High harmonic driven attosecond and femtosecond
molecular dynamics
byCraig Hogle
B.A., Carleton College, 2007
M.S., University of Colorado, 2011

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
2014This thesis entitled:High harmonic driven attosecond and femtosecond molecular dynamics
written by Craig Hogle
has been approved for the Department of Physics

Margaret M. Murnane

Henry C. Kapteyn

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
Hogle, Craig (Ph.D., Physics)
High harmonic driven attosecond and femtosecond molecular dynamics
Thesis directed by Prof. Margaret M. Murnane

To fully understand atomic and molecular dynamics scientists must be able to probe andstudy dynamics on their fundamental time scales. The motion, structure, and arrangement ofmolecules play a fundamental role in chemical reactions. Analyzing these reactions is not only
important for their immediate insights, but the understanding is essential for the progress of many
areas of science and technology including biology, material science, and medicine.
These dynamics require a light source with the time resolution to capture attosecond andfemtosecond dynamics and access a large energy range of interesting processes. High harmonic
generation (HHG) provides a tunable coherent light source of high energy photons while remaining
table-top in size. These highly excited states can be investigated using coincidence electron andion spectroscopy with short time scale resolution.
The combination of high harmonic generation with coincidence spectroscopy allows for the
study of a variety of atomic and molecular systems. We were able to observe a new ionization
pathway enabled by intense laser fields in argon and xenon. With helium, we demonstrate theability to optically induce full electromagnetic transparency. The time resolved dissociation ofbromine allowed for the understanding of how molecular orbital structure changes to become atomic
in nature. In hydrogen we considered the interaction of electronic and nuclear wavepackets in a nonBorn-Oppenheimer regime in a new level of detail. We explore the coherent control in dissociatinga triatomic molecule with N2 O allowing for the ability to optically control the dissociation pathwayof the molecule. Additional molecules including the argon dimer, ethylene and ozone have also
been studied and analysis points to very interesting dynamics.

Dedication

To Ethan Townsend and Jing Yin.

v

Acknowledgements

I would like to thank my advisors Margaret Murnane and Henry Kapteyn for the many
opportunities they presented me.
I would like to thank my parents and family for being an incredible support for me. This
would not have been possible with you and your never-ending encouragement.
Thanks to William Peters, Predrag Ranitovic, Wen Li, and Vandana Sharma for the help
running experiments and analysis. This would not have been possible without their guidance andteaching. Thanks to Xiao-Min Tong, Agnieszka Jaroń-Becker, and Fernando Martı́n and manyothers for their incredible theoretical support.
I would have been completely lost without Philip Makotyn. He was there when I needed
him the most. Many thanks to Will, Jen, Ben, Tory, Ariel, and Betsy and many others for helpful
conversations, and reminding me what is important.
Thanks to Vincent Crowder who traveled most of this journey with me.
Many thanks to my coworkers for help along the way especially to all within the K-M group.
Many thanks also to the JILA machining, electronic, and computing support and to the all the staff
helping with no expectation of recognition. To Daisy Raymondson for her friendship and sharing
her expertise with the amplifier. And thanks to the many at KM Labs for their continued technicalsupport.
To Melina, Ross, Kassie and John, thanks for getting me past Olin and continuing to be in
my life.
For everyone that I have danced with over the last seven years, you provided many incredible

vi
experiences and support when you didn’t know I needed it.
I would like to thank Ken for being such a good friend and for helping me keep my sanity
and most of all keeping me responsible. Thank you to Ross for his support and always encouraging
me to stay focused.

vii

Contents

Chapter
1 Introduction

1

2 Experimental Apparatus

4

2.1

2.2

2.3

2.4

Ti:sapphire Amplifier System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

2.1.1

Amplfication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

2.1.2

Laser Amplifier Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6High harmonic generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

2.2.1

3-step model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

2.2.2

Phase matching/gas-filled waveguide . . . . . . . . . . . . . . . . . . . . . . . 12

COLTRIMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1

Gas Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.2

Electric Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.3.3

Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3.4

Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.5

Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Beam Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Argon
3.1

34

Laser Enabled Auger Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.1.1

Experimental Generation of a ns Hole . . . . . . . . . . . . . . . . . . . . . . 35

viii
3.1.2

Theoretical Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.1.3

Calculation of the LEAD Rate . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2

Ar+ vs. Ar2+ Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3

Extension of LEAD to other Noble Gases . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.1

Argon and Xenon Experimental Results . . . . . . . . . . . . . . . . . . . . . 48

3.3.2

Attosecond Time Scale Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 51

4 Helium
4.1

4.2

54

Ionization pathway interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1.1

Two-Color Multiphoton Processes . . . . . . . . . . . . . . . . . . . . . . . . 55

4.1.2

Theoretical Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

Resonance Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.2.1

Tuning for Full Transparency . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5 Bromine64

5.1

Visualization of electron dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.1.1

Experimental Bromine Dissociation. . . . . . . . . . . . . . . . . . . . . . . 66

5.1.2

Power Dependence of Br+ Yield . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.2

Calculated and Experimental KER . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.3

Angular Ion Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.4

Laser Field Driven Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6 Deuterium

75

6.1

Coherent Control of Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 76

6.2

Phase-Locked VUV + IR Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.3

Theoretical Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6.4

Multiscale Quantum Control of Electronic and Nuclear Dynamics . . . . . . . . . . . 83

6.5

Nuclear Wavepacket Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

ix

6.6

6.5.1

Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

6.5.2

Visualization of Wavepacket Coherence . . . . . . . . . . . . . . . . . . . . . 88

Electron Wavepacket Interferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7 Nitrous Oxide
7.1

93

Coherent Control of N2 O Dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.1.1

Coulomb Explosion of N2 O . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

7.1.2

Photoion-Photoion Coincidence . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7.1.3

Electronic configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7.1.4

Ionization Yield and KER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.2

Dissociation Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

7.3

Selective Bond Breaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7.4

Angular Distribution of N2 O2+ fragments . . . . . . . . . . . . . . . . . . . . . . . . 105

7.5

Autoionization Pathway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

8 Complex Systems

109

8.1

C2 D4 isomerization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.2

Argon dimer Inter-Coulombic Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

8.3

Laser-Induced Ultrafast dynamics of Ozone Double Photoionization . . . . . . . . . 120

9 Conclusion

126

Bibliography

128

x

FiguresFigure2.1

Laser amplifier schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

2.2

Keldysh parameter schematic showing laser-induced ionization . . . . . . . . . . . . 11

2.3

3-Step semi-classical model for high harmonic generation . . . . . . . . . . . . . . . . 12

2.4

Waveguide phase matching schematic

2.5

Tunable phase matched harmonics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.6

COLTRIMS diagram showing electron and ion paths . . . . . . . . . . . . . . . . . . 16

2.7

Inner COLTRIMS schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.8

Supersonic gas jet schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.9

DLD image of supersonic gas jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

. . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.10 DLD image of effusive gas jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.11 COLTRIMS main chamber schematic . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.12 Electron radius vs. time-of-flight plot showing multiple nodes . . . . . . . . . . . . . 24
2.13 Schematic of detection electronics and digital conversion . . . . . . . . . . . . . . . . 26
2.14 Electron momentum rings showing multiple harmonics . . . . . . . . . . . . . . . . . 27
2.15 Beam line schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.16 Typical electron energy and momenta for XUV only . . . . . . . . . . . . . . . . . . 31
2.17 Typical electron energy and momenta for XUV and IR . . . . . . . . . . . . . . . . . 32
3.1

Laser enabled Auger decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

xi
3.2

Calculated laser enabled Auger decay rates . . . . . . . . . . . . . . . . . . . . . . . 41

3.3

Schematic diagram for IR-enabled Auger decay rates . . . . . . . . . . . . . . . . . . 43

3.4

Schematic of high harmonics reflected for single and double ionization . . . . . . . . 44

3.5

Single ionization of Ar experiment and theory . . . . . . . . . . . . . . . . . . . . . . 46

3.6

Photoelectron energies experiment and theory . . . . . . . . . . . . . . . . . . . . . . 47

3.7

Photoelectrons energy and yield in coincidence with Ar2+ . . . . . . . . . . . . . . . 47

3.8

Auger decay for Xe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.9

Ion yields and photoelectron energy for Ar . . . . . . . . . . . . . . . . . . . . . . . . 49

3.10 Ion yields and photoelectron energy for Xe . . . . . . . . . . . . . . . . . . . . . . . . 51
3.11 Ion yields for Xe+ and Xe2+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.1

Excited pathways and calculated He cross section . . . . . . . . . . . . . . . . . . . . 56

4.2

Experimental and theoretical He+ yields . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.3

Induced XUV transparency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1

Molecular orbitals and Br+ ion yield . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.2

Power dependence of Br+ yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.3

Br+ ion yield vs. time delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.4

Calculated and experimental kinetic energy release . . . . . . . . . . . . . . . . . . . 71

5.5

Angular distribution of Br+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.1

D2 potential energy surfaces, excitation probabilities, and experimental ion yields . . 77

6.2

D2 theoretical yields for phase matching conditions . . . . . . . . . . . . . . . . . . . 82

6.3

D2 coherent control ionization pathways . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.4

D2 nuclear wavepacket evolution in B and EF potentials . . . . . . . . . . . . . . . . 85

6.5

D2 theoretical nuclear wavepacket progression and Fourier transform . . . . . . . . . 87

6.6

D2 ion momenta, KER, and wavepacket at 0fs . . . . . . . . . . . . . . . . . . . . . . 89

6.7

D2 ion momenta, KER, and wavepacket at 46fs . . . . . . . . . . . . . . . . . . . . . 90

xii
6.8

D2 potential energy surface and oscillating yields . . . . . . . . . . . . . . . . . . . . 91

7.1

Double ionization of N2 O and fragmentation pathways . . . . . . . . . . . . . . . . . 96

7.2

KER enhancement of N2 O fragments . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

7.3

Illustration of N2 O ionization dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.4

Kinetic energy release of Coulomb explosion fragments . . . . . . . . . . . . . . . . . 101

7.5

Momentum distribution of N2 O fragments . . . . . . . . . . . . . . . . . . . . . . . . 104

8.1

Potentials and dynamics of C2 D4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

8.2

C2 D4 time-of-flight spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

8.3

Full scan C2 D4 fragmentation yields . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

8.4

Attosection resolution of C2 D4 fragmentation yields . . . . . . . . . . . . . . . . . . 114

8.5

Argon dimer potential energy curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

8.6

Argon time-of-flight spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

8.7

Argon dimer coincidence ion TOF vs. ion TOF . . . . . . . . . . . . . . . . . . . . . 118

8.8

Argon dimer kinetic energy release . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

8.9

Argon dimer kinetic energy release at 50fs . . . . . . . . . . . . . . . . . . . . . . . . 120

8.10 Ozone potential energy schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.11 Ozone time-of-flight spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8.12 Ozone experimental trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.13 Ozone photoion-photoion coincidence . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8.14 Ozone kinetic energy release . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Chapter 1

Introduction

To fully understand atomic and molecular dynamics scientists must be able to probe andstudy those dynamics on their fundamental time scales. In molecules, these dynamics span fromattosecond time scales characteristic of electronic dynamics, to femtosecond time scales characteristic of vibrations and dissociations, to picosecond time scales characteristic of rotations. The
motion, structure, and arrangement of molecules play a fundamental role in chemical reactions.
Analyzing these reactions is not only important for their immediate insights but the understandingis essential for the progress of many areas of science and technology including biology, materialscience, and medicine.
With the development of the laser over 50 years ago, scientists gained a crucial tool forstudying atomic and molecular processes. Shortly thereafter, the use of nonlinear processes provided
a coherent source of high energy photons. With the advent of femtosecond lasers, observing thetransition states in a chemical reaction [1], and controlling the reaction itself, became feasible.
Recent advances allow the production of coherent photons spanning well past the ultraviolet portionof the spectrum into the soft x-rays with the tremendous potential for pushing towards even higher
energies.
Molecular dynamics call for a light source with not only the time resolution to capture attosecond and femtosecond dynamics but also can select between dissociating pathways, single and double ionization, and other highly excited electronic states. This energy range includes super-excited
shake-up and shake-off states that involve electron-electron correlations and complex electron-nuclei

2interactions that are not well understood. Even the lowest driven dynamics call for photons of several eV and the most exotic states require higher energies of tens of eV. Visible spectrum photons
are suited for studying valence electron dynamics, but will ionize outer electrons before probing
the states of inner valence or core level excitations. Only with shorter wavelength photons can one
probe these dynamics directly. Involving the inner electrons allows for the study of multi-electron
processes. The coherent manipulation of chemical systems on their natural time scales, as a means
to control the evolution of a reaction, is a pivotal goal.
The combination of ultrashort pulsed lasers and high harmonic generation (HHG) provides
for a coherent photon source that spans from the deep ultra-violet all the way to soft x-rays [2].
Here, we will focus on the extreme ultraviolet (XUV) portion of the spectrum as a probe of these
dynamics. The emission of harmonics as a pulse train maintains the ability to keep the time
resolution necessary to capture these dynamics due to time-bandwidth limits set by the uncertainty
principle. High harmonic generation is also a tunable light source allowing the control to probe
specific electronic states while being table-top in size. This allows real time experiments to be
performed on a dedicated detector with a variety of targets that can be limited on large scale
sources like synchrotrons and free electron lasers.
A sensitive detection technique is required to properly analyze the complex processes thatare induced or probed with high harmonic generation. Often multiple reactions are caused by therange of frequencies used, so accurate filtering and statistical analysis is required. This not only
requires the reliable generation of interesting dynamics but the ability to detect both the electronic
as well as nuclear dynamics. One effective way to achieve this is to detect ions and electrons incoincidence. Cold target recoil ion momentum spectroscopy (COLTRIMS) is a powerful techniquefor coincidence detection and provides full momentum resolution [3–5]. This apparatus allows for
3D momentum to be captured in a geometry that allows for the collection of all trajectories. Bothelectrons and ions from each event can be slowed and redirected to sensitive detectors without lossof information. With the full momentum of each particle available, the nuclear and electronic states
can be fully analyzed.

3
Chapter 2 provides a brief explanation of the experimental apparatus including the processesof the laser amplification, high harmonic generation, and ion and electron detection. Chapters 3
through 8 discuss specific experimental results. Chapters 3 and 4 deal with atomic systems, focusing
on argon and helium, respectively. With argon, a new ionization pathway enabled by intense laser
fields is explored, and with helium, the ability to induce full electromagnetic transparency is shown
to be experimentally possible. Chapter 5 deals with the time resolved dissociation of bromine andthe understanding of how molecular orbital structure changes as the dissociation process occurs.
Chapter 6 examines the simplest molecule, hydrogen, in a new level of detail. It considers theinteraction of electronic and nuclear wavepackets in a non-Born-Oppenheimer regime. Chapter 7
extends the analysis to coherent control in dissociating a triatomic molecule showing the ability to
optically control the dissociation pathway of the molecule. Chapter 8 discusses brief results of theargon dimer, ethylene and ozone.

Chapter 2

Experimental Apparatus

This Chapter discusses the important concepts of the experimental apparatus including theTi:sapphire amplifier system, high harmonic generation (HHG) and the experimental detector.
HHG provides an important tool relevant to studies of atomic and molecular dynamics and presents
a means of creating an extreme ultraviolet (XUV) pulse that allows for both attosecond scale
resolution while maintaining the necessary control over the spectral resolution. There are moredetailed explanations of the technical considerations [6] and scientific aspects [7–9] of HHG available
in the literature. The behavior of molecules when irradiated by laser light has been a subject ofinterest in the scientific community for many years. Atomic and molecular spectroscopy allows fordeeper fundamental understanding as well as the ability to coherently control molecular dynamics[10–15]. It is the combination of this light source with a detection scheme able to resolve these
dynamics occurring at the characteristic time scales, from attoseconds and femtoseconds, whichallows for acquisition of useful and worthwhile information about atomic and molecular dynamics.
Cold target recoil ion mass spectrometry (COLTRIMS) allows for this resolution while providing
both nuclear dynamics and electronic excited state information in coincidence.
This chapter covers the broad technical aspects of the molecular dynamics experimental setup.
Specific changes to the apparatus will be discussed within each experimental chapter, however manyof the fundamental concepts and techniques remain similar for each result.

5

2.1

Ti:sapphire Amplifier System
The large gain bandwidth of a Ti:sapphire crystal, spanning over 200 nm and centered around

800 nm, makes it useful for many ultrafast laser systems [16]. The first self mode-locked laser
demonstrated the ability to use this large bandwidth to create pulses with femtosecond duration [17].
Many improvements have been made since the first Ti:sapphire amplifier systems were developed.
To achieve the high pulse energies necessary to drive the nonlinear high harmonic generation process
as well as probe using strong-field techniques, the ultrashort pulses from the oscillator pass through athree stage multipass chirped pulse amplifier. The additional stages are required in order to achievea higher repetition rate than would be possible on a single stage system. Increasing repetition ratewith coincidence detection allows for an increase in the number of events detected in real time.
While many experiments benefit directly from increased photon flux, for coincidence detection only
one event can be recorded per laser shot. Therefore, the signal-to-noise is primarily limited by the
number of total events that can be recorded.

2.1.1

Amplfication

Chirped pulse amplification (CPA) allows for amplification to high intensity without the riskof damaging the gain medium or other amplification optics [18–21]. Stretching the pulse duration
by several orders of magnitude the intensity of the pulse can be safely increased while remaining
below damage threshold. The pulse is then recompressed, undoing the added chirp.
Gain inside the amplifier is given by:

ln G +ḡ(ν)I1(G − 1) = γ0 (ν)lg
Is

(2.1)

where G is the gain factor given by the ratio of the amplified intensity to the output intensity,
G = I2 /I1 , Is is the saturation intensity, ḡ(ν) is the normalized line shape factor, γ0 is the small
gain factor per unit length, and lg is the length of the gain medium.
For a final output, I2 , much smaller than the saturation intensity, equation 2.1 behaves as

6
the simple amplification law:

I2
= G0 (ν) = eγ0 (ν)lg
I1

(2.2)

where lg is the length of the gain medium. For I1  I2 the gain equation becomes
γ0 (ν)IsI2 = I1 +
lg
ḡ(ν)

(2.3)

This region of linear gain that occurs when saturation is reached, minimizes the power fluctuations of the amplifier and must be reached in the first amplifier stage. When saturation is notachieved the power fluctuations make the amplifier too unstable to use. The latter stages allow forincreasing the power that allows for high harmonic generation and strong-field ionization but thesestages will only intensify power fluctuations from the first stage.

