1Figure 8.1: Level structure for the narrow-line MOT. (a) Maroon arrow indicates the transition
used in the red MOT. Gray lines indicate microwave mixing which closes rotational branching.
Red line indicates v”=1 repump, the same as used in the orange MOT. (b) Zeeman structure andMOT scheme. g represents the corresponding magnetic Landé factor. Large arrows indicate counter
propagating circularly polarized laser beams. Both F ”=0 → F 0 =1 and F ”=1→F 0 =2 transitions
can effect a MOT action (maroon arrows).

Once molecules have been cooled with the orange MOT, we wish to further cool them utilizing
the narrow X 2 Σ to A02 ∆3/2 transition. This is acheivable by exciting from the N ” = 0 level to
the A02 ∆3/2 , J 0 =3/2 level, as in Figure 8.1(a). Decays from A02 ∆3/2 can be to either N ”=0 or
2. To maintain cycling, we use microwave mixing to address the v”=0, N ”=0↔1, and N ”=1↔2
rotational transitions, with frequencies 2B0 and 4B0 , where B0 is the rotational constant for thev”=0 level. Similarly, higher vibrational levels can be mixed by applying microwaves resonantwith the N ”=0↔1 and N ”=1↔2 rotational transitions of that vibrational level, e.g. at 2B1 and101
4B1 for v”=1. Additionally, this microwave mixing scheme allows v”>0 vibrational levels to be
repumped with the same lasers used in the orange MOT. The rotational constants for the first few
vibrational levels have been determined and so mixing will be straightforward to implement [65, 66].
The saturation intensity required Isat = (πhc)/(3λ3 τ ), is 60 µW/cm2 , an intensity obtainable withcommercially available diodes.
In addition to the possibility of an optical molasses based on this transition, it is apparent thata narrow-line MOT is also achievable. While a MOT can be made using any or all F ” states due toa non-zero g-factor for both the ground and excited states, the number of frequency components andpolarization considerations go up considerably with the number of states [48]. The simplest possible
MOT action in this system is that for the transition from the N ”=0 level to the A02 ∆3/2 state. The
N ”=0 level has G values 0 and 1, split by ∼760 MHz. A type-I MOT can be performed on bothsublevels, from G”=F ”=1 to F 0 =2 and from G”=F ”=0 to F 0 =1, as depicted in Figure 8.1(b).
Additionally, since in type-I MOTs no Zeeman dark states can form, experimental implementation
is simplified because it will not be necessary to perform the magnetic field switching and polarization
chopping used in the orange MOT.

8.4

Narrow-line MOT simulation
We simulate the red MOT in one dimension with counter-propagating circularly polarized

light with components addressing both the N ”=0, G"=0 and G"=1 manifolds and exciting toavailable A02 ∆3/2 states. Initial conditions are given by a 1 mK distribution using the parameters ofan orange MOT with a trap oscillation frequency of ωM OT = 2π×155 Hz [21]. Because the Doppler
broadened linewidth at 1 mK is significantly greater than the narrow transition, we model the laser
light with multiple frequency components spanning the broadened linewidth, each with saturation
parameter s0 [33, 35]. We use a carrier plus two pairs of sidebands spaced by 2π×1 MHz, withthe detuning of the highest energy sideband from resonance labeled δ1 . Since microwave mixing
and vibrational repumping are both fast compared to the optical cycling on this transition, we
make the following assumptions about the population distribution in the ground state. Because

102of the 760 MHz hyperfine splitting, G”=0 manifolds are only mixed with other G”=0 states, andG”=1 manifolds with other G”=1 states. So, population in a given G” manifold is weighted by
the branching ratio from the A02 ∆3/2 state, which is 1/4 and 3/4 into the G”=0 and 1 levels
respectively. For a given G” level, the population is evenly distributed among all available v”=0,
N ”=0,1,2 states due to the microwave mixing. For a two level system, the force from a laser beamfrequency component resulting in absorption and followed by spontaneous emission can be written
as [67]F =~ks0 γ/2
1 + s0 + (2δ/γ)2(8.1)

where k is the wavenumber, s0 is the saturation parameter, δ the detuning experienced by the0molecule, and γ = 1/τ . In a MOT, δ can be written as δ = δ0 − kv + µ Ar/~, where δ0 is thenominal detuning of the laser frequency component from resonance, v the velocity, A the magnetic
0

field gradient, r the molecule’s position, and µ the differential magnetic moment for the transition.
To compute the average force felt by an N ” = 0 molecule, the force is averaged over the transitions
available to all N ” = 0 sublevels, and summed over both laser beams and all frequency components.
Since we only optically address N ”=0 which contains 1/9 of the microwave mixed states, theaverage force felt by a molecule mixed between N ”=0,1,2 is F̄total =F̄N ”=0 /9. In addition, we
simulate heating due to spontaneous emission by adding a random momentum kick when a photon
is absorbed. For small detunings, the force reduces to F̄total = −βv − κr, where β is the damping
cofficient and κ the spring constant, which together characterize the trap.