2.1.2

Laser Amplifier Geometry

The amplifier design is shown in Figure 2.1. It employs a multipass ring geometry andincludes two additional double-pass amplifier stages, each with its own Ti:sapphire crystal andpump laser.
The oscillator shown in Figure 2.1 is a stable cavity aligned for mode-locked performanceand for generation of the short pulses. A continuous-wave (CW) laser at 532 nm is focused into
the Ti:sapphire crystal, where energy is stored through population inversion. The ultrashort pulses
are generated by the oscillator through Kerr-lens mode-locking at approximately 80 MHz. The
pulses then pass through a Pockels cell which selects the output repetition rate of 10 kHz. Eachpulse is amplified with every additional pass through the following crystals. The filtering conditions
allowed through COLTRIMS (as discussed in Section 2.3) make a higher repetition rate desirable
to improve the statistics of the experiment. To achieve these conditions the laser must be aligned
to its maximum efficiency while keeping a short pulse duration and good mode quality.
For the experiments discussed in Chapter 5, the amplifier was a simpler, single stage multipass

7

Figure 2.1: Schematic of the laser amplifier system. Short pulses (<30 fs) generated from an oscillator are stretched by several orders of magnitude after passing through a stretcher. A repetition
rate of 10 kHz is selected by the first Pockels cell and then amplified by 14 passes through thefirst stage crystal. A second Pockels cell preserves the pulse contrast by suppressing any amplified
spontaneous emission (ASE) from the first stage that would later be amplified in the latter stages.
The pulse is additionally amplified by two passes each through the 2nd and 3rd stages. The pulsein then shortened to close to the original duration by passing through the compressor.

system with an output of ∼1.8 mJ, 30 fs pulse duration, with a repetition rate of 2 kHz and a beamprofile M2 measurement of 1.5. An entire new oscillator and amplifier were built to replace this,and were used for all remaining experiments. Additional details of the newer design can be foundin [22]. Adding two additional amplifier stages and pump lasers allowed for an output of ∼3 mJ,
30 fs pulse duration, with a repetition rate of 10 kHz and a beam profile M2 consistently below
1.3. The new amplifier design included the addition of a compressed helium cryorefrigerator (fromCryomech, Inc.). The additional cooling allowed for the use of necessary pumping powers for thehigher repetition rate while maintaining a temperature range with increased thermal conductivity
and avoiding the introduction of thermal lensing effects. Improvements were added periodically,
allowing for additional power and pointing stability and thermal control due to changes in the
crystal mounting geometry as well as two oscillator redesigns. To maintain a consistent output

8energy, the original DM-100 532 nm pump lasers (from Photonics Industries) were replaced by a100W Patara-HP (from Northrop Grumman Cutting Edge Optronics) and later by a 150W LDP300MPQ (from Lee Laser).
Included in the change from one to the three stage amplifier were designs to make the system
more compatible for carrier envelope phase stabilization. Included in these designs were copper‘foils’ designed to decouple vibrations from the cryogenic cooling to the Ti:sapphire crystal mounts.
These foils were designed with a large surface area that eventually proved to be too costly due
to outgassing issues generated with the vacuum chambers for each amplifier crystal. These were
replaced with solid copper mounts mounted directly to the cryogenic cooling, and proved to be an
overall improvement.

2.2

High harmonic generation
High harmonic generation spanning from vacuum ultraviolet (VUV) spanning into the soft

x-ray (SXR) region and approaching the hard x-ray portion of the electromagnetic spectrum [2]has become an important tool for various spectroscopic techniques [23–26]. Much of this has been
made possible with the advancement of femtosecond duration lasers [27–29] as well as developmentin phase matching techniques [30,31]. When intense femtosecond laser pulses are focused into a gas,
the nonlinear interaction between the strong electric field of the light pulse and the electrons of theatoms cause high harmonics of the driving laser frequency to be radiated. The high-energy photons
generated from this process have been experimentally observed up to 1.6 keV and theoretically
predicted to be able to extend to higher energies [2]. Each atom experiences the same coherent
electric field resulting in the emission of high harmonic photons which are also coherent. This
results in a coherent laser-like high harmonic beam to be emitted collinear with the fundamental
light.
Additionally, high harmonic generation produces short bursts of photons with attosecond
scale durations on each half cycle of the driving frequency due to each maximum intensity of theelectric field. This time structure makes for a particularly useful tool for the study of atomic and9molecular dynamics in the time domain. To properly study many molecular dynamics, experiments
require both spectral and temporal resolution, within the limitations of the uncertainty principle.
An attosecond pulse train (APT) balances time and energy resolution while still spanning a broad
spectrum, with each pulse having a relatively narrow bandwidth. This form of radiation is thus
suited for initiating or probing atomic and molecular dynamics in real time, while also retaining
spectroscopic selectivity [23, 32–34].
While it may seem preferential to excite dynamics with a single, short VUV or XUV attosecond pulse from a time domain perspective, a short pulse will have a broad bandwidth which will
excite many ionization/dissociation channels with limited control or state selectivity. Probing for
certain coherent electronic and nuclear quantum dynamics cannot be done with such a pulse. An
isolated 200-attosecond pulse around 15 eV requires a bandwidth of ∼5 eV [23]. A pulse train fromhigh harmonic generation produces a comb of odd harmonics in the frequency domain, with eachharmonic having a full-width at half-maximum (FWHM) bandwidth typically a fraction of an eV.
Additionally, such pulse trains can be tuned in the frequency domain (as discussed specifically in
Chapters 3, 4 and 6) to coherently and selectively excite multiple electronic states. The mechanism
responsible for this control is discussed in Section 2.2.2.

2.2.1

3-step modelHigh harmonic generation is the nonlinear interaction between an intense laser pulse anda medium that results in the generation of harmonics of the driving laser field. Whereas thegeneration of low-order harmonics can be solved theoretically, high harmonic generation cannot
be described completely by perturbation theory. The characteristics of high harmonic generation
often used to distinguish it are a sharp cutoff where the high-harmonics signal drops rapidly, a longplateau of harmonics with similar intensities and intense low-order harmonics, whose intensities dofollow perturbation theory.
It is common to describe the regime in which ionization processes occurs by the Keldysh
parameter, γ, which is defined as the ratio of the laser frequency to the tunneling frequency [35]:

10

s
γ=

Ip
2Up

(2.4)

where Ip is the ionization potential of the atom, and Up is the ponderomotive potential given
by:

Up =

e2 E02(4me ω02 )(2.5)

where e is the fundamental charge, E0 is the electric field strength of the driving laser, me is
the mass of the electron, and ω0 is the laser angular frequency. The ponderomotive energy is thetime-averaged kinetic energy gained by an electron in an electric field.
Figure 2.2 shows a typical plot of the dependence of the Keldysh parameter on the laser
intensity and frequency for a given atomic Coulomb potential. When γ  1, the ionization process
and the laser frequency are fast, such that ionization occurs in the multiphoton regime. The
laser intensity is small compared to the Coulomb potential, so that qualitatively the electronic
wave packet remains trapped and localized by the potential until it can absorb enough photons
for ionization. When γ ≤ 1, ionization occurs in the tunneling regime and the laser frequency
is slow such that the ionization can be approximated as quasistatic ionization occuring in thetunneling regime. The electric field significantly distorts the effective potential, allowing the electron
wavepacket to tunnel through the potential barrier. When γ  1, ionization occurs in the abovebarrier regime. The effective Coulomb potential is lowered by the field such that it is below theground state.
For the typical situation of neutral argon (Ip = 15.76 eV) interacting with an 800 nm laser
pulse, tunnel ionization becomes the dominant mechanism for intensities greater than 1014 W/cm2[36]. A formalism for the tunnel ionization probability of an atom in an oscillating field, known as
ADK ionization rate, was developed by Ammosov, Delone, and Krainov [37]. Using ADK rates,
the ionized population as a function of time due to a laser field exhibits a stepwise increase at eachhalf cycle of the fundamental laser pulse cycle. Typical intensities in HHG experiments are greater

11

Figure 2.2: Schematic for photoionization processes for different laser intensities: a) multiphoton
absorption (γ  1), b) tunneling (γ ≤ 1), and c) above barrier ionization (γ  1). The gray dashedline corresponds to the Coulomb potential, while the red line corresponds to the Coulomb potential
modified by the laser field.

than 1014 -1016 W/cm2 , making tunnel ionization the dominant ionization mechanism.
A semiclassical and therefore more intuitive description of HHG has been developed by Ken
Kulander, Paul Corkum, as well as others, that explains HHG as a three-step process [7,9,38] where
the parent atom is initially ionized, the electron is accelerated in a classical electric field due to thedriving laser, and the accelerated electron recombines with the parent ion. This process is shown
schematically in Figure 2.3.
The driving laser pulse electric field deforms the atom potential well, allowing part of theelectron wavepacket to tunnel out of the well. After ionization, the electron wavepacket is thenaccelerated by the electric field of the laser and gains energy. When the electron recombines withthe parent ion, it releases that energy in the form of a high energy photon. Solving the equations of
motion for the electron classically (Equation 2.6) reveals that the maximum energy an electron cangain in the laser field and still recombine with the parent atom is given in terms of the ponderomotiveenergy and is ≈ 3.17Up .

12Figure 2.3: Schematic of the intuitive three-step model. The atom potential bends due to thedriving laser pulse electric field, allowing part of the electron wavepacket to tunnel out of the well.
The laser electric field accelerates the electron wavepacket causing it to gain energy. The electronthen recombines with the parent ion releasing a high energy photon.

eE0cos(ωt) + v0 t + x0
ω2m
(2.6)
eE0
v(t) =sin(ωt) + v0
ωm
The classically calculated value agrees with the cut-off of the harmonic plateau that was firstx(t) = −observed experimentally [38]:hνmax = Ip + 3.17Up(2.7)

The energy cut-off applies to the high harmonics generated from a single atom.

2.2.2

Phase matching/gas-filled waveguide

The three step model considers the high harmonic generation process in terms of a single atom.
For high harmonic generation in bulk, one must consider the phase difference of the harmonics
generated at different points in the medium. This difference can be described in terms of thecoherence length:

13

Lcoh =

π
∆k

(2.8)

The coherence length is defined as the length necessary for a phase shift of π to develop
between the signal that propagates over that length and the signal that is immediately generated.
For high harmonic generation, it is the length over which the harmonic signal increases before
interfering deconstructively due to the phase velocity mismatch of the high harmonics and thefundamental frequency. Without consideration to phase matching, the high harmonic flux thatbuilds over a coherence length will then periodically interfere with out-of-phase light generated in
the next section of the medium. Overall signal will not increase but will oscillate over each coherence
length. Early attempts at high harmonic generation were typically done using a gas jet of noblegas [39], where the interaction length is limited by the size of the jet, so efficient generation ofhigh-harmonics was not achieved. Later, phase matching in a hollow, gas-filled waveguide throughpressure tuning was demonstrated [40,41]. The hollow waveguide results in a dispersion term (∆kw )in addition to the neutral gas (∆kn ) and free electron (∆kp ) terms. This waveguide term can beused to correct for the phase mismatch of the other terms. Assuming the neutral gas has an index
of refraction ∼ 1, and that the HHG signal is generated with a small spatial profile such that it
does not interact with the waveguide, the phase mismatch in a hollow waveguide is given by:∆k = ∆kn + ∆kp + ∆kw
2πqP δn (1 − η) ηP Natm re
λ
qu2 λ
=
−
(qλ − ) − nm2
λPatm
Patm
q
4πa

(2.9)

where λ is the fundamental wavelength, q is the harmonic order, re is the classical electron
radius, unm is a constant corresponding to the propagation mode in the waveguide, a is the waveguide radius, η is the fractional level of ionization, P is the gas pressure, Patm is the atmosphericpressure, δn = ngas − 1 is the deviation of the neutral gas index of refraction from that of a vacuum,and Natm is the gas density at atmospheric pressure. Phase matching thus requires a balance ofthe neutral gas term with the resultant plasma dispersion against the dispersion of the waveguide.
This is primarily done by adjusting the gas pressure inside of the waveguide.

14

Figure 2.4: Coherent phase matching of high harmonic photons in a gas filled waveguide. Highharmonic XUV light copropogates with the driving beam. From [6].

Figure 2.5 illustrates the concept of phase matching with a gas-filled waveguide. The gaspressure inside the waveguide, P in Equation 2.9, acts as a tunable knob that can be controlled.
This allows for experimental control over the term ∆kp so that ∆k is close to 0 causing Lcoh to be
maximized. For appropriate pressures, tuning the pressure will change the frequencies that are bestphase matched, as well as provide a bright harmonic source with enough flux for efficient detection.
Figure 2.5(a) shows the photoelectron energies for an argon target in the gas jet and xenon gas
in the high harmonic waveguide. As discussed in Section 2.3, the harmonics above the ionization
potential of argon, 15.76 eV, are the signal that is visible. The 11th and 13th harmonic of thedriving laser are always above that potential. As the pressure is increased the phase matched highharmonics blueshift. Also shown is how the high harmonic energies affect the ionization yield as
they are tuned in part (b). When the 9th harmonic is below the ionization threshold the presenceof an additional IR photon allows for ionization, giving a strong enhancement of ionization counts,
shown in the positive delays. Once the 9th harmonic is tuned above the ionization thresholdthe enhancement disappears. This demonstrates the importance of controlling pressure in the15aL 0.85 torrIntensity @arb. UnitsD

9th

10 torr

0.6

15 torr

0.4
11th

0.2
13th

0.0
0

2

6
Energy @eVD

4

8

10

12

bL
Ar+ Yield @arb. unitsD

1.0
0.8
0.6

æ æ æ
æ
æ æ æ
æ
æ æ æ æ
æ
æ
æ
æ
æ
æ æ æ
æ
æ
æ
æ
æ
æ
æ
æ
æ æ
æ
æ
æ æ
æ
æ æ æ
æ æ æ æ æ
æ
æ æ æ
æ
æ
æ

0.4
æ æ æ æ æ æ æ æ

5 torrææ æ

10 torr

0.2
0.0
-150

15 torr-100-50

Delay @fsD

0

50

100

Figure 2.5: Because of the control over the phase matching conditions the harmonics can be tuned
towards a resonance. Part a) shows photoelectron energies for three different gas pressures insideof the capillary. The 11th and 13th harmonic of the driving laser are always above that potential
and as the pressure is increased the phase matched high harmonics blueshift. The 9th harmonic
eventually blueshifted above the ionization threshold. Part b) shows the ionization yield as afunction of IR probe delay. Once the 9th harmonic is tuned over the ionization threshold thepresence of the IR probe does not induce further ionization and the yield becomes flat versus delay.

waveguide. A full explanation of the time delay is given in Section 2.4.

2.3

COLTRIMSThe cold target recoil ion mass spectrometry (COLTRIMS) reaction microscope detects the

charged particles that are generated by an atom or molecule interaction with photons (from the16
IR pulse, XUV pulse or a combination). The charged particles are guided to position sensitive
detectors by electric and magnetic fields. The detectors allow for full momentum reconstruction ofeach detected particle which in turn captures the atomic or molecular dynamics.
Figure 2.6 shows the paths of the electrons and ions detected for a typical coincidence experiment (results in Chapters 7 and 8 show specific results for such an experiment). The Figure
shows the electrons undergoing a spiral path because of the cyclotron motion of the uniform magnetic field. The two positive ions shown have a conservation of momentum that allows for filtering
against false background coincidences.

Figure 2.6: Schematic showing the typical paths for ions and electrons in COLTRIMS. The electrons
take a spiral path because of the cyclotron motion of the uniform magnetic field. The electrons areaccelerated in the same uniform electric field as the ions initially and then go through a zero field
drift region. The more massive ions do not experience noticeable deflection due to the magnetic
field. Two positive ions are shown dissociating from the interaction region. Note that a second
electron is not shown for clarity and represents a realistic coincidence collection of the detector.

A schematic of the COLTRIMS geometry as well as the axis convention that will be used

17
throughout this text is shown in Figure 2.7. The calculation for the momenta reconstruction requires
exact knowledge of the parameters of the detector (electric field, magnetic field, and acceleration
distances) as well as the initial position and final position of a charged particle. The individualcomponents of the spectrometer and of the detector and the analysis are given in this Section.

Figure 2.7: Simplified schematics of COLTRIMS showing a smaller representative number of copper
plates to form the electric field, the copper coils to form the magnetic field, and ion and the electron
detectors. Adapted from [42].

2.3.1

Gas JetThe COLTRIMS detector was originally designed to only support a supersonic molecularbeam; a effusive jet was later added to expand the range of available experiments. It was determinedthat a supersonic gas jet would provide a better sample over an effusive needle where a needle needs
to be close to the interaction region. The supersonic jet provides a much more confined interaction
region and greatly decreases the thermal broadening of the energy features. It was also believed
it would allow for a better controlled main chamber pressure. However, the limitations of seedinga relatively small interaction region and requiring a high backing pressure make having both thesupersonic jet and effusive needle available incredibly advantageous in allowing the study of many

18
molecules that could not be studied otherwise. A good example of such an experiment was ozone,
as discussed in Chapter 8, where high backing pressures of ozone are both impossible to form as
well as potentially dangerous. Ozone spontaneously detonates above 20 torr.

Figure 2.8: Schematic showing the area of stability from in a continuum free-jet expansion. From[42].

The supersonic gas jet is created by the expansion through a 30 µm nozzle. The input sideof the nozzle is kept at over 1 atm while the output side is maintained at 5 × 10−5 torr. A low
divergence portion of the supersonic expansion is selected by a 300 µm skimmer. The skimmer also
serves as a barrier (differential pressure) between the gas jet chamber and the detector chamber.
The geometrical shape of the gas jet chamber helps with gas conductance and with efficiently
evacuating the background gas to keep the gas jet chamber pressure low. The gas jet chamber ispumped by a 2000 L/s MAG turbo pump (from Leybold). The area around the skimmer is also
shaped as a cone to help reduce possible back-scattering that would be detrimental to the gas jet.
For the experiments discussed in Chapter 5, the main detector chamber included a ‘catcher’to minimize the increase in the chamber pressure. A tube was inserted inside the chamber with
its orifice as close to the interaction region as the detector allows (∼9 cm). The tube is directly
connected to a small pumping chamber and turbo pump (300 L/s) to efficiently evacuate the gas.
Despite this, the detector chamber pressure would typically increase to 1 × 10−7 torr during gas
jet operation (compared to a pressure of 2 × 10−9 torr in standby mode). It was later determinedthat this was not the limiting factor in minimizing the main chamber pressure during operation.

19
The catcher (the turbo pump and differential pumping) was replaced so the port could be used tobuild the effusive gas jet.

Figure 2.9: Ion DLD image for the supersonic gas jet. A faint horizontal line along the center ofthe detector arises from the interaction of the XUV pulse train propagating through the chamberinteracting with the background gas. The intense region at the center is the interaction of the XUVpulse train with the supersonic gas jet where the molecules have a high initial momentum in thepositive y direction.