200
0

−200
−1

Acceleration (m/s2)

Acceleration (m/s2)

(a)

100
0

−100

0

1

0
-0.5
0.5
Position (mm)Velocity (m/s)(d)
Temperature (K)(c)
Velocity (m/s)

103

(b)

0.4
0

-0.4

0
-0.5
0.5
Position (mm)

−4

10

−5

10

−6

10

0

20

Time (ms)40

Figure 8.2: Results of simulation. (a) Velocity dependent force due to optical molasses. (b) Position
dependent force due to magnetic field gradient for stationary molecules. (c) 1 mK distribution
produced from orange MOT (blue) and distribution after red MOT has been on for 20 µs (red). (d)Temperature vs time after red MOT is turned on and the orange MOT is turned off. Oscillationof modeled temperature after 20 ms is an artifact of the limited number of molecules in the Monte
Carlo simulation

We first model an optical molasses as shown in Figure 8.2(a) for the parameters δ1 = -1.5γ
and s0 = 3, chosen to provide force to all moving molecules in an initial 1 mK distribution. Fromthe slope, we can extract β and so the damping rate ΓD = 2β/m = 950 Hz. Likewise, we extract κfrom the rate of change of force with position for zero velocity molecules, as shown in Figure 8.2(b).
Under the same parameters, and magnetic field gradient A = 3 G/cm, we find a MOT oscillationp2
frequency ωM OT = κ/m of 2π×33 Hz. The characteristic trapping time is then ΓD /ωM
OT = 20 ms

104[67]. The simulation clearly shows phase space compression (Figure 8.2(c)), reaching a temperatureof <10 µK at 20 ms, as shown in Figure 8.2(d). The simulation indicates a photon scatter rate
∼104 per second, and cooling to <10 µK requires only ∼200 photons. Naively extrapolating tothree dimensions by dividing κ and β by three gives ω3D = 2π×19 Hz, Γ3D =317 Hz, and requires∼600 photons to cool. We estimate the v” = 3 limited MOT lifetime to be >1 second. We notethat for a molecule at rest, the maximum acceleration due to the three dimensional MOT is ∼5
times that of gravity, allowing successful trapping. In sum, we find that the red MOT is capable oftrapping and further cooling the molecules captured in an orange MOT, requiring only the additionof one 690 nm laser with frequency components 760 MHz apart to the current system, one for theG”=0 and the other for the G”=1 to A02 ∆3/2 transition.

8.5

Conclusion
We have identified a transition in YO suitable for secondarily cooling a MOT on the X 2 Σ toA2 Π1/2 transition by using a narrow-line transition from the X 2 Σ to A02 ∆3/2 state. Two estimatesindicate a lifetime of τ ≈1 µs for the A02 ∆ state, allowing a final temperature of ∼10 µK. We
have also determined that the vibrational branching from the A02 ∆3/2 state is favorable enough to
not necessitate any more vibrational repump lasers than the first stage MOT. Simulations indicate
parameters for the red MOT of a damping rate of 317 Hz and a MOT frequency of 2π×19 Hz.
There are a few other future experimental directions that we also find very exciting. Effective
slowing has been shown in strontium by using chirped adiabatic stimulated emission slowing [68].
The method relies on using a sufficiently narrow transition such that stimulated emission can occur
before spontaneous emission. The atoms are slowed by interacting with two laser beams, whichhave their frequency swept across resonance in such a way that the atoms absorb a photon fromthe counter-propagating beam and stimulatedly emit into the copropagating beam. This meansthat every absorption and emission cycle transfers 2~k of momentum from the atom. Additionally,
because the mechanism involves stimulated emission, branching into undesired rotational or vibrational states is supressed. Because we have identified a narrow-line transition in our molecule, this105
seems to be a viable course of action. The buffer gas cell would have to be modified to allow for alaser beam to copropagate with the molecules in the slowing region, but otherwise the experimental
implementation would be relatively straightforward. In addition to slowing, the method can also
be used to produce a robust narrow-line MOT, as in reference [69].
Another route that is promising is that of a gray or blue molasses, which has already beenshown to produce sub-Doppler cooling in molecular MOTs, as in References [29, 30, 31]. Thesemethods rely on first loading the MOT, then simultaneously blue detuning the trapping lasers. Because these MOTs are operating on a type II cooling transition, this allows for Sisyphus sub-Doppler
cooling. This method has proven to be a robust way to laser cool molecules to the ∼50 µK level.
We also note that recently some more sophisticated theory calculations have been performed[70] using coupled-cluster methods. These calculations suggest that the level of mixing between
the A2 Π3/2 state and the A02 ∆3/2 state is smaller than we’d expect, on the level of 0.1% rather
than 2.5%. This lower level of mixing would indicate a significantly narrower linewidth of theA02 ∆3/2 state. At this time we don’t have an explanation for the lack of congruence between our
experimental in-cell absorption estimate of the lifetime and these new calculated results. In thenear future, we plan to more carefully measure the lifetime of the X 2 Σ→A02 ∆3/2 transition in themolecular beam or in the MOT itself in order to constrain the linewidth further. The more accurate
measurement will both be useful for us moving forward with the narrow-line cooling as well as togive further insight on the theoretical methods.

Appendix A

MOT coil layout and assembly

A.1

Coil design
Design of the coils is done using Mentor Graphics SSD PADS Layout. The program allows

precise drawing of arcs and shapes where the copper is to be left, as well as various holes that need
to be in place. PADS can convert to .dxf files which can be used on CNC machines to automate
the cutting of the traces.

Figure A.1: PADS design for MOT coil boards.

107
In Figure A.1 are the schematics for the MOT coils, where blue (the ‘top’ trace) indicates the
direction away from the MOT, and pink towards. Pink is not adjusted for flipping over the board,that is, the trace is correct as viewed from above, like the blue. For each separate half of the board,a little board will be outside of the larger inner board. The two inner boards are not identical toallow for a mounting bar to go between J13 of both. The drive connections for each board will beplaced at the large and the small pads on the side, with the small pad being ground. The tuning
capacitor will go between the two large pads, making the internal large pad the high voltage pointon the board. This high voltage pad will be connected with a wire to the blue pad on the smallboard. Finally, the vias for the small board pink pad will connect to the blue pad on the large board
vertically in line with them, that is J8 on the small board will connect to J16 on the big board.
All larger vias are through holes used for mounting purposes. This new design allows for the two
separate boards to be run in parallel, instead of in series as done previously. The symmetry should
reduce the large electric field gradient between boards seen in the previous design.

A.2

Coil assembly
Assembly of the coils is somewhat tricky, first the two halves of the boards are partiallyassembled separately, there is a layer of indium, copper foil, and indium sandwiched between boards
on a single side, where the heatlink will attach. Additionally, a layer of kapton film is between theseboards as well across the non indium section to prevent shorting or arcing. The screws (2-56) noton the indium side have washers to hold the distance between boards at a millimeter. Then, therectangular mating piece is attached via two 4-40 screws to the large L-shaped heatlink. The boardson the heatlink side are then connected through the c-clamp shaped pieces into the rectangularmating piece with 2-56 screws. The second set of boards are then attached to the c-clamp pieces(also with 2-56 screws), along with inserting the copper spacer on the non heatlink side between
boards (attached via a 1-72 threaded rod). Finally, the whole construction is placed into the vacuum
chamber, and the L shaped heat link is affixed to the feedthrough with two 8-32 screws. Each step
must be done carefully and tightly to assure a good fit, as all heat transfer is done through direct

108contact. I have not yet found a vacuum safe thermal grease that is sufficiently vacuum compatible
even at temperatures above 50 degrees C. Apiezon H has a vapor pressure of ∼5×10−8 Torr at
50 degrees C, and rises quickly to 1×10−6 Torr at 90 degrees C. It is possible that in the future
we may find this acceptable. The capacitors used for setting the frequency of the MOT coils arefrom American Technical Ceramics, with part number 800E470GMN7200X for the 47 pF version.
They are specified to have low equivalent series resistance, high Q, and can handle a voltage of
7.2 kV. Because of the resonant voltage enhancement in a LC tank circuit, we estimate we haveapproximately 1.5 kV peak voltage across the capacitor, necessitating a high voltage rated capacitor
for this purpose.