Figures 2.9 and 2.10 show the distinct difference between the supersonic and effusive gas jetson the ion delay-line detector (DLD) image. A description of this detector will be given in Section
2.3.4. The Figures show the supersonic jet is much more localized, causes very little backgroundsignal and therefore provides an effective means to filter the data. Figure 2.9 is an image of the x
and y position of the ion impacts on the delay line detector that will be described in more detail in
Section 2.3. In both Figures 2.9 and 2.10 there is a faint horizontal line of greater counts centeredon the detector and a small intense region offset in the y direction. The line shows the propagation

20

Figure 2.10: Ion DLD image for the effusive gas jet. A faint horizontal line along the center ofthe detector arises from the interaction of the XUV pulse train propagating through the chamberinteracting with the background gas. The intense region at the center is the interaction of the XUVpulse train with the effusive gas jet where the molecules have a lower initial momentum comparedto the supersonic jet, and in the negative y direction.

of the XUV ionizing background gas. The small offset region corresponds to ionization events fromeach gas jet. The offset comes from the y momentum component, in the positive y direction for thesupersonic gas jet and in the negative y direction for the effusive gas jet. Considerable care must be
put into achieving the correct backing pressure for the effusive jet so that the main chamber pressure
is not prohibitively raised. A high background pressure will cause the detectors to saturate withcounts, obscuring the jet signal and possibly causing damage to the detectors. Even when achieving
the correct pressure there is still a much greater background signal than with the supersonic jet.
While the increased count rate with the effusive jet is necessary for certain experiments it must be
weighed against a decreased signal-to-noise ratio due to the significant background counts. A major

21advantage of COLTRIMS is being able to filter for counts originating only from certain pathways,
which can include filtering on events only from the interaction region.
Because the effusive jet must be inserted within the copper plates which generate the electricfield it must be biased at the correct voltage in order to appear ‘invisible’ within the electric field.
A simple calculation can be done using the set potentials of the two ends of the copper plates.
Further adjustment can be done experimentally by minimizing the spread of the ions from the gas
jet.
The supersonic jet provided the source for experiments in Chapter 5 and Chapter 7. The
effusive gas jet was used in experiments in Chapter 4 and Chapter 6. Both jets are discussed in
Chapter 3 and Chapter 8.

2.3.2

Electric Field

A series of copper plates connected to a resistance chain creates an even potential drop,
producing a near-uniform constant electric field. These copper plates surround the interaction
region and are responsible for the acceleration of both the ions and electrons. There are 41 copper
plates connected in series with 100 kΩ resistors. A typical experiment puts the voltage at -150 V on
the plate closest to the electron detector and -450 V on the plate closest to the ion detector. Giving
the acceleration region an overall negative potential relative to the grounded vacuum chamber
prevents low energy background electrons from being accelerated and detected. The 3 center plates
are cut to allow the insertion of the laser and the supersonic gas jet. The acceleration region
is approximately 119 mm in the direction of the ion detector and 125 mm towards the electron
detector.
There is an area with no electric field referred to as the drift region between the acceleration
region and the electron detector that is approximately 245mm long. The region is kept at thesame negative potential as the electron end of the acceleration region (typically -150 V), again to
reduce low energy background electrons from being detected. This region is designed to refocus
the electrons in the time-of-flight direction, correcting for systematic error due to the size of the22

Figure 2.11: Schematic of the spectrometer inside the vacuum chamber. The main magnetic copper
coils and the gas jet chamber and catcher are also shown. The catcher, used for earlier experimentto maximize signal to noise, was later replaced with an effusive gas jet used to increase the countrate. From [42].

interaction region. The interaction region’s size is set by the finite spot size of the laser focus andthe gas jet. Electrons ionized closer to the detector will spend less time in the acceleration region
and have a slower velocity in the time-of-flight direction than electrons ionized further from thedetector. The electrons ionized further from the detector will therefore arrive at the detector closer
in time to the electron that was ionized nearer to the detector. Such a region is not necessary forthe ions, as they will not experience the same degree of spread because of their larger mass.

2.3.3

Magnetic Field

A constant magnetic field in the same direction as the electric field is generated by four coilsof copper wire. The purpose of the magnetic field is to allow for 4π angular resolution of highenergy electrons. Electrons with large momentum perpendicular to the time-of-flight direction thatwould otherwise escape detection will be put into cyclotron motion, allowing them to be accelerated

23
towards the detector. Each coil is made up of 100 turns of 10 gauge square copper wire with atypical current of 2.7 A and producing an overall magnetic field of approximately 5.5 Gauss. An
additional four coils of wire are used to fine tune the magnetic field in the x and y directions
to correct for the Earth’s magnetic field. These coils are 37 turns of computer cable and carryapproximately 1.7 A of current.
The magnetic field in the x and y directions can be adjusted to center low energy electrons
on the detector. The magnetic field in the z (time-of-flight) direction must be adjusted to detect
the highest energy electrons. Because the motion is dependent on the magnetic field a simple
calculation for the maximum radius detected can be done:√
re = 2

2me KeqB(2.10)

where Ke is the electron’s kinetic energy, me is the electron mass, q is the fundamental charge,
and B is the magnetic field.
As the magnetic field is changed depending on the experiment, it can be calibrated by lowering
the electric field so that there are multiple periods of cyclotron motion. The time between nodes
gives the magnetic field according to:

B=

2πme
eτ

(2.11)

where τ is the time between nodes.
Figure 2.12 shows a plot of electron radius of detection versus time-of-flight with a typicalcalibration set-up. Multiple nodes can be used to accurately find τ and therefore find B.

2.3.4

Detection

Detection of the charged particles is done with microchannel plates (MCP) on each side of
the spectrometer, coupled with a delay-line detector (DLD). Each MCP is biased at approximately
2.1 to 2.6 kV, set to maximize detection. Behind each MCP there is a wire grid delay line detector.

24

Figure 2.12: A plot of electron counts with their radius from the center of the detector vs. timeof-flight. With a lower electric field multiple nodes are present and can be used for magnetic fieldcalibration as well as an effective measurement for time zero. For data collection, the electric field
is adjusted to avoid multiple nodes when possible to maximize resolution.

Each channel on the plate acts as an electron multiplier producing a signal that then travels to thedelay line detector (“DLD” for ions and “HEX” for electrons) where it generates a small, measurable
current. The pulse of current travels both directions along the wire and the time of the signal isrecorded and then compared to a common fixed trigger signal taken from the laser amplifier. By
comparing the detection of one end of the wire to the other it provides the position of the particle
detected. Comparing the signals to the common trigger provides the time of detection. Assuming
the initial position from the interaction region, knowledge of the time-of-flight, and final x and final
y positions provides the ability to determine the full momentum of the particle detected.
The MCP for each detector has an active diameter of 120 mm. Consideration must be given

25
to setting up the experimental conditions such that the detector provides maximum resolution. By
maximizing the active area of detection energy resolution can be improved, however care must be
taken that counts can be ‘missed’ on the edge of the detector.
The electrical signal from each delay line is digitized to be recorded. First, each electrical signal passes through a set of differential amplifiers and constant-fraction discriminates in acommercial RoentDek ATR19 module. This provides an adjustable threshold to filter real signals
from background noise. The signals are amplified and made into negative nuclear instrumentation
module (NIM) pulses. Figure 2.13 shows a schematic of the electronic signal processing. Electronic
signals from the DLD are amplified before converted into a digital signal withEach module has adead time of more than 20 ns. This can present an issue with multi-hit detection. The NIM pulses
go to an 8 channel time-to-digital converter (TDC) each using a LeCroy MTD133B chip. Each TDC
has a resolution of 500 ps and can acquire up to 16 hits per laser shot. The TDCs has a deadtime
around 10 ns. Software provided by RoentDek processes and records the data from the TDCs to
the hard disk. More detailed technical information of the various components of the COLTRIMS
detector can be found in the RoentDek manuals available on their website (www.roentdek.com)
and [42].
While multiple hits can be recorded with each laser pulse, this should not be mistaken for theability to detect several separate ionization events. Detection is set up with the goal of achieving
one real coincidence event with each pulse. Because of Poisson statistics the expectation value
must be kept less than one event per shot in order to prevent increasing the number of ‘false’
coincidences caused by multiple ionization events. Once certain experimental conditions have beenmet, increasing the flux rate of either the number of photons or particles in the gas jet is notbeneficial to detection. This was mentioned briefly in Section 2.1 and is the reason for needing sucha high of a repetition rate from the amplifier while still producing high energy pulses to create highharmonics and generate the desired molecular dynamics.

26

Figure 2.13: A schematic of detection, signal processing by the electronics and digital conversion.
It is important to note that the differential amplifier and constant fraction discriminator occurs
within the same module (ATR19) though each waveform can be viewed.

2.3.5

Equations of Motion

The paths of ions in the system can be described by the equations of motion for the ion
detector. Using the known parameters of the apparatus and the time and position detection
information the ion momentum can be calculated:

pi,x =


pi,y = mipi,z =

m i xi
T OFi

yi− VjetT OFi(2.12)



mi Li
qE
−
T OFi
T OFi
2

(2.13)(2.14)

Where (xi ,yi ) is the final ion position, T OFi is the ion time of flight, Li is the length of the27
ion acceleration region, mi is the ion mass, and Vjet is the gas jet velocity, q is the fundamental
charge and E is the electric field. The equations assume a centered initial position.

Figure 2.14: A plot of electron momentum showing the capability to determine the exact harmonicenergies of the high harmonics from the photoelectron energies. The data has been filtered to takea narrow slice of values in y momentum.

Figure 2.14 shows the capabilities of the electron detector. Four clear energies are visible inthe momentum distribution of the photoelectrons from argon. Getting such a distribution requires
setting the experimental parameters exactly.
Equations of motion for the electron detector:

qB
pe,x =
2







qE
qE
−xe cos
T OFe /sin
T OFe + ye
2me
2me

(2.15)







qE
qE
ye cosT OFe /sin
T OFe − xe2me2me

(2.16)

qB
pe,y =228


pe,z = −me

Le,d
qE
−
T OFe,aT OFe − T OFe,a me
(2.17)

where (xe ,ye ) is the final electron position, B is the magnetic field, T OFe the electron time offlight, Le,a is the length of the electron acceleration region, Le,d is the length of the drift region, meis the mass of the electron, and T OFe,a is the time of flight of the electron inside the acceleration
region. Because T OFe,a is not a measurable quantity with the apparatus it must be solved for byinserting equation 2.17 into

Le,a =pe,zqE
2
T OFe,a +T OFe,ame
2me(2.18)

which produces the following third order equation:



qE
2me



3
T OFe,a
+




−qE
2
T OFe T OFe,a+ (Le,a + Le,d ) T OFe,a − Le,a T OFe = 02me(2.19)

This is equation is solved for within the COLTRIMS analysis routine.
Similarly consideration must be given to making sure the ion detector is maximized for
resolution but that counts are not missed. With the knowledge of the expected maximum kinetic
energy release (KKER ) of two positively charged ions, the electric field (E) can be set by theequation:

2mi Li
E=
2
qRDLD

s 
Vjet +

2

m2
m1



KKER
m1 + m2

!2(2.20)

where RDLD is the radius of the DLD MCP.

2.4

Beam LineTime domain spectroscopy requires the ability to optically start an atomic or molecular

dynamic and then probe the molecule with a second pulse at various time delays. The shortduration of the amplified Ti:sapphire pulses as well as the high harmonic generation provide the29
Ion Holder
Ion Signal/Reference
Ion MCP backIon MCP front
Ion Spectrometer End
Electron Spectrometer End
Electron MCP Front
Electron MCP Back
Electron Signal/ReferenceElectron Holder

65 V
180 V
0V
-2100 V-450 V-150 V-24 V
2650 V
2800 V
2900 V

Table 2.1: Typical operating voltages for COLTRIMS.

time resolution as the second pulse is scanned. The beam path geometry for the XUV-IR, pumpprobe configuration that was used for all atomic and molecular dynamics experiments with the
exception of Chapter 5 is shown schematically in Figure 2.15. For Chapter 5 a cross-beam geometry
was used. The 800 nm (IR) beam out of the amplifier is split before the XUV waveguide. The XUVpulse is generated in the waveguide and its output mode is imaged to the center of the COLTRIMS
main chamber with a pair of multilayer mirrors specifically coated for our apparatus, each designed
to reflect one or more of the harmonics. One of the mirrors has a 1 m radius of curvature, allowing
for 1-to-1 imaging of the output of the waveguide to the interaction region of the detector. The IR
light is sent through a variable delay stage and is recombined collinearly with the XUV beam using
a mirror with a 3 mm drilled hole in the center.
The variable time delay between the IR and XUV beams is controlled by a motorized stage,
with a total travel of 5 cm. Using our own calibration we found the smallest step size allowed was
260 attoseconds and the setup was interferometrically stable for sub-optical cycle resolution. The
IR beam is focused into the center of the detector with a 2 m radius of curvature mirror. Whileprevious work used a lens for focusing, it was determined that this produced too much dispersion
and would not allow for a short pulse in the interaction region. Due to the pump-probe geometry,it is difficult to precompensate for the added dispersion with a transmissive optic in only one armof the interferometer without affecting the stability. The recombination mirror only reflects anannular portion of the IR beam and therefore loses much of its intensity. Previous calculations

30
show that the focal spot size only changes by a few percent compared to a Gaussian profile, thoughconsideration must be taken for the lost energy [42]. With typical experimental conditions the IR
beam focuses to approximately 50 µm in diameter.

Figure 2.15: Schematic of the recombination of the XUV and IR beam lines before entering the
COLTRIMS main chamber. The high harmonic beam reflects off of two multilayer mirrors before
passing through the center of an annular mirror. The IR beam is focused with a curved mirror
directly before being collinearly recombined with the annular mirror.

The XUV spot size is also approximately 50 µm in diameter. This number is approximatedby assuming good imaging of the waveguide output to the center of the detector. The gas-filledcapillary has an inner diameter of 150 µm and only portions of the guided wave with sufficient
intensity cause the high harmonic process. We assume to be close to the optimal waist size ofω0 = 0.64a where a is the inner bore radius [6].
Overlapping the XUV and IR beams temporally and spatially in the interaction region isdone with a kick-out mirror in the differential pumping chamber. A CCD camera is placed at thesame distance as the interaction region inside the COLTRIMS chamber. This allows for accurate
resolution of each beam’s spatial profile. The IR beam that copropagates with the XUV canpass outside of vacuum and can be used to find temporal overlap by looking for constructive
and destructive interference fringes from the two coherent beams. This interference allows for31
a measurement equivalent to a cross correlation. The XUV beam follows the same path as its
copropagating IR. This procedure assumes the IR beam is well aligned with the XUV waveguide.
Because the beams are collinear, once spatial overlap is found, it should be consistent along thebeam path. Spatial overlap is therefore checked after the beams pass through the COLTRIMS
chamber as well.

Figure 2.16: A plot showing typical electron momentum and electron energy which demonstrates
the capability to determine the exact frequency of the high harmonics from the photoelectronenergies. This requires exact knowledge of the detector parameters but allows for knowledge of the
XUV pulse train energies.

Figures 2.16 and 2.17 give an example of checking spatial and temporal overlap with thedetector. Figure 2.16 shows the photoelectron energies and momentum distribution for ionization
due to only the XUV pulse. As shown clearly by the inset of the electron momentum, the ionization
comes primarily through the 11th harmonic which sits well of above the ionization threshold ofargon. The 13th harmonic is also visible.
Figure 2.17 shows the photoelectron energies and momentum distribution changed for ionization due to the XUV pulse overlapped with the IR pulse. An effective 10th harmonic energy
peak appears due to the interaction of the XUV and IR. This interaction allows for a 9th + 1ω and11th − 1ω interaction. Figure 2.17 is normalized for comparison purposes and does not show theincreased count rate from Figure 2.16. The calculation of photoelectron energies will be discussed

32

Figure 2.17: A plot showing typical electron momentum and electron energy which demonstrates
the capability to determine the photoelectron energies in the presence of both the high harmonic
pulse train and the IR pulse during temporal overlap.

in further detail in Section 2.7.
After high harmonic generation, the beam line must be in vacuum until it reaches the detector
in order to allow the XUV light to propagate. The deep UV and XUV portions of the spectrum
are highly dispersive and absorptive in the atmosphere. This presents experimental difficulties,
as the most sensitive optics for beam alignment must also be under vacuum. Motorized mirror
mounts are used for the multilayer mirrors. A 300 L/s turbo pump, designed to maintain a 10−5 10−6 torr pressure inside the box, was decoupled from the recombination vacuum box to allow forinterferometric stability.
A second prechamber exists to allow for the “kick-out” mirror to be inserted to check for
spatial and temporal overlap as well as to maintain a low operating pressure in the main chamber
through differential pumping. This kickout chamber is pumped with an additional 300 L/s turbo
pump and contains none of the possible outgassing components of the recombination chamber.
An additional aperture was added to allow for differential pumping between the kickout chamberand multilayer mirror chamber in additional to the existing differential pumping before the mainchamber. With the addition of this 6 mm aperture the main chamber can maintain an operating

33
pressure below 5 × 10−9 torr while open to the beam line.

Chapter 3
Argon1This Chapter will discuss the results and analysis for studies done with argon as the target in
the gas jet with applications to other noble gases. The Chapter covers several experimental photon
energies and set-ups that all contribute towards a greater level of understanding. In rare-gas atoms,
Auger decay in which an inner-valence shell ns hole is filled is not energetically allowed. However,in the presence of a strong laser field, a new laser-enabled Auger decay channel can open up to
increase the double ionization yield. This process is efficient at high laser intensities, where an ns
hole can be filled within a few femtoseconds of its creation. This novel laser-enabled Auger decay
process is of fundamental importance for controlling electron dynamics in atoms, molecules, andmaterials.

3.1

Laser Enabled Auger Decay
Auger decay is an important decay process in highly excited systems, that is, relevant toradiation physics, x-ray spectroscopy, x-ray lasers, and atmospheric chemistry. In Auger decay,
absorption of a high-energy photon leads to the ejection of an inner-shell primary photoelectron.
The resulting hole is then filled by an electron from an outer shell, with any excess energy carriedaway by ejecting a second Auger electron. Advances in laser and x-ray technology now makeit possible to create an inner-shell core hole using a femtosecond or attosecond burst of x-rays
1

The results of this chapter are in part based on “P. Ranitovic, X. M. Tong, C. W. Hogle, X. Zhou, Y. Liu,
N. Toshima, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 106, 053002 (2011)” [43] and “X. M. Tong, P.
Ranitovic, C. W. Hogle, M. M. Murnane, H. C. Kapteyn, and N. Toshima, Phys. Rev. A 84, 013405 (2011)” [44].