Appendix B

Frequency calculation and locking for slowing and trapping

B.1

Introduction
In order to achieve the correct scanning frequencies during slowing as well as maintaining

the appropriate stable frequencies during trapping, some care must be taken to the configurationof the lasers and their locks to the comb. While in the past when doing only slowing, we changed
frep during the slowing and so moved all of the lasers along with the comb. Now however, as we
require stable versions of all transitions, I have implemented the locking in such a way that the
comb and all the master lasers (excepting the 1228 nm diode laser for doubling and slowing) canremain stationary.
The following are the lasers that we need to stabilize: the vibrational repump master lasers(1 and 2), the 1228 nm diode laser (for slowing) and the Toptica laser (for the MOT beams), andeventually a 690 nm diode laser for our narrow line cooling transition.
The resonance frequencies for our transitions of interest are here tabulated for the G”=0
hyperfine component:
Label

Transition

Frequency (MHz)Main Cooling Transition

X 2 Σ, v"=0, N"=1 → A2 Π1/2 , v=0, J=1/2

488492552.6

v=1 Repump

X 2 Σ, v"=1, N"=1 → A2 Π1/2 , v=0, J=1/2

462837939.0

v=2 Repump

X 2 Σ, v"=2, N"=1 → A2 Π1/2 , v=1, J=1/2

461735964.9

Narrow Line Transition

X 2 Σ, v"=0, N"=0 → A02 ∆3/2 , v=0, J=3/2

434703100 (30)110
A more detailed explanation of the locking scheme for each laser follows, but in summary the
final frequencies of the lasers when locked to the comb are:Raman = 2 ∗ (fco + n0 ∗ frep − beatraman + 2 ∗ of f setAOMraman )(B.1)

T optica = Raman + V COdye − beattoptica(B.2)

v1 = fco + n1 ∗ frep − beat1 + of f setAOM1(B.3)

v2 = fco + n2 ∗ frep − beat2 + of f setAOM2(B.4)

Then the final frequencies as they enter the vacuum chamber for the slowing beam are:Slowing0 = Raman + slowAOMraman(B.5)

Slowing1 = v1 + 2 ∗ slowAOM1(B.6)

Slowing2 = v2 + 2 ∗ slowAOM2(B.7)

And the final frequencies for the MOT are:M OT0 = T optica + motAOM0(B.8)

M OT1 = v1 + motAOM1(B.9)

M OT2 = v2 + motAOM2(B.10)

Because the slowing lasers need to change frequency, the lasers are shifted by modifyingof f setAOMraman , slowAOM1 , and slowAOM2 . Because we want the Toptica laser to stay fixed,
V COtoptica is also scanned.

B.2

Comb
Two parameters determine the frequencies of our comb teeth, the carrier offset frequency fco

and the repetition rate frep , such that any tooth can be described as ftooth = fco + n ∗ frep for
integer n. Incidentally, this is true for the "doubled" comb as well, because addition happens withand between all teeth when doubling. Typically, we lock fco to a couple tens of MHz, while frep (≈99.5 MHz) is phase locked to (1 GHz - fsynth )/10, where the 1 GHz signal comes from the Wenzel
oscillator.

111

B.3

Raman Laser
The Raman laser consists of a 1228 nm seed laser which is then Raman amplified and doubled

up to 614 nm for use in slowing. We choose lock the 1228 nm seed laser to the comb directly in theinfrared, reducing the need to double the 1228 nm section of the comb spectrum. The optical setup
is shown in Figure B.1. The double pass AOM before the comb beat allows the comb/1228 nm beatnote to remain still as we vary the diode laser frequency.
Figure B.1: Optical setup for the Raman laser+11228 nm-1

Raman amp

84 MHz AOM

To slowing

To dye beat
60-76 MHz
AOM

B.4

To comb beatToptica Laser
The Toptica laser is locked to the Raman laser after the Raman laser has been doubled to

the visible. The optical setup for the toptica laser is shown in Figure B.2 In order to keep theToptica laser stationary in frequency, the beatnote between the raman and dye laser is then mixed
with a VCO which we scan from ∼230 MHz to ∼160 MHz. The resultant signal is then locked to∼-30 MHz.

112
Figure B.2: Optical setup for the Toptica laser

70 MHz AOM

Dye-1
To MOT

To raman beat

B.5

v=1 Laser
The v=1 master laser is locked to the comb light that has been doubled up to the visible,

using a PPLN doubling crystal. In order to scan the frequency of the slowing repump light, thedouble passed AOM frequency is changed before seeding the tapered amplifier. The optical setup
before the TAs is shown in Figure B.3.

113
Figure B.3: Optical setup for v=1 repump+1
97.5 MHz AOM

V=1

To comb beat0
Seed slaves-1

121-89 MHz
AOM

132 MHz AOM

To slowing TA-1 To MOT TA

v=2 Laser

B.6

The locking setup for v=2 is very similar to that of v=1, its optical setup is shown in Figure
B.4.
Figure B.4: Optical setup for v=2+1
102 MHz AOM