35
and to observe or manipulate the resultant photoelectron or Auger electron using an ultrafast
infrared (IR) laser. Laser-assisted photoemission was first observed in atoms and more recently insolids [45, 46]. It is now used to characterize x-ray pulses and to capture fast electron dynamics
in atoms and materials [32, 47]. In a laser-assisted process, an atom or material is simultaneously
irradiated by ultrafast x-ray and laser pulses. Characteristic sidebands appear surrounding thephotoemission and Auger peaks, corresponding to simultaneous absorption and emission of laser
photons in addition to the x-ray photon. The magnitude and shape of these sidebands change
as the time delay between the x-ray and laser pulses is changed, encoding information about the
x-ray pulse duration as well as any underlying electron dynamics in the atom or material [48–52].
However, to date laser-assisted Auger decay represented a means by which an existing Auger decay
channel could be modified and exploited. It was not understood that a strong laser field can also
turn on and control the Auger decay process itselfwhich is a fundamental decay mechanism for
matter exposed to ionizing radiation.

3.1.1

Experimental Generation of a ns HoleWe identify, through theory and experiment, a novel ionization channel that opens up only inthe presence of an intense laser field. Experimentally we find that in the presence of a sufficiently
intense IR laser and an extreme ultraviolet (XUV) field, the double ionization yield of Ar is enhanced
by 50% compared to the case when the laser pulse arrives after the XUV pulse. Although Ar2+
can also be produced by sequential and nonsequential absorption of XUV and IR photons (shakeup
and shake-off processes), the observed ratio of doubly to singly ionized argon is larger than canbe theoretically explained by these processes alone. Therefore, we need to include a new double
ionization pathway: IR laser-enabled Auger decay (LEAD), which is energetically forbidden without
the presence of the IR field. Normally in a rare gas atom, Auger decay following the creation of anns hole by an XUV photon is not energetically allowed. However, our theoretical predictions showthat the laser-enabled Auger decay rates are even larger than the radiative decay rates for laser
intensities above 1013 W/cm2 , and thus the inner-valence hole can be filled by the LEAD process

36
on few-femtosecond time scales. This novel decay channel is also quite general, representing afundamentally new mechanism for generating ions and Auger electrons that must be considered inultrafast x-ray experiments. It also provides a new route for controlling electron dynamics using
ultrafast light fields.
Figure 3.1 (b) illustrates the possible single and double ionization channels in Ar. We consider
three cases: the IR pulse precedes the XUV pulse (region I); the two pulses overlap in time (regionII); and the IR pulse follows the XUV pulse (region III). Figure 3.1 (a) shows that the Ar2+ yieldis negligible for region I, while the yield increases dramatically for positive time delays, peaking
in region II when the XUV and IR pulses overlap. The enhancement of the Ar2+ yield in region
III is due to field ionization of Ar+∗ and Ar∗∗ states excited by the XUV pulse, and due to the
LEAD process. We note that without the IR pulse the 3p−1 and 3s−1 highly-excited Ar+ statesradiatively decay on a nanosecond time-scale. The most interesting behavior, however, occurs inregion II when the XUV and laser pulses overlap in time. The observed enhancement in the Ar2+
signal strongly suggests that the laser field modifies the mechanism for populating the Ar+∗ /Ar∗∗states created after the absorption of a single XUV photon. There are two possible mechanisms forthe observed enhanced Ar2+ yield in region II: first, the laser field can influence the shake-up andIR-ionization sequence by modifying, broadening, and shifting of the Ar+∗ resonances [15, 53]; andsecond, the laser field can provide the additional energy required to open up a shake-off channel,
which does not occur in region III (where the XUV pulse excites unperturbed Ar+∗ states that aresequentially ionized by the IR pulse).
To investigate the physical origin of the Ar2+ signal we note that there are four possible
ways to create Ar2+ in the presence of simultaneous IR and XUV (42 eV) fields: (a) IR assisted
shake-off and shake-up processes in regions II and III, (b) knockout ionization processes, (c) single
photon double excitation by the XUV pulse, followed by IR-induced double ionization, and (d) a
new mechanism of IR-enabled Auger decay of an XUV-induced 3s hole.

37

Figure 3.1: (a) Ar2+ and Ar2+ /Ar+ yields as a function of the XUV pump and IR probe delay. The
three regions correspond to the different relative delays of the XUV and IR pulses. (b) Schematic
diagram of double ionization pathways in different regions. In region II, the main double ionization
channels are labeled as shake-off and IR-enabled Auger decay. In region I, since Auger decay is
not energetically allowed, the XUV pulse creates Ar+ and Ar2+ states. These states, respectively,
radiatively decay and autoionize, and do not contribute to the Ar2+ yield. In region III the IR
pulse arrives after the XUV pulse, and doubly ionizes the Ar+ and Ar2+ states created by the
XUV pulse, and opens up the LEAD channel. In region II the IR field enhances the Ar2+ yieldby altering the atoms electronic structure, influencing thus the LEAD, shake-up or shake-off, andother allowed channels. (c) The laser-enabled Auger process is shown through the creation of a 3s
hole with an XUV pulse and then ionization with additional IR energy. This process contributes
to the double ionization yield in both regions II and III.

38
3.1.2

Theoretical Calculations

The double ionization probability of Ar through channels (a) and (b) depends on the excessenergy available above the double ionization threshold of 43.5 eV in Ar [54]. Field ionization by
the IR field provides this excess energy when Ar is exposed to a combined action of XUV and IR
fields. Thus, to estimate the expected Ar2+ /Ar+ ratio from channels (a) and (b), we first calculate
the photoelectron yields above and below the double ionization threshold. Second, we calculate
the shake-up and shake-off ionization probabilities from the 3s and 3p orbitals. We do this bysolving the time-dependent Schrödinger integral equation [55] by the split-operator method in theenergy representation [56] to obtain the above-threshold ionization (ATI) distribution dP (E)/dE
from both 3s and 3p orbitals. The IR intensity used in the calculation was 5 × 1012 W/cm2 . The
detailed numerical method can be found elsewhere [57]. The double ionization yield depends on
the ATI spectra with total energy higher than the double ionization threshold, according toP ++ =Z

dP (E)
dE
dE
E>Ec

(3.1)

where E is the ATI electron energy and Ec is the minimum energy needed to open the double
ionization channel. We find that the ATI electrons above the Ec threshold contain 30% of the total
ATI yield. On the other hand, the total shake-off (including shake-up) probability after removing
a 3p or 3s electron can be calculated by using the sudden approximation

P = (1 − hψ̃3p |ψ3p i2 )nocc(3.2)

where ψ̃3p and ψ3p are the 3p wave functions of Ar and Ar+ calculated by utilizing density
functional theory with the self-interaction correction method [58], while nocc is the number of thevalence Ar+ electrons. We find the shake-up or shake-off probability to be P = 4%, after thesudden removal of 3p and 3s electrons. By multiplying this probability with the double ionization
photoelectron yield calculated above, we find that the upper limit for the shake-off yield is 1.2%.
However, the measured fractional Ar2+ yield shown in Figure 3.1 (a) peaks at 4% near time zero,
which means that channels (c) and (d) must also contribute significantly to double ionization.

39
In the case of process (c)-single-photon double excitation to Ar∗∗ by the XUV pulse followed
by IR-induced double ionizationthe first step of creating Ar∗∗ has been studied using synchrotron
light in the energy range considered here [59, 60]. In the presence of an additional IR field, the
XUV-induced Ar∗∗ states can be promoted into the double ionization continuum, thus contributing
to the total Ar2+ yield. Because doubly excited states in general autoionize on femtosecond timescales, their signature would be seen as a decay in the Ar2+ yield at long time delays, as indeed
seen in region III of Figure 3.1(a). Calculating exactly how the IR laser influences the creation of
doubly excited states in region II still remains a theoretical challenge.
Route (d), which represents a novel IR-enabled Auger decay route for the XUV-induced 3shole, as shown in Figure 3.1(b), is also possible. After the creation of a 3s hole with the XUV pulse,the 3p-3s Auger decay is energetically forbidden. However, this double ionization channel can be
opened up in the presence of a sufficiently high IR laser field. In the case of Ar, an Auger-induced
3p electron needs 14.8 eV of extra energy to reach the double ionization continuum. Assumingthat the wave functions of the atomic ion with a subshell hole (N − 1 electron system), the doubly
ionized ion core (N − 2 electron system), and the Auger electron are Ψh (N − 1), Ψc (N − 2), andψa with the corresponding Hamiltonians Hh (N − 1), Hc (N − 2), and ha , respectively, we can write
the time evolution of the Auger electron wave function as

Z t
ψa (r, t) = −i

Rt

0

0

e−i τ ha (t )dt e−i(Eh −Ec )τ F (r)dτ

(3.3)

−∞

Here Eh and Ec are the total energies of the Ψh (N − 1) and Ψc (N − 2) states, respectively.
To derive the above equation, we assume that the IR laser only affects the Auger electron and thatit does not perturb the occupied orbitals in Ψh (N − 1) and Ψc (N − 2). Since the Auger process isa two-electron process, F (r) is evaluated as

F (r) =N−2X

hΨc (N − 2)|i=11|Ψh (N − 1)i|r − ri |(3.4)

which does not depend on the IR field. The Hamiltonian of the Auger electron in the IR40
laser is written asha (t) = −∇2+ Vef f (r) − zE(t)
2

(3.5)

where Vef f (r) is the model potential [61] of the atomic ions, z is the electron coordinate along
the IR polarization direction, and E(t) is the IR field strength. For Ar, |Ψh (N − 1)i can be written
as |3s3p6 2 Si, which can be represented as [62]1|Ψh (N − 1)i = √ |3s(3p4 1 S)3p2 2 Si
15
1
+ √ |3s(3p4 1 D)3p2 2 Si
3r
3+|3s(3p4 3 P )3p2 2 Si
5

(3.6)

|Ψc (N − 2)i is |3s2 3p4 1 Si or |3s2 3p4 1 Di. The last term in Equation 3.6 does not contributeto the LEAD due to conservation of the angular momentum and parity. The final doubly charged
ions created by the LEAD can be in the 1 S (the upper limit is 1/15) or 1 D (the upper limit is 1/3)
states, limiting the total double ionization yield to be 40% of the hole population.
By defining a radial function f (r) asZ ∞f (r) =
0r<
R3s (r1 ) 2 R3p (r1 )R3p (r)r12 dr1
r>

(3.7)

where r< (r> ) is the smaller (larger) one of the r and r1 , and R3s and R3p being the radial
wave functions of 3s and 3p states, we obtain − √1 f (r)Y00 (r̂)
3
F (r) =q − 2 f (r)Y2M (r̂)
15

for 1 S
(3.8)
for 1 D

1 S (1 D) stands for the final state of the doubly ionized species. Using the expression for F (r),we calculate the Auger election wave function from Equation 3.3 numerically [56]. Again, the single
electron wave functions of the occupied orbitals in |Ψh (N − 1)i and |Ψc (N − 2)i are calculated fromthe density functional theory with the self-interaction correction method [58].

41
2

2

To speed the convergence of the simulation, we add a temporal window function e−τ /T in
Equation 3.3. Thus, after a long propagation time we can expand ψa with a set of wavefunctionsasZ
ψa (r, t → ∞) =C()ψ (r)d(3.9)

where ψ (r) is the laser-field-free atomic continuum wave function, and  is the Auger electronenergy [55]. The energy distribution of the emitted electron can be expressed asdP ()= |C()|2d(3.10)and the LEAD rate can be written as
√

2π
Ra =
T

Z ∞
0

dP ()dd

(3.11)

Figure 3.2: Calculated IR laser-enabled Auger decay rates for Ar. At lower laser intensities, theleading decay channels are the 1 S and 1 D (M=0) states. As the IR laser intensity increases, thecontribution from the 1 D (M=0) state is larger than that from the 1 S state. Radiative 3p-3s decay
is represented by the dashed line.

42
The

√

2π/T term is introduced because we added a temporal window function. If there is no

IR laser field present, Equation 3.11 reduces to the standard expression for the Auger decay rate.
Because of the energy deficiency, the Auger decay rate goes to zero for an inner-valence 3s vacancy
of Ar without the presence of the IR field.

3.1.3

Calculation of the LEAD Rate

Based on the above approach, we can now calculate the LEAD rate in Ar. From Figure 3.2
we see that laser intensities of ≈ 1013 W/cm2 can indeed open up a new laser-enabled Auger decay
channel, with a rate of 4.3 × 10−4 fs−1 , which is comparable or even larger than the radiative
decay rate of the 3p electron. Thus, the contribution to the Ar2+ yield from the LEAD channel iscomparable to contributions from the shake-off channel, and must therefore contribute to the total
Ar2+ yield.
New ionization pathways are possible when matter is irradiated by intense laser and x-ray
fields. In this work, to explain the yield of Ar2+ ions in the presence of combined IR and XUVfields, we needed to include a new double ionization pathway: IR laser-enabled Auger decay, whichis energetically forbidden without the presence of the IR field. Our theoretical predictions showedthat LEAD rates are even larger than the radiative decay rates for laser intensities above 1013
W/cm2 , and that the 3s hole can be filled by the LEAD process on few-femtosecond time scales.
This novel decay channel is also quite general, representing a fundamentally new mechanism forgenerating doubly charged ion cores, ionic Rydberg states, and Auger electrons. It also provides a
new scheme for controlling electron dynamics in atoms, molecules, and solids using IR fields.

3.2

Ar+ vs. Ar2+ Control
In a different experiment, a spectrally tailored high harmonic beam, with both VUV and XUV

harmonics, was used to coherently excite Rydberg states of argon below the single and double
ionization thresholds by means of the 7th-9th, and 25th-27th harmonics of the driving IR laser
field. Figure 3.4 shows the set-up for reflecting both low and high harmonics in a non-blueshifted43

Figure 3.3: Schematic diagram of IR-enabled Auger decay in a rare-gas atom.

(phase matched for a fundamental energy of 1.61 eV) and blueshifted case (phase matched for a
fundamental energy of 1.69 eV). By tuning the pressure of the harmonic generation medium wecan blue-shift the central energy of the harmonic combs in such a way that the VUV harmonics(i.e. 7th and 9th) are either nonresonant (depicted in red) or resonant (depicted in blue) with
the Ar∗ Rydberg states. At the same time, the multilayer mirror, coated to reflect photons withenergies around 42 eV, can select either one dominant (i.e. 25th) or two dominant XUV harmonics(25th and 27th) that can directly double ionize and excite Ar+ slightly below the double ionizationthreshold. By adding a weak IR field (∼3 × 1011 W/cm2 ), delayed relative to the harmonic beam,
we can couple the states excited by the VUV/XUV beam directly into the single/double ionization
continuum and control the phases of the interfering electron wave packets, which in turn results in
the Ar+ and Ar2+ yield modulation.
In Figure 3.4 inset part (a), a theoretical simulation shows the total Ar+ yield when theresonant and nonresonant VUV beam acts as a pump, and the IR field acts as a probe. The
oscillation of resonant and nonresonant cases are dephased from one another. Since in this caseonly one IR field is present, only the quantum interferences play a role in the total yield modulation.
By keeping the IR probe pulse the same, and by adding a second, weak IR pulse phase-locked to
the VUV pulse, shown in inset (b) in Figure 3.4, we start mixing optical and quantum interferences
as the probe IR beam is delayed. The optical interferences in between the two IR pulses have the44

Figure 3.4: Schematic of the low (VUV) and high (XUV) harmonic reflectivity curves and ionizationlevels for Ar. The inset part (a) shows the simulated Ar+ yield when the resonant and nonresonant
VUV beam acts as a pump, and the IR field acts as a probe. The oscillating yield occurs due toquantum interferences. The inset part (b) includes a second IR pulse phase-locked to the VUVpulse in the simulation, therefore including optical and quantum interferences as the probe IR beam
is delayed.

same phases in both resonant and nonresonant cases, while the phase of the quantum interferenceschanges as we tune the VUV harmonics in and out of the Ar∗ resonances. From Figure 3.4(b),we see that when the optical and quantum interferences are in phase (i.e. the resonant case), thetotal Ar+ yield oscillates with a full cycle periodicity. In the nonresonant case the quantum andthe optical interferences are off phase, which results in the total yield modulation close to half a45cycle oscillation.
Figure 3.5 directly demonstrates tuning the VUV harmonic frequencies over a resonance.
Figure 3.5 parts (a),(c) show the experimental Ar+ yield as a function of IR delay where negative
delays refer to the IR pulse arriving before the XUV pulse train. In Figure 3.5(a) the harmonics
are minimally blue shifted (nonresonant case). In part (c) the harmonics are blue-shifted such thatthe 9th harmonic resonantly excites the atom resulting in a clear change in the femtosecond scale
yield. In both cases the IR probe pulse does not have significant intensity to ionize Ar without
interacting with the XUV pulse. Parts (b) and (d) show the theoretical simulations for the sameenergies. They are in excellent agreement. The Figure shows both the cycle-averaged behavior aswell as an inset showing sub-optical cycle resolution. We note that in part (a) the single ion yieldoscillates with a half-cycle periodicity (or a period of 1.3 fs) whereas in part (c) this changes tofull-cycle (or a period of 2.6 fs).
Figure 3.6 shows the photoelectron data for the same non-blueshifted and blueshifted cases
described for Figure 3.5 along with the theoretical simulations. Again we note agreement between
experiment and the simulation. In particular the Figure highlights the difference between half
optical cycle oscillation (parts (a) and (b)) and full optical cycle oscillation (parts (c) and (d)).
Figure 3.7 shows the photoelectron energies for electrons collected in coincidence with Ar2+
in the resonant case. Although the photoion-photoelectron count rate was low for this experiment
it demonstrates our ability to simultaneously probe the photoelectrons from the double ionizationthreshold as well as the single ionization.