V=2

To comb beat0
Seed slaves-1

121-89 MHz
AOM

132 MHz AOM

To slowing TA-1 To MOT TAAppendix C

PMT characterization and transimpedance amplifier

We want our PMT to collect all incident photons, be insensitive to MCS discriminator level,
have photon shot-noise limited error bars, and not have many coincident clicks (indicating we should
be in current integration, not photon counting mode) We found that our previous mode of operation
was very sensitive to MCS discriminator level, and did not register all counts. We were using a
Hamamatsu R10699 PMT driven at 1000 Volts without any sort of transimpedance amplifier after
it, and a MCS discriminator level of -2.6 mV falling, likely too close to the noise floor. In graphs,
this will be labeled no amp 1000V.
We tried out a few different things to improve its performance: running the PMT at a higher
voltage, as well as using a transimpedance amplifier on the output with a few different gains. (bychanging R18 in the diagram C.1, at values of 226 ohms, 330 ohms, and 450 ohms)

QQ077A2.sch-1 - Fri Jun 01 15:15:26 2012

115

Figure C.1: Circuit schematic for PMT transimpedance amplifier.

In the remaining graphs please note that we tried to increase the light scatter for a given
MOT beam power above what is normal by opening up all MOT beam irises and fully opening the
PMT iris to give ourselves the largest range. Our usual operating conditions are more like the 5mW scatter shown here than the 25 mW, even though we usually run with 20-30 mW per beamduring MOT data collection.

116

Figure C.2: Photons counted vs MOT beam laser power for different transimpedance amplifier
gains.

By looking at signal counted vs photons applied in Figure C.2we can see that we were definitely
missing counts with no amplifier, on the order of a factor of 4 (depending on beam power) We canalso see that with the amplifier, particularly with the 20 x gain, that we are saturating the MCS’s
ability to distinguish separate counts at high (larger than 107 )count rates.

Figure C.3: Signal to noise ratio, for same acquisition time, for different amplifier gains vs laser
beam powers.

We can also look at the signal to noise for these different scenarios, as in Figure C.3 Here we
see that signal to noise is improved with the amplifier as opposed to without it. Now it is important
to determine why the signal to noise ratio is better, so we check the exponent of the dependence on
signal by putting them on a log-log plot, as in FigureC.4. looking at the fit, we see that all cases

117
show a 0.5 power scaling (for powers in the 0-5 mW regime. using the amplifier above 5 mW we see
an increase in the exponent), indicating the noise is behaving as shot noise. The increased signal tonoise ratio with the amplifier is then because we are collecting more photons with the amplifier as
opposed to without it.

Figure C.4: Log-log plot of signal/noise vs signal for different transimpedance amplifier gains. All
are well fit with y=.5x +b function, implying a square root dependence on signal/noise on signal.

Regarding sensitivity to discriminator level: we want ourselves to be in a situation where
small dc fluctuations don’t drastically alter our count rate. So, by parking at 5 mW and changing
the discriminator level we can see how sensitive we are, as shown in Figure C.5. This shows thateven running at a higher voltage still leaves us with a narrow window where our count rate is flatwith respect to discriminator voltage, whereas using the amplifier can decrease our sensitivity toelectrical pickup. We also find that running the amp at 10x gain doesn’t bring the count rate up as
high as with 15x or 1200 volts.

118

Figure C.5: Counts registered by MCS vs discriminator level for various PMT voltages and transimpedance amplifier gains.

MCS settings currently in use:
10.24 us, 16k bins per record trigger 2 volts rising discriminator level 10 mV rising 15x
transimpedance amplifier 1000 V supply for PMT

Appendix D

Data Acquisition

D.1

Introduction
The primary ways in which we analyze our experiment is through the photons collected byeither the photomultiplier tube (PMT) or the CCD camera both of which are directed at the MOT
region. The PMT allows time-sensitive detection, while the CCD can give us spatially dependent
information. However, in addition to these two devices, we also have the ability to change many
aspects of how our experiment is run, which we achieve through the use of a PulseBlaster timing
card, a couple of function generators, and some digital electronics. All the various components arecontrolled through a series of Matlab GUIs. In this section I detail how these various components
interact with each other and enable us to run our experiment as desired. I also give a brief overview
of how we typically process the data acquired in this way.

D.2

Acquisition devices

D.2.1

CCD

We have a CCD camera aimed at the MOT region, with a field of view of approximately 1 cm
by 1 cm. We can pull frames off of the camera and directly onto the computer. Setting up the
CCD to acquire data is achieved through the Matlab GUI, as shown in Figure D.1. From the GUI
we can turn the cooler on and off and set the set temperature (usually -30 degrees C) We can tell
the camera how many exposures to expect and how long the exposures should be. Finally, we can

120
Figure D.1: GUI for interfacing with the CCD

specify the region of interest on the sensor, and the on-chip binning. By allowing the camera to do
binning itself, we can reduce the amount of time it takes to transfer data from the camera to thecomputer, as well as reduce the readout noise. The total number of camera pixels are 1024 by 1024.
The camera can bin over entire rows, but has a maximum binning of 6 columns. We typically run
with 6 by 6 binning, which yields 170 by 170 binned pixels. After modifying the geometry settings,
the Update Geometry button must be pressed to load the settings. The left side of the GUI displays
the first frame of the most recently aquired data, which can be useful for troubleshooting.

D.2.2

PMT

We have a photomultiplier tube that is looking at the MOT region. Its signal is then amplified
and then plugged into the multichannel scaler (MCS) which records the voltage spikes as photon
counts. There are no parameters to be set for the PMT itself.

121
D.2.3

Multi-channel scaler

The MCS is a photon counting device that accumulates data into time bins. Upon receiving
a trigger, it starts accumulating. The total number of bins can be set to be any multiple of 1024
from 1 to 16. We typically run with 10 µs bins, and 9216 bins. With repeated triggers, the MCS
continues to accumulate photon counts into the same bins until it reaches the specified number ofrecords for which to acquire, and so the final signal is the total number of photon counts per binover all the records. We usually convert this total number into a number of counts per second, inorder to more easily compare values across different data sets which may have different numbersof records per acquisistion. Since the screen is not functional, all communication with the MCS isdone via GPIB through Matlab.

D.2.4

Scope

When performing Doppler scans with the dye laser, we apply a sinusoidal voltage scan to
the VCO that sets the offset between the dye laser and the raman laser. In order to know whatfrequency the laser is at what time, we put the VCO control voltage on the scope and save thescope trace in the data file, to later be able to plot signal vs VCO frequency (or velocity). The only
parameter we usually change is the number of triggers the scope will average over (The number of
averages field of the GUI shown in Figure D.2) Typically this is best matched to the number ofrecords that the MCS is acquiring for. We have not been using the FastFrame capability within thelast few years.

122
Figure D.2: GUI for interfacing with the TDS7104 scope

D.3

Control
The timing control of our system is controlled through a variety of elements. In this section

I step through the various components and explain their use in running the experiment.

D.3.1

Digital Delay Generators

The master timing of our experiment is controlled through a digital delay generator (DDG)
running at 10 Hz. This master DDG is continuously running and triggers things that prefer not to
be interrupted. For example, we fire the YAG ablation laser every 100 ms regardless of whether the
rest of the experiment is running, as it helps keep the optical power of the YAG more constant. Thismaster DDG also usually triggers any voltage chirps (explained further in the function generator
subsection). Finally, when we are running, the master DDG triggers a secondary DDG when we
decide to run the whole experiment through the use of an AND gate (explained further in theArduino subsection). This secondary DDG is used to trigger the PulseBlaster timing card.

D.3.2

PulseBlaster Timing Card

The timing card (a programmable TTL pulse generator) is used to control all other triggeredparts of our experiment. For example, we trigger the MCS and CCD via the timing card, as well
as shutters for slowing, phase switching of the MOT coils, and to turn off the 760 MHz hyperfine
component when doing Doppler-sensitive detection. The timing card is programmed via a gui, but

123
once a program is loaded it is then triggered via a DDG. I’ll go into more detail of the programmingof the PulseBlaster in a later section.

D.3.3

PulseBlaster breakout board

The first 12 of the timing card outputs are broken out to various BNC outputs on the breakout
board. All channels are default TTL low except when set high by the timing card. Some of thechannels have been set up with a rotary switch. For these channels, we have an additional level ofcontrol available. These channels have 5 choices of settings: normal, on, off, not, and toggle. Normalmeans that the channel is triggered via the timing card as expected. On and off settings override
the timing card settings, forcing that TTL high or low always (for on and off settings respectively).
The not setting gives the inverse of the signal determined by the timing card (high when set low,
and low when set high). Thus the timing is still controlled by the timing card, but the inverse of theusual setting. Finally, the toggle setting means that the channel goes through an AND gate with
the Toggle Out signal from the MCS. I’ll go into more detail on the Toggle output of the MCS later,
but this means that the channel is triggered with the set timing when the MCS Toggle output ishigh, but is not triggered when the Toggle output is low. All channels without rotary switches arecontrolled solely from the timing card settings. Channels 13-24 have not yet been necessary, and sohave not been broken out to BNC outputs.

D.3.4

Function generators

We have three function generators we use to manipulate the experiment. The Lecroy function
generator is used to sinusoidally vary a voltage which is then combined with a voltage to form
the dye-raman offset VCO control voltage. Because of the setup of our frequency locking scheme,
this then sinusoidally scans the dye laser frequency. This laser can then be utilized to perform
Doppler-sensitive detection of multiple velocities in a single data acquisition. We currently program
the Lecroy function generator by hand, setting it to a sin output in gated mode. The timing of thescan can then be triggered by a channel on the timing card.