3.3

Extension of LEAD to other Noble Gases
To find further evidence of LEAD processes, we performed experiments on the double ion-

ization of Ar and Xe atoms using time-resolved femtosecond IR and 36 eV XUV pulses. For argon,
36 eV is well below the double ionization threshold, and several possible double ionization channels
open up in the presence of an IR pulse as intense as 7 × 1012 W/cm2 [43]. For xenon, the 36 eV
photon energy is just above the double ionization threshold and the number of double ionization

46

Figure 3.5: Single ionization yield (a) Nonresonant experiment (b) Nonresonant theory; both show
half cycle oscillations, (c) Resonant experiment (d) Resonant theory; both show full cycle oscillations. The nonresonant theory and experiment uses harmonics phase matched to a fundamental of
1.61 eV. The resonant theory and experiment uses harmonics phase matched to a fundamental of
1.69 eV.

channels significantly reduces compared with the ar case. For example, Xe∗∗ (5p4 ) and Xe+∗ (5p5 )states are not possible, as was the case in Ar. In Xe, a 36 eV XUV photon can create a 5s hole andleave the singly charged Xe in the ground state after a 5p-5s radiative relaxation, or leave 5s Xe ina highly excited state as shown in 3.8 lower panel. In the former case, the IR pulse can ionize Xe+
through the LEAD process with rates several orders of magnitude larger than the radiative 5p-5s
decay as shown in Figure 3.8 upper panel. The ability to enable Auger decay with rates significantly
higher than radiative decay opens up possibilities for controlling electron-electron interactions inatoms and molecules. Using part of the laser output, high harmonics are generated in Ar gas andthen refocused multilayer XUV mirrors which reflect photon energies around 36 eV. A 200 nm
thick Al filter is inserted in the XUV beam to attenuate the driving IR pulses reflected from the
XUV mirrors. This results in higher reflectivity of lower harmonics. In this case, the 13th and 15th

47

Figure 3.6: Photoelectron energies vs. delay (a) Nonresonant experiment (b) Nonresonant theory;both show half cycle oscillations, (c) Resonant experiment (d) Resonant theory; both show fullcycle oscillations. The nonresonant theory and experiment uses harmonics phase matched to afundamental of 1.61 eV. The resonant theory and experiment uses harmonics phase matched to afundamental of 1.69 eV.

Figure 3.7: Photoelectron energies vs. delay filtered in coincidence with Ar2+ . The photoelectrons
also show full optical cycle oscillations.

harmonics are reflected from the XUV optics as seen in the Ar photoelectron spectrum shown in
Figure 3.9 (lower panel). The probing IR has an intensity of approximately 7 × 1012 W/cm2 .

48

Figure 3.8: Upper: IR-enabled Auger decay rates for Xe, with Xe2+ ions in the 1 S state (solid line)
and 1 D states (dashed lines). The horizontal dashed line indicates the radiative decay rate of thehole. Lower: (a) Xe energy diagram for the lowest single and double ionization thresholds with a
5s electron ionized by an XUV pulse. (b)A 5p electron can be ejected to an Xe+∗ Rydberg orbit
or the Xe2+ continuum through the LEAD process after a respective absorption of at least one orseven IR photons.

3.3.1

Argon and Xenon Experimental Results

Figure 3.9, upper and lower panels, respectively, shows the argon double ionization yield aswell as the ratios of Ar2+ /Ar+ yields, and a photoelectron yield, taken in coincidence with Ar+

49

Figure 3.9: Ar2+ and Ar2+ /Ar+ yields as a function of the delay between the XUV and IR pulses(upper panel). The photoelectron spectra taken in coincidence with Ar+ ions in the overlap region(lower panel).

atoms, as a function of the XUV-IR relative delay. Negative delays represent the case when the IR
pulse precedes the XUV pulse, while positive delays present the case when the IR pulse arrives after
the XUV pulse. The two pulses overlap temporally for the delays between -30 and +30 fs (overlap
region). Figure 3.9, upper panel, shows that the moderate IR field enhances the Ar2+ yield byroughly 30 times in the overlap region, while the Ar2+ /Ar+ ratio maximizes at about 1.6%. The
photoelectron yield taken in coincidence with Ar+ ions (Figure 3.9, lower panel) shows a peakaround 20 eV corresponding to photoionization of a 3p electron by the 36 eV XUV photon. If the
XUV pulse ionizes a 3s electron (binding energy 29.2 eV), we expect to see a photoelectron signal

50
around 6.2 eV, after subtracting the ponderomotive potential of about 500 meV. The photoelectron
yield in that region shows two lines at 4.2 and 7.4 eV, corresponding to a 3p electron ionized by the
13th and 15th harmonics leaking though the XUV reflective optics. Since the 36 eV XUV photonis 7.5 eV below the double ionization threshold, the Ar2+ enhancement in the overlap region could
come from coupling of the Ar+∗ and Ar∗∗ 3p states into the double ionization continuum by the IR
pulse. Single-photon double ionization is a resonant process and the Ar2+ yield of IR field ionizationof Ar∗∗ should be sensitive to the XUV energy. The pattern of the Ar2+ /Ar+ yield obtained by
the 36 eV XUV photon is similar to the one obtained by the 42 eV XUV source [43]. Therefore,
the additional double ionization yield enhancement also comes from a LEAD process where the36 eV photon ionizes a 3s electron, while the IR field couples an Auger 3p electron to the double
ionization continuum.
Figure 3.10, upper and lower panels, respectively, shows a Xe double ionization yield as wellas the ratios of Xe2+ /Xe+ yields, and the photoelectron yield, as a function of XUV-IR relative
delay. The data was taken by using similar XUV and IR parameters as for the Ar data shown in
Figure 3.9. By doubly ionizing Xe using a 36 eV XUV pulse, we make sure that the highest double
ionization threshold (1 D2 35.5 eV) is still below the XUV photon energy. By doing so, we eliminate
the double ionization contribution from the Xe+∗ /Xe∗∗ 5p states ionized by the IR pulse. This
results in a significantly smaller enhancement of the Xe2+ yield in the overlap region, comparedwith the Ar2+ enhancement (30:1.7 in favor of Ar), and in a higher Xe2+ /Xe+ ratio (4:1.6 in favorof Xe). The flat Xe2+ yield for positive IR delays shows that short-lived, autoionizing double
excited states probably do not play a significant role in this case. From the photoelectron spectra[Figure 3.10 (lower panel)], we notice that the lower harmonics (13th and 15th) contribute moresignificantly to the Xe+ yield compared with the Ar case. Thus, the Xe2+ /Xe+ yield coming fromthe 36 eV photon channel is probably even higher than shown in Figure 3.10 (upper panel). In
the case of Xe, 7 × 1012 W/cm2 IR intensity can ionize Xe, as seen at 0.2 eV electron energy
at both positive and negative delays in Figure 3.10. By setting up the experiment in this way,
we make sure that the LEAD process is experimentally possible, since the Xe LEAD deficiency is

51
only 9.80 eV. However, even though we were able to decrease the number of the IR-enabled double
ionization channels by using an XUV photon energy just above the double ionization threshold,isolating unambiguously the LEAD process remains an experimental challenge.

Figure 3.10: Xe2+ and Xe2+ /Xe+ yields as a function of the delay between the XUV and IR pulses(upper panel). Photoelectron spectra taken simultaneously with the Xe ions (lower panel).

3.3.2

Attosecond Time Scale Dynamics

In addition to exploring femtosecond delays, we performed a time-resolved experiment withattosecond resolution in the overlap region. Figure 3.11 shows the Xe2+ versus Xe+ yield as afunction of the XUV-IR delays. In this experiment, in addition to the 36 eV XUV harmonic we52allow the lower harmonics (lower than the Xe ionization potential) to populate neutral Xe∗ states.
We did this by taking the Al filter out of the XUV beam. By doing this, we lock a weak IR pulse(3 × 1011 W/cm2 ) to the XUV pulse in the time domain, and let both beams copropagate. The
inset of Figure 3.11 shows the XUV and IR pulses in the time domain. As we delay the probe
IR beam (7 × 1012 W/cm2 ) on an attosecond time scale relative to the XUV–IR pump beam, wechange the total intensity the atom sees at the instant of the strobe XUV pulse [15, 63]. By doing
so we control the Xe2+ /Xe+ yields both by modulating the total IR intensity and by interfering theelectron wave packets. The phase difference of about a half optical cycle is telling us that different
processes are responsible for the coherent control of the single and double ionization Xe yields. Theinterference of the two electronic wave packets with the final energy of the 8th harmonic (7th +IR and 9th − IR) are responsible for the modulation of the Xe+ yield, while the modulation of
the Xe2+ yield can occur through several different channels. The LEAD channel is very sensitive
to the IR intensity as shown in Figure 3.8, but also it is possible that the phase of the XUV and
IR pulses plays a role. Thus, we are not surprised that the Xe+ and Xe2+ yields get modulated at
different phases, and with different amplitudes. We expect that the LEAD process would dependon the time delay between the attosecond XUV pulse (creation of the hole) and the probing IR
field (induced Auger decay). Thus we can both induce Auger decay by employing an IR laser fieldand control the process by tuning the time delay between the two pulses.

53

Figure 3.11: Xe+ and Xe2+ yields as a function of the XUV-IR pump and IR probe pulses. The
XUV and IR pulses in the time domain are shown in the inset.

Chapter 4
Helium1

High-order harmonic generation (HHG) is a unique source of ultrashort-pulse light spanningthe ultraviolet and soft x-ray regions, that is ideal for initiating and probing fast dynamics inatoms, molecules, and materials [47, 64–67]. Atoms irradiated with combined femtosecond laserand extreme ultraviolet (XUV) fields ionize through multiphoton processes, even when the energyof the XUV photon is below the ionization potential. However, in the presence of two different
XUV photons and an intense laser field, it is possible to induce full electromagnetic transparency.
Taking helium as an example, the laser field modifies its electronic structure, while the presence of
two different XUV photons and the laser field leads to two distinct ionization pathways that caninterfere destructively. This Chapter discusses a new approach for coherent control in a regime ofhighly excited states and strong optical fields.

4.1

Ionization pathway interference
Because the high harmonic field is perfectly synchronized to the generating laser field, complex

reaction pathways relevant to radiation physics and chemistry can be probed [14, 68, 69]. In suchhighly excited processes, the laser field plays a crucial role in initiating, interrupting, or probing areaction. However, the full influence of the laser field on highly excited reaction pathways is still
being uncovered [70, 71], despite a wealth of theory and experiments exploring these processes. For
example, calculations that model how dynamics are probed by HHG generally ignore the dynamic
1

The results of this chapter are in part based on “P. Ranitovic, X. M. Tong, C. W. Hogle, X. Zhou, Y. Liu, N.
Toshima, M. M. Murnane, and H. C. Kapteyn, Phys. Rev. Lett. 106, 193008 (2011)” [63].

55
modification of the electronic structure of the atom or molecule by the laser field itself. Moreover,although helium is fully accessible to state-of-the-art theoretical calculations, even a simple twocolor ionization process has to date proven to be far from simple to understand [15, 34, 57, 72–74].

4.1.1

Two-Color Multiphoton Processes

We study one of the simplest multiphoton processes: two-color multiphoton ionization ofhelium in combined infrared (IR) laser and extreme ultraviolet (XUV) high harmonic fields in a
regime where two different ionization pathways can interfere coherently: 13th + 3ω and 11th + 5ω.
We show both theoretically and experimentally that this two-color multiphoton ionization process
can be viewed intuitively as a double-slit interference experiment in the frequency domain, andthat ionization can be turned on or off by manipulating the two interfering pathways and shown in
Figure 4.1. In addition to participating in the multiphoton absorption process, the strong IR fieldalso alters the He excited state electronic structure by Floquet state (or dressing state), resulting
in energy sidebands [57]. This allows us to adjust the position, amplitude and phase of the two
multiphoton ionization channels, by tuning the XUV fields to the laser-dressed He 2p absorption
resonance. Most importantly, by analyzing the multiphoton ionization process in the frequency
domain, we develop an intuitive understanding of strong field two-color ionization to show, for the
first time, that full laser-induced XUV electromagnetic transparency in He is possible. In the twophoton absorption schemes widely used for coherent control using visible laser fields [75–81], thephase of a weak, nonperturbative IR pulse can control absorption through interfering two-photontransitions. A multicolor, multiphoton XUV + IR ionization process is similar in some respects,
except that in this case, the final state is in the continuum. Moreover, we show that a strong
IR laser field can play multiple roles in a multicolor, multiphoton, XUV + IR ionization process,as is illustrated schematically in Figure 4.1. Specifically, by coherently populating laser-dressed
excited states of He with the two tunable XUV harmonics (11th and 13th), and simultaneously
using the same IR laser to couple the excited states to the continuum with equal amplitudes butwith opposite phases, it is possible to make a He atom fully transparent to multiphoton XUV +56
IR ionization. The phases of the two interfering channels are controlled by introducing suboptical
cycle delays between the XUV and IR pulses, while the amplitudes are controlled by using the
IR field to modulate the electronic structure of the He atom, thus changing the absorption crosssections of the two XUV harmonics through ac and dc Stark shifts that move and broaden theatomic resonances [15].

Figure 4.1: (a) Tuning of the harmonics in the frequency domain into the IR-created 2p double
slit by varying the phase-matching conditions in a xenon-filled waveguide. The dashed verticallines represent the calculated sidebands of the dressed Floquet 2p state of He. The two interfering
quantum pathways are 11th + 5ω and 13th + 3ω. (b) Calculated He excitation cross section, withand without the presence of an IR field of intensity 4 × 1012 W/cm2 . The relative amplitudes of
the harmonics are shown on the right axis. By changing the absorption cross section of He using
the IR laser field, the amplitudes of the two interfering quantum pathways are controlled.

57
We note that the modulation of the He+ ionization yield, when irradiated by a combined
laser and comb of XUV harmonic fields, can also be explained as a time-domain process resulting
from interferences between transitions to many different states [72]. This time-domain picture isuseful for attosecond phenomena, whereas the frequency domain approach presented here is best
suited for understanding how to coherently control highly excited processes, including for example,
how to induce XUV transparency in atoms.
For this experiment, high harmonics are generated in Xe gas and then refocused into a theeffusive gas jet seeded with helium. using a pair of multilayer XUV mirrors which reflect photon
energies up to ∼22 eV. A 100 nm thick Al filter is inserted in the XUV beam to attenuate thedriving IR pulses reflected from the XUV mirrors, and to eliminate harmonics lower than the 11thorder. The amplitudes of the harmonics can be controlled using different combinations of XUVmirror coatings, while the exact energies of the harmonics can be continuously tuned by the phasematching conditions via pressure tuning of Xe. Figure 4.1(a) shows that we can adjust the relative
amplitudes of the XUV harmonics to be 4:1 in favor of the 11th harmonic, and change the phasematching conditions in the waveguide to continuously drive the energy of the 13th harmonic acrossthe 2p resonance in He. Another part of the laser beam is temporally and spatially recombinedwith the XUV beam in a collinear fashion, and focused onto the He target at a laser intensity of ≈4 × 1012 W/cm2 . The XUV pulse duration was approximated to be 10 fs.

4.1.2

Theoretical Calculations

To predict the amplitude of a multicolor or multiphoton absorption or ionization channel andto compare with our experimental data, we calculate how a weak IR field modifies the absorption
cross section of He (at the same IR intensity used in the present experiment), using an approach
outlined in [53]. This calculation, shown in Figure 4.1(b), provides a photoabsorption map thathelps us to compare the relative amplitudes of the two ionization channels. In general the intuitive
picture of how an IR field broadens the resonances is confirmed by this calculation: the presence of
the IR field shifts and broadens the He resonances, and modifies the electronic structure, leading

58
to a drop in the absorption cross section for the resonant XUV energies, and an increase in theabsorption cross section between the resonances. We note that the width of the resonance represents
the lifetime or the ionization rate of the dressed state, and the ionization probability is proportional
to the absorption cross section. Therefore, in the following discussion, we will not distinguishabsorption and ionization. We also see that the IR field modifies the electronic structure of He
by inducing fine-structure features in the absorption cross section. For our coherent control ofmultiphoton XUV + IR ionization, the IR wavelength defines the width of the 2p double slit (twoIR photons), while the IR intensity defines the position of the double slit in the frequency domain.
To experimentally observe how the IR field modifies the amplitude of the 13th + 3 IR
photons ionization pathway as a function of the exact XUV photon energy, we monitor the timedependent He+ yields on the femtosecond time scale, as the 13th harmonic is scanned across the
2p resonance. Figure 4.2(a) plots the He+ yield for three different XUV 13th harmonic energies
below (red curve), at (green curve), and above (blue curve) the He 2p resonance, as a function of
IR laser time delay. The easiest way to see how the IR pulse modifies the absorption cross sectionof He is to tune the 13th harmonic into the He 2p resonance (green curve corresponding to a 765/13= 58.8 nm XUV wavelength), and compare the ion yields for different time delays of the IR laser
pulse. At zero time delay between the XUV and IR fields, absorption of the 13th harmonic occurs
in the presence of the IR-modified resonance [Figure 4.1(b)]. This significantly decreases the He+
yield compared with when the IR laser arrives well after the XUV field (positive IR delays). The
inset of Figure 4.2(a) shows the experimentally observed and theoretically calculated photoelectron
momenta at IR laser time delays of 200 fs. A g-wave angular distribution with 4 nodes in thepositive px direction confirms that the XUV pulse excites only the 2p eigenstate of He, which isthen sequentially promoted into the continuum by absorption of at least 3 IR laser photons.

4.2

Resonance Tuning
When the XUV photon energy is tuned above the 2p resonance (blue curve of Figure 4.2(a)corresponding to a 750/13 = 57.7 nm XUV wavelength), the He+ yield reveals a slight asymme-

59

Figure 4.2: (a) He+ yields for XUV and IR illumination (laser intensity of 4 × 1012 W/cm2 ), in thecase of the three different two-color XUV spectra of Figure 4.1(a). The inset shows the theoreticaland experimental photoelectron momenta at 200 fs IR delay, along the negative and positive pz
axis, respectively. (b) Theoretical calculation of the He+ yield under the same conditions as (a).
The inset shows calculated photoelectron energies corresponding to the 750/11 nm and 750/13 nm
XUV beams. The 13th + 2ω (2 IR photon) channel appears at ±25 fs IR delays.

try around zero time delay. The enhancement of ionization for the positive IR delays is rather
counterintuitive, and has not been observed previously. However, it has very recently been predicted theoretically [15], and can be explained as follows. In combined XUV and IR laser fieldsof duration 10 fs and 30 fs, respectively, small negative IR time delays correspond to the case of

60
ionization of He on the leading edge of the IR laser pulse (IR pulse arrives later in time than the
XUV pulse). For small positive IR delays, He is ionized on the trailing edge of the IR laser pulse (IRarrives before the XUV pulse). When He is ionized as the laser intensity is increasing, the IR field
ponderomotively drives the electron to periodically reencounter its parent ion, making it possible
for the continuum photoelectron to recombine. This reduces the overall level of ionization by asurprisingly substantial amount. When He is ionized on the trailing edge of the laser pulse (i.e., 20
fs delay), electrons are released after the peak intensity is gone. This shuts off the recombination
channel that effectively reduces the ionization rate.
Figure 4.2(b) plots the theoretical He+ yield as a function of time delay between the XUV
and IR fields. Good qualitative agreement with the experimental data can be seen. For thethree XUV photon energies spanning the He 2p resonance, the calculated ion yield exhibits theobserved yield asymmetry around zero delay. To explain different asymmetric yields for the twononresonant XUV photon energies [red and blue, Figure 4.1(a)], we calculated the photoelectronenergies corresponding to the 750/13 nm XUV wavelength. The inset of Figure 2(b) shows thatthe additional enhancement at ±25 fs delay comes from absorption of 2 IR photons. The 13th +2 IR photons ionization channel only turns on for long relative time delays between the XUV andlaser fields. This channel shuts off at higher intensity (around zero delay) because the He ionization
potential is ponderomotively increased [15, 73].
Armed with the knowledge of the roles the XUV and IR fields play in 2-color multiphoton
ionization, we now demonstrate experimentally and theoretically that we can very sensitively control
multicolor multiphoton ionization of He by interfering two ionization pathways, with the potential
to completely shut off the ionization process. Varying the time delay between the XUV and IR
pulses with subcycle resolution introduces ultrafast modulations of the He+ yield. Experimental
and theoretical results for different XUV photon energies and amplitude ratios are plotted in Figure
4.3. Figures 4.3(a)-4.3(c) show how the amplitude of the oscillation in the ion yield changes as the
11th-13th harmonic pair is scanned across the He 2p resonance that forms the Floquet double slitin the laser field, for different amplitude ratios of the 11th and 13th harmonic. Figure 4.3(d) plots

61
the experimentally observed oscillation in the He+ yield when the 13th harmonic is below the 2p
resonance. This measurement is in very good agreement with the superimposed calculated ion yieldfor the same IR laser intensity of 4 × 1012 W/cm2 , and for a 4:1 amplitude ratio of the 11th and13th harmonics. Thus, we have confidence in our ability to predict the ionization yield in the twocolor, laser-dressed, multiphoton XUV + IR ionization process.