124
The second function generator that we use is the Tegam, which provides the control voltage
for our slowing chirps. It is programmed via a GUI, as shown in Figure D.3. The GUI allows
Figure D.3: GUI for interfacing with the Tegam function generator

programming of flat sections and ramps of arbitrary timing. A waveform file must first be made,and then can be uploaded to the function generator. The Tegam is then be triggered by the master
DDG.
Finally, we can set the Agilent synthesizer (which determines the value of frep ) via the Agilent
GUI. It will likely break the lock if this frequency is changed while frep is locked. Opening the GUI
will read the current value of the synthesizer, allowing the value to be saved with the data files.

D.3.5

ArduinoWe have a couple of Arduino controlled TTLs that can be talked to via Matlab. The GUI
allows control of the Yag shutter and the timing card. The timing card is triggered when it’s channel
is high AND the master DDG hits time 0. The Yag shutter channel goes through an OR gate withthe timing card Yag control.

D.3.6

Altbins box

The box has a switch on the front to be in "normal" or "altbins" mode. When in normalmode, the PMT signal goes directly to the MCS. When in altbins mode, the bin clock signal and125
the Toggle out of the MCS go through an XOR gate, which then gates the PMT signal to the
MCS. Note, the bin clock output is NIM logic, not TTL. We use a comparator in the altbins box
to convert it to a TTL signal.

D.4

Data acquisition modes
In order to have flexibility when acquiring data, several different acquisition modes have been

implemented.

D.4.1

MCS acquisition modes

The MCS can be set in three different modes: add, external, and toggle. This is controlled
via the MCS gui in Matlab.
Add modemeans that every record’s bins are added to the total. This can be considered

the default operation of the MCS.
External modemeans the MCS checks the TTL status of its Subtract input at the timeof the trigger, and if the input is high it will subtract photons counted from each bin, while if the
input is low it will add photon counts to each bin as in add mode. We control this TTL with the"MCS subtract" channel on the timing card. When the MCS is not in external mode, the status of
this TTL has no effect.
Toggle modeis one wherein the MCS controls its own addition and subtraction. In thismode we need to set the toggle number (N). For the first N records the MCS acquires it will subtract
photon counts from its bins, while for the second N records it will add photons counted to bins. This
continues until the MCS has reached the total number of records it is acquiring for. It is important
to note that if the total records is not divisible by 2N, the number of added and subtracted records
will not be the same, which is usually not desired. In Toggle mode the MCS also changes the stateof its Toggle output synchronously with the records it is acquiring. The Toggle out will be TTL
high when the MCS is subtracting and TTL low when adding. We utilize the Toggle out in a coupleof ways. After buffering, it goes into the altbins box and the timing card breakout board. It is used126
in the altbins box as discussed in subsection D.3.6. The toggle out is utilized with the timing card
breakout board as discussed in subsection D.3.3. More information about the MCS can be found inits user manual here.

D.4.2

PulseBlaster acquisition modes

The timing card can be utilized in two main ways, single-state or multi-state. If the numberof states is set to one, timing will be uploaded in single state mode, while if the number of states isanother number, timing will loaded to the board in multi-state mode.
Single-state mode

uploads a single sequence to the timing board, that will be looped overuntil either the CCD or MCS (or both, depending on which are enabled) have been triggered as
many times as they are expecting. Upon pressing Acquire Data in the Master GUI, the timing cardis enabled by setting the Arduino timing card output high, allowing the timing card to be triggeredby the secondary DDG. Once the MCS or CCD have enough records or exposures respectively, theyreport back to the main program that they are done, and the timing card is turned off again.

Figure D.4: GUI for interfacing with the PulseBlaster timing card

127
The sequence that is loaded is determined by the table in the upper left of the PulseBlaster
GUI, as shown in Figure D.4. If the checkbox for a channel is not enabled, it will remain TTL low
always. If the checkbox is enabled, then the channel will have a pulse at the time marked by startand lasting for the time labelled duration, after each time that the timing card is triggered. Hereit is important to note that according to the timeframe of the timing card, the YAG trigger is fired
at 20 ms. We incorporate this 20 ms delay to allow for things like the MCS subtract pulse, which
need to be active before the experimental time 0. Additionally, it is necessary to not have the total
time (start plus duration) for any channel to exceed the experimental rep rate, as the timing cardcannot accept a new trigger while it is already running. When running at our usual 10 Hz, thatmeans that no total times can exceed 100 ms.
Multi-state mode