Figure 4.3: (a)-(c) Calculated modulation of the He ionization probability for different ratios of the
11th:13th harmonic fields, and for two-color 765/(11,13) nm, 785/(11,13) nm, and 750/(11,13) nm
XUV beams, respectively. (d) Experimental and theoretical modulation of the He+ yield for a laser
intensity of 4 × 1012 W/cm2 , and a 785/(11,13) nm XUV field. The red curve of (a) demonstrates
that a ratio of 256:1 for the 11th vs the 13th harmonic can result in nearly complete cancellationof XUV absorption.

At the IR-dressed 2p resonance and for an 11th:13th harmonic amplitude ratio of 256:1, we
observe a near perfect modulation of the He+ yield, with the maximum-to-minimum ratio of ≈ 40
[red curve of Figure 4.3(a)], thus demonstrating the potential to completely shut off the multiphoton

62
ionization process. For 785/13 nm wavelength XUV beams [red curve Figure 4.3(b)], the ratio is≈ 30, while for 750/13 nm XUV beams and 11th:13th ratio of 256:1 [red curve Figure 4.3(c)],the modulation of the ion yield drops to only 5. We note that in the latter case, the maximum
yield is slightly shifted from zero delay, unlike the other two cases that both maximize at zero.
The highest amplitude of the oscillation, leading to complete electromagnetic transparency at thecorrect relative time delays, occurs for the case when the two XUV photons excite the He 2p Floquet
states exactly through two sidebands (two Fourier components), as shown in Figures 4.1 and 4.3(a).

4.2.1

Tuning for Full Transparency

The intuitive Young double-slit picture is that for harmonic photon energies of 765/11 nm
and 765/13 nm, the two XUV photons go through a double-slit interference in frequency space thatis created by the IR laser field, as shown in Figure 4.1(a). Below the resonance, the photon pairdoes not go fully through the double slit, but still partly overlaps with the 2p sideband at 17.7 eV
and 20.9 eV, as seen in Figure 4.1(b), and more robustly in Figure 4.1(a). Above the 2p resonance,
the two XUV photons almost completely miss the double slit (Figure 4.1(a) and Figure 4.1(b)),
which results in a small modulation in the ionization yield in Figure 4.3(c). Moreover, in this casethe 3p Floquet sidebands start playing a role, making the two XUV photons to go through two
double slits in series, which are displaced with respect to each other in the frequency domain. Thiscan be seen in Figure 4.1(b), where the 13th harmonic overlaps with the 3p (and higher) IR-dressedstates at 21.5 eV. This also results in shifting of the maximum yield from zero delay, as shown in
Figure 4.3(c).
In conclusion, we demonstrate that full electromagnetic transparency to XUV light in helium
can be achieved by destructively interfering two distinct multiphoton ionization pathways. Throughcombined theory and experiment, we show how a laser field can modify the electronic structure of
an atom, optimizing the destructive interference between two ionization pathways under the correct
conditions. This approach opens up new possibilities for coherent control of highly excited states,and emphasizes the important and complex role the IR laser field plays in strong-field ionization.

63
We believe that this concept can be applied to induce and control the outcome of chemical reactions,as well as in condensed matter physics where the concept of the resonance dressing, shifting, andbroadening can be applied to the electronic band structure.

Chapter 5
Bromine1

Imaging and controlling reactions in molecules and materials at the level of electron dynamics
is a grand challenge in science, relevant to our understanding of charge transfer processes in chemistry, physics, and biology, as well as material dynamics. Direct access to the dynamic electron
density as electrons are shared or transferred between atoms in a chemical bond would greatly
improve our understanding of molecular bonding and structure. In this Chapter, we show how theentire valence shell electron density in a molecule rearranges, from molecular-like to atomic-like, asa bond breaks. An intense ultrashort laser pulse is used to ionize a bromine molecule at different
times during dissociation, and we measure the total ionization signal and the angular distributionof the ionization yield. Using this technique, we can observe density changes over a surprisingly
long time and distance, allowing us to see that the electrons do not localize onto the individual
bromine atoms until the fragments are far apart (∼5.5 Å), in a region where the potential energy
curves for the dissociation are nearly degenerate. These observations agree well with calculationsof the strong-field ionization rates of the bromine molecule.

5.1

Visualization of electron dynamics
Probing the dynamic electron density distribution during a chemical reaction can provide

important insights, making it possible to understand and control chemical reactions. For example,
1

The results of this chapter are in part based on “W. Li, A. A. Jaroń-Becker, C. W. Hogle, V. Sharma, X. Zhou,
A. Becker, H. C. Kapteyn, and M. M. Murnane, Proceedings of the National Academy of Sciences 107, 47, 20219(2010)” [82].

65
during the passage through a conical intersection, electronic excitation is rapidly converted into nuclear motion, and the nature of how the electron cloud rearranges is still poorly understood. Three
distinct and promising approaches make it possible to probe electron dynamics in molecules. First,
high harmonic generation from a molecule can exhibit characteristic features because of quantum
interferences and diffraction of an electron originating from and then recolliding with the same
molecule. Although the conditions under which accurate reconstruction of a complete electronic
wave function is possible are still a topic of intense debate, nevertheless, these characteristic interferences can reveal dynamical changes in the nuclear and orbital structure of a molecule as it changes
configuration [83–86] or dissociates [87]. In the case of dissociation, by measuring the amplitude
and phase of the high harmonic signal from a dissociating molecule, destructive interferences in
the high harmonic signal were observed that were attributed to recombination of a lone electron
in a single excited state [87]. To follow multielectron dynamics in a molecule, further work will beneeded, because the quantum interference signal can be masked by competing contributions fromdifferent nearly degenerate valence orbitals, in particular at large internuclear distances.
A second approach for obtaining information about electron dynamics is to map the electron
density distribution in the valence shells of a molecule, simply by measuring the molecular frame
ionization yield after illumination by a strong laser field. Past work probing static molecules in the
ground state has shown through both theory and experiment that the resulting ion yield reflects
the symmetry of the molecular orbital from which the electron is ionized [88–93]. As a result,strong-field ionization should be particularly attractive for capturing electron orbital dynamics
because it directly relates to the electron density distribution (i.e., orbital shape) of a molecule. Ina third approach, the coupling between an excited electron and nuclear motion in a molecule canbe probed by using time-resolved photoelectron spectroscopy (TRPES) [12, 68, 94]. In TRPES, avacuum ultraviolet (VUV) pulse is used to single-photon ionize a molecule, making this techniqueparticularly useful for measuring how the binding energies of electrons in different valence orbitals
change as the molecule dissociates. However, the linear response in a photoelectron spectroscopy
measurement makes it challenging to follow shifts in the binding energies and to directly probe

66
the varying electron density in the bond, on time and length scales for which the potential energy
curves become nearly degenerate. A femtosecond laser strong-field ionizes a molecule as it undergoes
photodissociation. The dissociation itself is initiated in a simple, single-photon transition by using
a pump pulse. A higher intensity probe pulse is then used to ionize the molecule at various timedelays, causing the fragments to fly apart rapidly with a distribution that reflects the instantaneouselectron distribution. Both the detected ionization rate and fragment angular distribution directlyreflect how the entire valence shell electron density in a molecule rearranges, from molecular-liketo atomic-like, as a bond breaks. The experimental results can be successfully interpreted throughcareful comparison with theory. This also shows an ability to capture multielectron dynamics in areaction up to significantly larger internuclear distances than with other methods. It also exhibitshigh sensitivity to small variations in the binding energy and electron density, as well as excellent
time resolution compared with other approaches. This approach thus allows us to see that theelectrons do not localize onto the individual bromine atoms until the fragments are far apart (∼5.5
Å), in a region where the potential energy curves for the dissociation are nearly degenerate.

5.1.1

Experimental Bromine Dissociation

The sample consists of a bromine molecular beam from the supersonic gas jet. Dissociationof the Br2 is initiated by a 400 nm ultrafast laser pulse (intensity ∼2 × 1011 W/cm2 , pulse duration∼40 fs) generated by frequency doubling the 800 nm laser output. The absorption of a single 400
nm photon excites the bromine molecule from the ground state to the C (1 Πu ) dissociative state.
To confirm that the Br+ ions are indeed originating from strong-field ionization of the dissociative
C state, we measured the Br+ yield as a function of pump beam power and found it to be linear as
shown in Figure 5.2. An intense time-delayed 800 nm (∼4 × 1013 W/cm2 , ∼30 fs) laser pulse, withpolarization orthogonal to the 400 nm pump, is used to ionize the dissociating bromine molecules
to produce Br+ . We then detect the angular distribution of the resultant ions at different times
during the dissociation as shown in Figure 5.1. Given that the dissociation is a prompt process, wetherefore know how the electron density in the molecule changes as the molecule dissociates into

67

Figure 5.1: Calculated electron density (molecular orbitals) as a function of Br2 internuclear separation and time after a 400 nm dissociating pulse causes the bond to rupture on the dissociative
C neutral state. Note that contributions from all 10 electrons in the valence shells are included.
Measured angular dependence of the Br+ ion yield from strong-field ionization of the Br2 molecule,as a function of time after the dissociating pulse. Both experiment and theory indicate that theelectrons localize onto individual atoms on a time scale 140 fs after the dissociating pulse.

two atoms.

5.1.2

Power Dependence of Br+ Yield

In order to confirm that the Br+ ions observed in this experiment are indeed originating fromstrong field ionization of the dissociative C state, we measured the Br+ yield as a function of pumpbeam power at a fixed pump-probe delay of 120 fs. The integrated Br+ yield for KER <0.8 eV
is shown in Figure 5.2. A linear dependence of the Br+ yield on the power clearly shows that the68pump step of our experiment indeed involves a single photon process (i.e., absorbing only one 400
nm photon). The experiment was performed with only 5 µJ of pump energy, corresponding to alaser intensity of 2 × 1011 W/cm2 . This intensity is at least 5 times smaller than that used in theextreme ultraviolet photoionization probe studies of Br2 dissociation performed previously [95, 96].
Thus we believe that our experiments have a relatively low probability of complications resulting
from multiphoton processes to other excited states in the Br2 molecule.

Figure 5.2: Power dependence of slow (i.e., KER < 0.8 eV) Br+ yield. Black squares correspondto the experimental Br+ count, as a function of pump (400 nm) power. The red line is a linear
fit to data. The measured slope of 0.99 verifies that our dissociation signal is initiated by a single
photon.

Figure 5.3 plots the total ion yield as a function of time delay between the 400 nm dissociating
pulse and the 800 nm probe pulse. The total ion yield initially increases for time delays up to 30 fs,
at which point it decreases slightly, followed by an increase at time delays around 100 fs. As we willshow below by comparing detailed theory and experiment, the first peak corresponds to ionizationof electrons from π orbitals, whereas second peak can be explained by additional ionization channels

69
opening up as different σ valence electrons are ionized. Finally, the ion yield drops quickly at timedelays between ∼ 120 and 140 fs, limited by the time resolution in our experiment.

Figure 5.3: Experimental Br+ total ion yield as a function of time delay between the 400 nm
dissociating pulse and the 800 nm probe ionizing pulse. The first peak corresponds to ionizationof electrons from π orbitals. The second peak can be explained by additional ionization channels
opening from σ valence electrons.

5.2

Calculated and Experimental KER
To interpret the experimental data, the ionization rate from the dissociative C state of Br2 was

calculated as a function of internuclear distance by using the molecular strong-field approximation[97]. The results of these calculations can be plotted in terms of the final kinetic energy release(KER) of the fragments as a function of time delay. The calculated KER is in very good agreementwith our experimental measurements as shown in Figure 5.4. We note that the characteristicfeatures of the distributions are slightly shifted to longer time delays in the theoretical results,
which may be attributed to the sensitive dependence of the conversion from distance to time delayon the specific form of the C-state potential energy curve.

70
The calculations of Figure 5.4 indicate that we are experimentally observing the entire valence shell of Br2 (all ten electrons) evolving in time as the bond breaks, as shown in Figure 5.1.
The electron configurations of the ground X and dissociative C states of Br2 are[core](1σg )2 (1σu∗ )2 (2σg )2 (1πu )4 (1πg∗ )4 (2σu∗ )0 and [core](1σg )2 (1σu∗ )2 (2σg )2 (1πu )4 (1πg∗ )3 (2σu∗ )1 ,respectively. Removal of one electron from different orbitals of the C state of Br2 leads to different
electronic configurations of the cation. For example, strong-field ionization of the singly occupied
molecular orbital (2σu∗ ) electron primarily produces Br2 + in its ground state X with electronic configuration: [core](1σg )2 (1σu∗ )2 (2σg )2 (1πu )4 (1πg∗ )3 (2σu∗ )0 . This state, as well as certain excited statesof bound character, will not produce Br+ at short internuclear distances during the dissociation
process. At short time delays (below 20 fs), slow Br+ ions are instead generated predominantly byionizing the inner valence orbital 1π u . After dissociating for about 20 fs, the atoms have gained
enough kinetic energy such that ionization from 2σg and 2σu∗ opens additional channels for the
dissociation of Br2 + . The additional channels that continue to open up also explain why the total
ionization yield increases as a function of time delay. At long time delays, fast Br+ ions originate
primarily from ionizing 2σg , with minor contributions from other orbitals. The peak around 60 fs
in Figure 5.4 results from strong contributions of electron removal from 2σu . Thus, we are able
to identify the specific molecular orbitals that contribute primarily to the ionization and kinetic
energy release signals up to a time delay of 140 ± 15 fs. This analysis indicates that the systemstill must be considered molecule-like and the electrons in the valence shell(s) of the system arestill rearranging their configuration at these relatively long times (corresponding to internuclear
separations larger than 5 Å). This finding is surprising because by then, according to calculations,the four valence orbitals in the Br2 molecule are nearly degenerate and the electron probability
density at the midpoint between the two nuclei is 10 orders of magnitude smaller than the peakmaximum.

71

Figure 5.4: Experimental (A) and calculated (B) total KER of the Br+ as a function of time after
the dissociating pulse. At short time delays (below 20 fs), Br+ ions are generated predominantly
by ionizing the inner valence orbital 1πu of the molecule. After dissociating for about 20 fs, theatoms have gained enough kinetic energy such that ionization from 2σg and 2σu∗ opens additional
channels for the dissociation of Br2 + .

5.3

Angular Ion Distribution
To physically interpret our findings, we plot the experimental angular distribution of Br+ as

a function of time delay for both the slow Br+ (Figure 5.5(A), kinetic energy release below 0.7 eV)and fast Br+ (Figure 5.5(B), kinetic energy release above 0.7 eV). We fit the angular distribution toa simple cosn (θ) [θ is the angle between the molecular axis and probe (ionizing) laser polarization].
Because photoexcitation of the C state is a perpendicular transition [98], the observed angular
distributions of Br+ are convolutions of the Br2 excited state molecule axis alignment [cos2 (θ)
distribution] and the angular dependence of the Br2 ionization rates. Thus, the sign of n − 2 (plusor minus) shows whether the ionization is peaked parallel (+) or perpendicular (−) to the laser
polarization, reflecting ionization from specific molecular orbitals. At short time delays, slow Br+
has an n below 2, indicating ionization from the πu state, whereas for fast Br+ , the ionization

72
yield is highest along the molecular axis, indicating ionization predominantly from a σ state. Thesefindings are in agreement with our calculations (Figure 5.1 and Figure 5.4). More importantly, weobserve such molecular-specific features up to time delays of 140 fs. After this time, the ion angular
distributions flatten and appear to resemble ionization from separated atoms; i.e., the distribution
reflects only the initial excited state molecule axis alignment in Br2 .

Figure 5.5: Angular distribution of Br+ at different time delays after the dissociating pulse, for boththe slow Br+ , (a) kinetic energy release below 0.7 eV, and fast Br+ , (b) kinetic energy release above
0.7 eV. At short delays slow Br+ indicates ionization from the πu state. Fast Br+ is predominantly
along the molecular axis and so mostly from a σ state

73

5.4

Laser Field Driven Dynamics
We also calculated the alignment dependence of the ionization rate, taking into account thatin the experiment, the excited Br2 are prepared with a cos2 (θ) alignment of the molecular axis tothe polarization direction. We believe that we are not inducing significant laser field driven electron
dynamics, for several reasons. First, the most important point in discussing the possible role ofstrong-field effects is that, although our technique uses a relatively strong laser pulse as a probeof the molecular dynamics, our technique allows us to avoid strong-field effects in initiating the
dynamics that we observe. Comparing our approach to TRPES, where the VUV probe pulse iscapable of photoionizing even ground-state Br2 , in TRPES, a relatively intense pump pulse has to be
used to obtain significant fractional population in the excited state. Thus, in TRPES, strong-field
effects in the excitation step might explain the more rapid dissociation times observed in previous
experiments (≈85 fs) [96]. In our experiment, an ion signal emerges only from the dissociating
molecules and is thus background free. The fact that we see a precipitous drop in signal at longtime and distance scales clearly shows that our signal discriminates against both the initial and thefinal state of dissociation, allowing us to observe the entire dissociation process that was initiatedby a clearly perturbative, single-photon, excitation (as demonstrated in Figure 5.2). Moreover, ourcalculations agree well with the data, even without including laser induced modifications of theinitial electronic state or charge resonance-enhanced ionization [99, 100]. Finally, the calculated
kinetic energy releases and angular distributions do not change for a range of probe laser intensities(4-5 × 1013 W/cm2 ) and for different ensembles of molecular orientations induced by the pumppulse.
In conclusion, we have demonstrated that we can image the electron density evolution ofmany electron states in the valence shell of a large diatomic molecular system up to time anddistance scales at which the potential energy curves become nearly degenerate. We have shown that,
because of the nonlinear interaction of an ultrashort intense laser pulse with the electrons, strongfield ionization can probe the electronic structure of a dissociating molecule even if the changes in

74
the potential energy surfaces are small. Our studies show that both the ionization rate and theangular dependence of the ionization yield still vary strongly for internuclear distances at least 2 Å
beyond where previous studies using photoelectron spectroscopy identified an establishment of theatomic electronic structure in Br2 . We believe that the existence of such a molecular-like complex
for large time and length scales is not restricted to Br2 and should have broad implications for many
fields such as photochemistry and reactive scattering dynamics. Interestingly, our observations andcalculations are in good agreement with electron localization function calculations [101,102], whichindicate delocalization of the electrons in the different orbitals until internuclear separations >5.0
Å for Br2 in the excited C state. Thus, using strong-field ionization as a probe, we can follow
electron dynamics in a bond over sufficiently long times to capture all the time scales during achemical reaction.