The Multi-state mode works very simlarly to single-state mode, with

two notable exceptions. The first is the use of the "inhibit checkboxes" table in the lower right of
the GUI. The inhibit checkboxes table has as many columns as the number of states specified. Eachstate will last for the number of shots entered in the shots per state box. If a box is checked in theinhibit checkboxes, that channel will not be triggered during that state. For example, if the slowing
shutter box is checked for state number two, but not for state number one, the slowing shutter willbe triggered as specified by its start and duration time given in the upper left table for the N shots
per state. Then for the next N shots the slowing shutter will be inhibited, and so will not fire. The
pattern entered into the inhibit checkboxes has no restriction.
The second difference between single and multi-state mode is that two channels become special
when in checkbox mode, those are the YAG channel and the phase switch channel. When multiple
states are used, these two channels will remain high or low for the entirety of the shots in thatstate, and will not obey the timing shown in the durations table in the upper left. Thus, if the
YAG shutter has a checkbox for state 1, it will remain closed for all shots during that state. If it is
not checked for state 2, it will remain open for all of state 2. Similarly if we have the phase switch
channel checked, it will remain TTL low for the entire state.
When loading timing files for multi-state mode, we sometimes wish to use the CCD. If we128
are using the CCD, the checkbox for "wait for CCD multistate" must be checked in order to allow
time to offload data from the CCD before starting the next exposure. If we are not using the CCD,
there is no need to wait for this time, and so the box should not be checked.
No matter the timing card mode, when uploading a timing file to the timing card, all thefollowing buttons must be pressed in order: Make Timing File, Load File onto Board, and Run
Program on Board. If all of these are not done, the behavior of the timing card will not be as
expected.

Appendix E

Replacing Y2 O3 targets in the cellE.1

Epoxying targets
We epoxy the Y2 O3 targets to a brass ring prior to placing them in the chamber. By affixing

the targets to a removable piece, we are better able to glue up new targets while the old ones are in
the chamber, as well as not have to fight against gravity. The cell is made out of copper, with a one
inch hole bored perpendicular to the molecular beam direction. The brass ring is just smaller than
one inch allowing it to fit snugly in the cell. We chose brass because it is well expansion matched tocopper under thermal cycling, but easier to machine. Also, when removing old targets from a ring
we do some mechanical scraping to remove old epoxy, and the brass holds up better than copper.
The epoxy we use is Stycast 2850 with catalyst 23LV. This epoxy/catalyst combination has
good cryogenic properties as well as thermal cycling properties. The epoxy needs to be mixed
according to weight in a well ventilated area, as the catalyst is rather noxious. We then epoxy twotargets to the brass ring, being careful to have neither the targets nor the epoxy extend beyond theedge of the ring, or it has to be sanded off before it will fit in the cell. We use a small teflon spacer
the same depth as the ring in order to hold up the targets while the epoxy dries. The cure time isusually overnight, though it can be rushed to a few hours by using a hot plate.

E.2

Disassembling
The targets are inserted in the cryostat from the side opposite the YAG beam, so that theablated molecules can start in the middle rather than the outer edge of the cell. The first step (after

130
warming up the chamber and purging it with helium) is to remove the rectangular side vacuum
flange on far side from the YAG. The flange is fastened with 10-32 bolts.
Figure E.1: vacuum chamber disassembly for target removal(a) outer rectangular flange(b) 40 K shield

After removal of the flange, the 40 K shield is visible, and can be removed with a small
screwdriver. Then the 4 K charcoal fin will be apparent, affixed with three screws at its top.
At this point, one can finally see the cell itself. Now is a good time to put tin foil down
below the cell to prevent things like screws from falling down into the cryostat. The window canbe carefully removed with a balldriver, but it is important to note that the window is not rigidly
attached to the brass mount, it is just held in place with a thin layer of Kapton film between thewindow and the brass. After extricating the window, the brass ring with the targets can be accessed.
It is sometimes fit in there snugly, so a short allen key can be used to try to pry the ring out. Now
is a good time to take a look at the far window and see if it needs replacement due to accumulationof a film or haze that appears after many ablations. If it does, the other side is disassembled inmuch the same way.

131
Figure E.2: vacuum chamber disassembly for target removal(a) 4 K fin(b) cell with window

Figure E.3: vacuum chamber disassembly for target removal(a) cell without window

E.3(b) empty cell

Reassembling
Now the entire process can be reversed to put in the new targets. When reinstating the 4 K

fin and the 40 K shield, if more thermal grease is needed then more can be applied. We use Apiezon
N for its good cryogenic properties. When placing the final vacuum flange on, it is important not
to overtighten the bolts, as the cryostat is made of aluminum and we do not want to strip the holes.

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