Chapter 6
Deuterium1

High harmonic light sources make it possible to access attosecond timescales, thus opening
up the prospect of manipulating electronic wave packets for steering molecular dynamics. However,two decades after the birth of attosecond physics, the concept of attosecond chemistry has not yet
been realized; this is because excitation and manipulation of molecular orbitals requires precisely
controlled attosecond waveforms in the deep ultraviolet (UV), which have not yet been synthesized.
In this Chapter, we present a unique approach using attosecond vacuum UV (VUV) pulse-trains tocoherently excite and control the outcome of a simple chemical reaction in a deuterium molecule ina non-Born-Oppenheimer regime. By controlling the interfering pathways of electron wave packets
in the excited neutral and singly ionized molecule, we unambiguously show that we can switch theexcited electronic state on attosecond timescales, coherently guide the nuclear wave packets to dictate the way a neutral molecule vibrates, and steer and manipulate the ionization and dissociation
channels. Furthermore, through advanced theory, we succeed in rigorously modeling multiscale
electron and nuclear quantum control in a molecule. The observed richness and complexity of the
dynamics, even in this very simplest of molecules, presents intriguing new possibilities for bridging
the gap between attosecond physics and attosecond chemistry.
1

The results of this chapter are in part based on “P. Ranitovic, C. W. Hogle, P. Rivire, A. Palacios, X.-M. Tong,
N. Toshima, A. Gonzlez-Castrillo, L. Martin, F. Martı́n, M. M. Murnane, and H. C. Kapteyn, Proceedings of the
National Academy of Sciences 111, 3, 912 (2014)” [23].

76

6.1

Coherent Control of Molecular Dynamics
The coherent manipulation of quantum systems on their natural timescales, as a means tocontrol the evolution of a system, is an important goal for a broad range of science and technology,
including chemical dynamics and quantum information science. In molecules, these timescales
span from attosecond timescales characteristic of electronic dynamics, to femtosecond timescales
characteristic of vibrations and dissociation, to picosecond timescales characteristic of rotations inmolecules. With the advent of femtosecond lasers, observing the transition state in a chemical
reaction [1], and controlling the reaction itself, became feasible. Precisely timed femtosecond pulse
sequences can be used to selectively excite vibrations in a molecule, allow it to evolve, and finallyexcite or deexcite it into an electronic state not directly accessible from the ground state [103].
Alternatively, interferences between different quantum pathways that end up in the same final
state can be used to control the outcome of a chemical reaction [76–78, 104–107].
In recent years, coherent high harmonic sources with bandwidths sufficient to generate either
attosecond pulse trains or a single isolated attosecond pulses have been developed that are also
perfectly synchronized to the driving femtosecond laser [108–110]. This new capability provides
intriguing possibilities for coherently and simultaneously controlling both the electronic and nuclear
dynamics in a molecule in regimes where the Born-Oppenheimer approximation is no longer valid,
to select specific reaction pathways or products. We perform a coordinated experimental andtheoretical study of dynamics of the simplest neutral molecule: deuterated hydrogen (D2 ).
The hydrogen molecule, as the simplest possible neutral molecule that can be fully describedtheoretically, has been the prototype molecule for understanding fundamental processes that lie
at the heart of quantum mechanics [111–114]. However, in such a small molecule, the coupledelectron-nuclear dynamics are in the attosecond-to-few-femtosecond regime, whereas the electronically excited states lie in the VUV region of the spectrum. Because of the challenge of generating
attosecond VUV pulses using traditional laser frequency doubling or tripling in nonlinear crystals, it has not been possible to date to explore the dynamics of an electronically excited hydrogen

77

Figure 6.1: Attosecond control of the excitation and ionization pathways of D2 on short timescales.
(right) Simplified potential energy surfaces of the D2 and D2 + . The purple and red arrows represent
the VUV harmonics and IR laser pulses used to coherently control the populations of the excitedneutral and ion states in the Franck-Condon region through two-pathway quantum interference ofelectronic wave packets in B, B∗ (single photon) and EF (two photon) states. (Lower left inset)
Calculated excitation probabilities into states of Σu and Σg symmetries of neutral H2 (dominated,
respectively, by the B and EF states) as a function of time delay. The blue lobes, plotted on
the right of the panel, are sketches of the Σu and Σg orbitals representing the excited electron
dynamics. Theoretical predictions show that the electronically excited populations can be switchedbetween the even B and odd parity EF potentials on attosecond timescales, which can in turncontrol how the molecule vibrates. (Upper left inset) The experimental photoelectron, D2 + andD+ yields modulate on full and half-cycle attosecond timescales, as the delay between the pump
VUV + IR and probe IR pulses is scanned.

molecule. Exploiting attosecond physics, however, only a handful of time-resolved experiments havebeen performed on H2 (D2 ), focusing mainly on controlling dissociation through electron localization in electronically excited D2 + ions [69, 115–120]. Recently it was realized that IR femtosecond
laser pulses, in combination with a phased locked comb of attosecond VUV harmonics, can be used
to control the excitation and ionization yields in helium on attosecond timescales, by interfering
electron wave packets [15, 72]. These experiments extended the Brumer-Shapiro [76–78, 104–107]

78
two-pathway interference coherent control concept to the attosecond temporal and VUV frequency
domain. More recently, it was shown that by manipulating the individual amplitude of VUVharmonics, it is possible to induce full electromagnetic transparency in helium, by destructively
interfering two electronic wave packets of the same amplitude and opposite phases [63]. Other
recent work used shaped intense femtosecond laser pulses to manipulate populations by controllingthe oscillating charge distribution in a potassium dimer [121].
Using attosecond scale VUV harmonics, we can coherently and simultaneously manipulate
multistate electronic and multipotential-well nuclear wave packet dynamics to control the excitation, nuclear wave packet tunneling, and dissociation and ionization channels of the only electronically excited neutral molecule where full modeling of the coupled quantum dynamics is possible,
H2 (for practical reasons, we used deuterated hydrogen in this experiment). By combining attosecond pulse trains of VUV with two near-IR fields, together with strong-field control that exploits
a combination of the two-pathway interference Brumer-Shapiro [76–78, 104–107] and pump-dump
Tannor-Rice [103] approaches, we demonstrate that we can selectively steer the ionization, vibration, and dissociation of D2 through different channels. Interferences between electronic wave
packets (evolving on attosecond timescales) are used to control the population of different electronic states of the excited neutral molecule, which can be switched on attosecond timescales.
Then, by optimally selecting the excitation wavelengths and time delays, we can control the vibrational motion, total excitation, ionization yield, and desired ionization and dissociation pathways.
State-of-the-art quantum calculations, which have only recently become feasible, allowed for theinterpretation of this very rich set of quantum dynamics, including both the nuclear motion and thecoherently excited electronic state interferences. Thus, we succeed in both observing and rigorously
modeling multiscale coherent quantum control in the time domain.

6.2

Phase-Locked VUV + IR Source
We note that our approach for control, using a combination of phase-locked VUV and IR

fields, where the VUV field consists of an attosecond pulse train with a 10 fs pulse envelope, is ideal

79
for coherently exciting and manipulating electronic and vibrational states on attosecond time scales,
while simultaneously retaining excellent spectral resolution necessary for state-selective attochemistry. Exciting electron dynamics in a molecule using a single, broad-bandwidth VUV attosecond
pulse would simply excite many ionization/dissociation channels with little state selectivity, potentially masking the coherent electronic and nuclear quantum dynamics. For example, the bandwidth
required to support an isolated 200 attosecond pulse around 15 eV is ∼5 eV. In contrast, the 10 fs
VUV pulse train used here corresponds to a comb of VUV harmonics, each with a FWHM bandwidth of 183 meV, which can be tuned in the frequency domain [63] to coherently and selectively
excite multiple electronic states.
Figure 6.1 illustrates our concept for attosecond coherent control of molecular dynamics. A
neutral deuterium molecule is electronically excited and ionized by combined phase-locked VUV
harmonics (7ω − 13ω) and ultrafast IR (ω) pump fields at a center laser wavelength of 784 nm.
A second control IR pulse is time-delayed with respect to the combined VUV + IR fields. For
simplicity, only the two most relevant electronically excited states of different parity in D2 areshown in Figure 6.1. As we will explain in more detail below, interferences between electron wave
packets excited by the combined VUV harmonics (i.e., 7ω, 9ω, and 11ω) and the IR field (ω) areused to manipulate the ionization and excitation probabilities of different electronic states of theexcited neutral molecule. To modulate the total electronic excitation in the neutral molecules on
attosecond timescales, we use two-pathway quantum interference of electronic wave packets excitedby 7ω + ω and 9ω − ω. Simultaneously, to modulate the total ionization yield on attosecond
timescales, we use two-pathway quantum interference of electronic wave packets excited by 9ω+ ω and 11ω − ω as the main mechanism. Finally, by tuning the VUV excitation wavelengths,
we achieve other degrees of coherent control of coupled electron-nuclear wave packet dynamics,
including vibration, ionization, and tunneling. First, we show how the population of two electronic
states can be switched (i.e., between EF and B) on attosecond timescales (Figure 6.1, Lower Left).
Second, we show that by tuning the energy of the VUV harmonic comb, we can excite and control
the population of different electronic and vibrational states, which in turn dictates how the neutral

80
molecule vibrates and ionizes. Third, by exciting D2 using tunable two-color VUV and IR fields, andthen probing the dynamics using a second IR pulse, we can control tunneling of nuclear wavepackets
in the EF potential of a neutrally excited D2 .
The seventh and ninth harmonics coherently excite the molecule from its ground state, creating two nuclear wave packets in the same, odd-parity (i.e., B 1 Σ+u ) potential energy surface of
D2 . When a small portion of the driving IR field (at an intensity of 3 × 1011 W/cm2 ) copropagateswith the VUV harmonics, we can also simultaneously populate the optically forbidden, even-parity(i.e., EF 1 Σ+g ) potential energy surface through two-photon (i.e., 7ω + ω, 9ω − ω) absorption
processes. A second, time-delayed, and stronger IR (ω) pulse (at an intensity of 4 × 1012 W/cm2 )is then used in two different ways. First, on short attosecond timescales, the delayed IR field interferes with the IR field that copropagates with the VUV harmonics, and serves as a knob to control
the excitation and ionization processes on attosecond timescales in the Franck-Condon region, bymeans of electron wave packet interferometry. Second, on long femtosecond timescales, the delayed
IR field serves as a femtosecond knob to control the dissociation process by selectively ionizing themolecule at some optimal time after excitation. All of the pulses (VUV attosecond pulse trains
and two IR fields) were linearly polarized in the same direction. The VUV pulse duration was 5-10
fs, and the IR pulse durations were 30 fs. By changing the pressure in the gas-filled capillary, we
can fine-tune the exact photon energies of the VUV harmonics while keeping the IR wavelength
constant. This capability is key for uncovering the control mechanisms.
We first examine the attosecond control pathways at early times, before the onset of largeperiod vibrational wavepacket dynamics. Figure 6.1, Upper Left plots the experimental photoelectron, D2 + , and D+ yields when the pump (VUV + IR) and the control (IR) pulses were overlappedin time, as a function of the time delay between them. Very rapid, suboptical-cycle modulationsin the photoelectron and D2 + yields result from the combination of optical interferences (two IR
pulses) and quantum interferences of electronic wavepackets (i.e., 9ω + ω and 11ω − ω interfering
pathways), as the phase of the control IR pulse changes relative to the pump VUV + IR pulse.
Half-cycle periodicity suggests that the two-pathway quantum interferences play an important role81
in this particular case [81]. The deep, full-cycle modulation of the dissociative D+ yield is simply
a result of the optical interferences between the pump and control IR pulses (both 30 fs long) thatlead to bond-softening of the ground state of D2 and ionization of the D2 ∗ excited states ∼10 fs
after the pump pulse. Because the dissociation by bond-softening occurs after the VUV pulse isgone, this signal provides a reference point of the absolute phase in between the two IR pulses at
each time delay, and allows us to precisely know the phase of the quantum interferences relative tothe laser field.

6.3

Theoretical Calculations
Theoretical calculations (Figure 6.1, Lower Left) show that the electronic population in the

excited states also oscillates, with the same half-cycle periodicity. Moreover, theoretically, we canremove the parity degeneracy in the total excitation yield and see that the populations in the gerade
and ungerade B and EF states are out of phase. Thus, a two-pathway quantum interference of theelectron wave packets driven by the lower two harmonics and the delayed IR field (i.e., 7ω + ω vs.
9ω − ω, Figure 6.1, Lower Left) can be used as an ultrafast population switch between even (EF)and odd parity (B) potentials; this demonstrates that the interference of electronic wavepackets
can be used to switch and steer the electronically excited states on attosecond time scales, allowing
simultaneous control of the electronic and vibrational excitation of an excited neutral D2 ∗ molecule.
Thus, we demonstrate how combined attosecond VUV and IR femtosecond fields can be used as aunique tool to coherently control chemical reactions on the fastest timescales.
It is worth noting that though there are other possible interfering pathways responsible forthe excitation and the ionization yield modulations, they are significantly less likely because theyrequire more photons. For example, the interference of electronic wave packets excited by 7ω + 3ωand 11ω − ω is possible. In this case, the total ionization probability is controlled by coupling thelower vibrational states of the B potential excited by the seventh harmonic, with the continuum
electron wave packets created by the 11th harmonic. Though this channel competes with the state
excited by the ninth harmonic, it requires absorption of four photons, and is thus much less probable82
compared with the pathway requiring absorption of two photons (one VUV and one IR).

Figure 6.2: Theory of attoseocond VUV coherent control of H2 ionization/dissociation channels.
(A-C) As the central energy of the VUV frequency comb is blue-shifted from an effective driving
laser wavelength of 784 nm to 740 nm, the total ionization yield switches to half-cycle periodicity
due to different electronic wavepacket interferences, thus demonstrating attosecond coherent control
over the interfering electron wave packets and ionizing pathways in molecules.

Because we solve the full 3D time-dependent Schrdinger equation (TDSE) for H2 exposed to
a combined VUV and IR fields, we can theoretically examine the attosecond control mechanisms
by fine-tuning the photon energy of the VUV pulse. The TDSE is numerically solved by expanding
the time dependent wave function in a large basis of Born-Oppenheimer molecular states, which
are obtained by diagonalization of the electronic and nuclear Hamiltonians of H2 . The method
includes all electronic and nuclear degrees of freedom and, therefore, accounts for electron correlation and the coupling between the electronic and nuclear motions. Time evolution starting fromthe ground state induces transitions between the Born-Oppenheimer states through laser-moleculeand potential couplings. To make these complex calculations tractable, in the simulation we used
IR and VUV pulses of 7.75 fs total duration. Although these pulses were shorter than the ones
used experimentally (30 fs and 5-10 fs, respectively), a direct comparison between the theory andthe experiment can still be made during the time-delay interval when the pump and probe pulses
overlap. The theoretical results are shown in Figure 6.2, and capture the main experimental observationsthat the total yields modulate on attosecond timescales, and that the periodicity andthe amplitudes of the oscillations strongly depend on the exact central energy of the VUV pulse.
Here, we keep the IR laser wavelength constant while blue-shifting the VUV central wavelength as

83
although the higher harmonics were generated by 784 nm, 770 nm, and 760 nm laser wavelengths
shown, respectively, in Figure 6.2. Not surprisingly, the modulation of the total ionization yieldstrongly depends on the exact energy of the VUV harmonics because the phases and the amplitudesof the interfering electron wave packets strongly depend on the laser-modified electronic structureof the molecule [3]. In the case of H2 , as the central energy of the VUV beam blue-shifts fromharmonics of 784 nm to harmonics of 740 nm, the ninth harmonic does not excite the B state in theFranck-Condon region, but accesses higher electronic states. In this regime the Born-Oppenheimer
approximation breaks down, because the evolution of the nuclear wavepackets in the B and EF
potentials is on the same timescale as the duration of the attosecond VUV pulse train (Figure 6.1,
Lower Left) and can influence the electron wave packet interference process as well. These results
thus demonstrate that we can precisely control which electronic states are excited by the tunable
VUV harmonics, and show how these states can be switched on attosecond timescales.

6.4

Multiscale Quantum Control of Electronic and Nuclear Dynamics
To show experimentally how tunable attosecond VUV pulse trains can be used to precisely

control the excitation probabilities of different electronic and vibrational states, and how to steer
ionization and dissociation in D2 ∗ , we delay the control IR field relative to the VUV + IR pumpfield on femtosecond timescales. Figure 6.3 illustrates several possible ionization and dissociation
pathways and plots the energies of the three different attosecond VUV harmonic combs we used tocoherently and simultaneously control electronic and vibrational excitation, as well as nuclear wave
packet tunneling in the EF potential. The combined 7ω + ω, 9ω − ω, and 9ω fields coherently
1 +populate the EF 1 Σ+
g and B Σu states, respectively. These nuclear wave packets oscillate withperiods that depend on the exact energy of the VUV harmonics, and can couple the ground state
to different vibronic bands of the B and EF potentials. The probe IR pulse can then ionize anddissociate D2 ∗ through different channels as the electronically excited neutral molecule vibrates.
Here we focus only on three channels that leave the most visible signature in the kinetic energy
release (KER) spectrum of D+ , which we label as two-step B, one-step B, and two-step EF (Figure

846.3). In the two-step B case, shown in Figure 6.3(A), the nuclear wave packet launched in the B
state by the ninth harmonic is first probed in the inner classical turning point of the B potential
energy curve by absorption of two IR photons, thus ionizing the Rydberg electron from the B
potential and launching a second nuclear wave packet in the 1sσg state of D2 + . When the nuclear
wave packet reaches the outer classical turning point of the 1sσg potential energy curve (after ∼ 10fs), absorption of another IR photon, from the same probe IR pulse, leads to an efficient couplingof the bound 1sσg and the dissociative 2pσu states of the ion, thus leading to dissociation into D+ D+ by a total absorption of 2 + 1 (i.e., three IR photons; Figure 6.3(A)). Through this two-stepchannel, the molecule dissociates with a kinetic energy release of ∼0.7 - 0.9 eV, typical for a bondsoftening process.

Figure 6.3: Combined coherent control of electronic and nuclear wavepacket dynamics on longer
timescales. (a) Two-step B mechanism (D+ high kinetic energy). (b) One-step B mechanism (D+low kinetic energy). (c) Two-step EF mechanism (D+ high kinetic energy). We also show thetuning range of the VUV harmonics on the y axis (effective driving laser wavelengths of 784 nm,
760 nm, and 740 nm).

In the one-step B case, shown in Figure 6.3(B), the neutral D2 ∗ molecule first stretches tointernuclear distances well beyond 9 a.u., which results in an increase of the effective ionization
potential. At the instant the nuclear wave packet reaches the outer classical turning point of the
B potential, the ionization of the molecule requires absorption of three IR photons. Through this85
channel, the nuclear wave packet is directly coupled to the 2pσu dissociative continuum and themolecule dissociates with lower KER compared with the two-step B case. Due to the absorptionof an extra IR photon at the outer turning point, a modulation of the ionization probability is
expected as the excited molecule vibrates in the B potential. Finally, in the two-step EF case,shown in Figure 6.3(C), the nuclear wave packet launched by two-photon absorption (7ω + ω and9ω − ω) is probed in the inner classical turning point of the EF potential energy curve by absorptionof three IR photons, which generates a nuclear wave packet in the 1sσg potential, but with smaller
probability compared with the two-step B case because the probability of observing this channel
corresponds to a sequential absorption of 3 + 1 IR photons.

6.5

Nuclear Wavepacket Dynamics

Figure 6.4: Theoretical calculations for the relevant potential energy curves show are coherent
nuclear wavepacket as proceeds through approximated one oscillation in the B potential. Also
shown is the wavepacket in the EF double well potential. Part (a) shows the initial excitation fromthe VUV harmonics. After ∼45 fs the wavepacket in the B potential hits a clear outer turning
point, as shown in part (b). After ∼83 fs the wavepacket returns to the Franck-Condon region, as
shown in part (c). This same oscillation is clearly shown in the experimental results.

Figure 6.4 shows the evolution of a calculated coherently excited nuclear wavepacket as
it is populated in and the evolves along the B potential. Because of the ability to capture elec-

86tronic and nuclear information in coincidence we can understand how shifting the pump wavelengthchanges the nuclear vibrations. Also shown in the same figure is the theoretical calculation for the
wavepacket in the EF potential.

6.5.1

Fourier Analysis

Figure 6.5 validates the rich opportunities for state-selective, coherent excitation of multiple
nuclear wavepacket dynamics of neutrally excited D2 , as well as a possibility of controlling bondbreaking and dissociation through the pathways illustrated in Figure 6.3. Figure 6.5(A) plots theexperimental D+ KER as a function of the pump-probe delay, whereas Figure 6.5(D) plots thecorresponding 2D Fourier transform (FT). One can clearly see oscillation periods of ∼83 fs and∼58 fs at a D+ KER of 0.7 - 0.9 eV, corresponding to the vibrational wave packets in the B and EF
states, respectively, that are obtained through the two-step B and two-step EF mechanisms. The
larger probability of the one-step B channel vs. the two-step EF channel (Figure 6.5(D)), confirms
the three vs. four IR photon absorption mechanisms. Moreover, Figure 6.5(A) shows that the twostep B channel (high KER) has a larger probability than the one-step B channel (low KER), due
to a lower effective ionization potential of the excited molecule at shorter internuclear separation.
Figure 6.5(A) also shows that the two-step B and the one-step B channels are dephased, because
the nuclear wave packet is probed at different times in those channels; this allows for steering ofa desired dissociative route by precisely timing the second IR laser pulse as the neutral molecule
vibrates.
As seen in Figure 6.1, to reach the outer turning point of the double-well EF potential andthe vibrational period of ∼58 fs, the nuclear wave packet needs to tunnel through the potential
barrier, which decreases the probability of observing the EF nuclear wave packet dynamics. The
calculations nicely confirm the observed periodicities of these multiple nuclear wave packet dynamics
in D2 (Figure 6.5(G) and (H)). To model the dynamics of D2 on femtosecond timescales, we firstsolved the TDSE to calculate the excitation probabilities, and then propagated the corresponding
nuclear wave packets in the given D2 ∗ potentials (see the SI Text for more detail on how the

87

Figure 6.5: Controlling the dissociation channels by tuning the photon energy and through nuclear
wave packet dynamics. (AC) D+ kinetic energy release resulting from dissociation using threedifferent VUV frequency combs that can be tuned to excite different D2 ∗ electronic and vibrational
states. (DF) Corresponding 2D Fourier transforms of the D+ kinetic energy releases. (G) Calculated
free evolution of the nuclear wave packets generated by the combined VUV + IR pulses in the B
potential energy surface. (H) The same for the EF potential energy surface.

calculations were done). For example, Figure 6.5(G) clearly shows how the EF nuclear wave packet
starts reflecting and tunneling through the inner barrier at about R = 3 a.u. and 10 fs after theexcitation. We also see that the nuclear wave packet tunnels with ∼20% probability comparedwith the main wave packet motion occurring in the inner well of the EF double-potential well.
Moreover, the other striking feature of this calculation starts at ∼45 fs, when the nuclear wave
packet in the inner well tunnels through the inner barrier for the second time and meets the outerwell nuclear wave packet on its way back from the outer classical turning point. The interference ofthe different nuclear wave packets is clearly visible from 45 fs onward. As the time evolves, multiple
reflections/tunneling events from both sides of the inner barrier and the interferences of the nuclear
wave packet in the EF potential are responsible for the fast decoherence of the EF nuclear wave
packet.
Finally, by blue-shifting the VUV harmonic wavelengths to effective driving wavelengths of

88
778 nm and 760 nm (while keeping the IR wavelength fixed at 784 nm), we can control the relative
population of the different neutrally excited states of D2 . Figure 6.5(B) and (C) show the KER
spectra as a function of pump–probe time delay, and Figure 6.5(E) and (F) plot the corresponding
2D Fourier transforms. Two striking features are apparent. First, by slightly increasing the energiesof the seventh and ninth harmonics, the vibration periods in the B and EF potentials simultaneously
increase due to excitation to higher vibrational levels in the Franck-Condon region. Second, therelative strength of the one-step EF channel increases compared with the two-step B channel. The
latter feature can be explained as follows. As seen in Figure 6.1 and Figure 6.3(C), simultaneousabsorption of 7ω + ω and 9ω − ω creates a nuclear wave packet that can tunnel through the innerpotential barrier (located at R = 3.5 a.u.) of the double-well EF potential. By slightly increasing theenergy of the seventh harmonic, the tunneling process becomes more probable, thus increasing thenuclear wave packet density that vibrates with longer periods; this increases the relative visibility ofthe two-step EF channel with respect to the two-step B channel. For an effective driving wavelengthof 760 nm, higher vibration levels of the EF potential are excited, allowing the nuclear wave packet
to propagate freely above the inner barrier, moving along the EF potential energy curve with avibrational period that is now close to that observed in the B state.

6.5.2

Visualization of Wavepacket Coherence

Figures 6.6 and 6.7 show experimental results combined with theoretical simulations. Shownin each Figure are momentum distribution at different times combined with the overall KER spectrum. One can recreate the nuclear wavepacket motion in a much complete view of the process
because of the ability to filter on counts coming from the dissociation channel. Additionally, withtheoretical simulations we can see the evolution of the coherent wavepacket as it is initially populated in the Franck-Condon region, oscillates to a larger internuclear distance turning point, andcomes back again. In this way, we accurately can produce a movie of the experimental and simulated
nuclear dynamics.
Finally, the two-step B channel also disappears when excited by 760 nm VUV harmonics,

89

Figure 6.6: Upper left: Direct D2 + ion momenta shows a definite dissociation energy and a preferential to ionize along laser polarization. Upper right: KER for the scan highlighting the region
around 0fs. Bottom: Theoretical simulation for wavepacket in the B potential. At 0fs, the placement of the wavepacket is due to the Franck-Condon region and the high KER results from thesmall internuclear distance.

because the coupling of the ground and B states dramatically decreases in the Franck-Condon
region. In this case, the ninth harmonic excites higher electronic states. Thus, we show how
tunable attosecond VUV radiation can be used to precisely control excitation of different electronic
and vibrational states.

6.6

Electron Wavepacket Interferences
Figure 6.8 is an extended version of Figure 6.1 and shows in more detail ground and excitedstates of a deuterated hydrogen molecule (D2 is the same as H2 ). We also show the photoelectron,
D+ , and D2 + yields, as well as kinetic energies of the electrons and the D+ ions, for two different

90

Figure 6.7: Upper left: Direct D2 + ion momenta shows a definite dissociation energy and a preferential to ionize along laser polarization. Upper right: KER for the scan highlighting the region around46fs. Bottom: Theoretical simulation for wavepacket in the B potential. At 46fs, the wavepacket
has traveled to a turning point with larger internuclear distance. This results in a lower KER but
the wavepacket remain coherent.

central wavelengths of the VUV frequency comb. The wavelength (photon energy) of the VUVharmonics was fine-tuned while keeping the driving and probing IR wavelengths unchanged byadjusting the Xe pressure (and thus the HHG phase-matching) in the gas-filled waveguide. As theXe pressure in the HHG waveguide was increased from 5 to 20 torr, the photoelectron energies
that result from ionizing Ar by the VUV HHG comb also increased because it is possible to phasematch at slightly higher photon energies. This ability to fine-tune VUV photon energies allows us
to distinguish between various excitation and control mechanisms.
Figure 6.8(E) shows how this phase-matching approach allows for fine control of the periodicity of the e− /D2 + yields that changes from full to half-optical cycle duration of the IR laser

91

Figure 6.8: a) Detailed potential energy surfaces (PES) of the H2 neutral and the H2 + groundand excited states (identical to those of D2 and D2 + ). The red and green arrows represent driving
and probing IR pulses, respectively. b) The photoelectron yield modulation results from the laserinduced interference of the electron wave packets created by the attosecond VUV frequency comb.
The IR laser wavelength was 784 nm, while the VUV photons were 7ω, 9ω, 11ω, etc.. c) The D+
dissociative yield modulation results from the intensity modulation of the interfering driving andprobing IR pulses. d) A comparison of the D+ /e− yields reveals that the ionization and dissociative
dynamics are out of phase. e) By increasing the energy of the VUV photons, we change the electronyield modulation period from full to half-optical-cycle periodicity.

field, as the harmonic energies were blue-shifted. We also see from Figure 6.8 that the periodicityof the D+ yield does not depend on the VUV photon energy; this is expected because the excitedmolecule was ionized in the combined field of the two IR pump and probe pulses, which determines the periodicity observed in the ion yield. Thus, the phase of the D+ oscillation provides areference for the instantaneous value of the total electric field that drives the dissociation of thebound 1sσg nuclear wave packet, as shown in the high kinetic energy release channel, as well as
the dissociation through the low KER channel. Though the high KER channel originates from abond-softening process, which is routinely observed in many strong-field processes, the low KER
channel originates from direct dissociation of D2 as the highly excited Rydberg states were ionizedat larger internuclear separations by the tail of the two IR pulses.

92
In conclusion, we present a powerful approach for using tunable VUV and IR attosecond
pulse trains to coherently excite and control an outcome of a simple chemical reaction in a D2
molecule. The interference of electronic wave packets excited by multicolor VUV and IR fields canbe used to control excitation and ionization on attosecond timescales while maintaining good energy
resolution and state selectivity. Selective bond-breaking is achieved by controlling the excitation
wavelength as well as the time delay between the pump and probe pulses. We also observe andcontrol the nuclear wave packet tunneling in the double-well EF potential. This demonstrates broad
and unique capabilities for doing attosecond chemistry.

Chapter 7
Nitrous Oxide1

In this Chapter we discuss the ability to coherently control the dissociation pathway of N2 O.
Such control of using laser light to not only direct molecular dynamics, but to extend the control tochemical reactions would be of tremendous impact. In the extreme ultraviolet (XUV) and soft x-ray
regions of the spectrum, light-matter interaction is dominated by photoionization. In molecularsystems, the sudden removal of an electron will initiate ultrafast electronic and nuclear dynamics
in the residual molecular ion. A particularly interesting aspect of these dynamics is the correlated
motions of electrons and nuclei, an understanding of which lies at the heart of chemistry. Here
we use a few-femtosecond high harmonic pulse and a weak infrared (IR) laser pulse to initiate andprobe the explosion of a triatomic N2 O+ molecular ion in real time, in a regime dominated bycoupled electron-electron and electron-nuclear dynamics. We also show that the branching ratio ofbond breaking can be altered in the presence of the laser field.

7.1

Coherent Control of N2 O Dissociation
Recent advances in generating ultrafast soft x-ray pulses using high harmonic generation(HHG) [31], combined with advanced molecular imaging techniques [122], now make it possible
to explore photoionization-driven [123] electron and nuclear dynamics in atoms [32, 124] and diatomic molecules [14, 68, 125] in real time for the first time. Owing to their greater mass, nuclear
dynamics usually occur on much slower timescales than electron dynamics, and in the well-known
1

The results of this chapter are in part based on “X. Zhou, P. Ranitovic, C. W. Hogle, J. H. D. Eland, H. C.
Kapteyn, and M. M. Murnane, Proceedings of the National Academy of Sciences 8, 3, 232 (2012)” [168].

94
Born-Oppenheimer approximation, electron and nuclear dynamics can be considered decoupled.
However, for highly excited molecules, nuclear motion on strongly repulsive adiabatic potential
energy surfaces can be very fast, so that electron and nuclear dynamics can occur on comparable
timescales and be strongly coupled [95, 126–130]. For example, previous work has shown that autoionization and pre-dissociation are competing decay channels for super-excited neutral molecules(including valence singly excited Rydberg states [95, 126] and core-excited states [127]). However,such ultrafast non-Born-Oppenheimer dynamics on femtosecond timescales are largely unexploredin the case of molecular ions, where electron-electron correlation can also be important, owing to
the lack of ultrashort XUV pulses.

7.1.1

Coulomb Explosion of N2 O

We probe and control the Coulomb explosion of a triatomic N2 O molecule after being ionized
by a few-femtosecond XUV high harmonic pulse. N2 O is a simple linear triatomic molecule withan asymmetric bond. By ionizing/exciting N2 O with a few-femtosecond XUV pulse, we create ahighly excited N2 O+∗ state near the double ionization threshold (with continuous energy structure
both below and above the double ionization threshold). The resultant decay dynamics of these
excited molecular ions include two competing processes: (1) ultrafast dissociation into ion-neutralfragments with only one singly charged component; and (2) autoionization of super-excited states(that is, emission of a second electron) resulting in an N2 O2+ dication, which subsequently Coulomb
explodes into two singly charged fragments, corresponding to breaking the N–N or N–O bond (thatis, N2 O2+ → N2 + + O+ or N2 O2+ → N+ + NO+ ). This competition between dissociation andautoionization has been suggested as the reason for the low double ionization quantum yield (ratio
between double ionization and single ionization) of small molecular ions above the double ionizationthreshold [131].
We also show that the presence of a moderately intense linearly polarized infrared field caninterrupt the neutral-ion dissociation channel and strongly enhance the double ionization yield,
because the excited N2 O+∗ cation can easily lose a second electron in the laser field. Furthermore,

95
the short duration of the double ionization enhancement transient, when the XUV and IR field areoverlapped in time, reveals the timescale of ultrafast dissociation. Finally, with the addition of theIR field, breaking of the N–O bond can be enhanced more compared with breaking of the N–Nbond, indicating the presence of laser-induced nonadiabatic multielectron dynamics. Our results
thus demonstrate optical control [78, 132] of fragmentation products in highly excited molecularions for the first time, in a regime dominated by coupled electron–electron and electron–nuclear
dynamics.
The N2 O molecules from the supersonic jet are excited with sub-10 fs XUV pulses centred
at a photon energy of 43 eV, which is above the 35.5 eV double ionization threshold of N2 O. This
photon energy is close to the wavelength of the He(II) lamp (40.8 eV), allowing us to compare ourdata with previous work [128]. In contrast to our previous studies of ionization dynamics in N2
and O2 diatomics [14, 68], there is no long-lived metastable N2 O2+ that can survive the flight time
to reach the detector (∼10 µs); because of a shallow potential well in the Franck–Condon region.
(The lifetime of metastable N2 O2+ has been determined to be less than 400 ns [133]). Because
the threshold for three-body dissociation into two charged atomic ions is barely accessible with our
43 eV photon energy [134], double ionization mainly results in two two-body Coulomb explosion
pathways:

Channel 1: N2 O2+ → N2 + + O+
(7.1)
2+

Channel 2: N2 O
7.1.2

+

→ N + NO+

Photoion-Photoion Coincidence

The recorded photoion-photoion coincidence (PIPICO) spectrum when N2 O is irradiatedwith the XUV pulse alone is shown in Figure 7.1(a). A momentum conservation filter between thetwo charged fragments is used to extract the counts corresponding to these two distinct Coulomb
exploding channels from the background. In Figure 7.1(b),(c), we plot the filtered PIPICO spectrumof channels (1) and (2). The branching ratio between these two Coulomb explosion pathways is

96

Figure 7.1: Illustration of double ionization of N2 O and subsequent two-body fragmentation. (a)PIPICO spectrum of N2 O2+ fragmentation using XUV pulse alone. (b) PIPICO spectrum filteredusing momentum conservation for the fragmentation channel N2 O2+ → N2 + + O+ . (c) PIPICO
spectrum filtered for the fragmentation channel N2 O2+ → N+ + NO+ .

approximately 1 to 2.6, which agrees with previous studies using He(II) lamps and synchrotron
radiation at similar photon energies. This ratio has been explained as the result of competition
between the two fragmentation pathways on the potential energy surfaces of the first few N2 O2+electronic states [135, 136].
Using a moderately intense infrared laser pulse (IR) to irradiate N2 O simultaneously with
the XUV pulse, it is possible to probe the very fast nuclear dynamics initiated by the XUV pulse,
and to control the branching ratio of channels (1) and (2). Figure 7.2(a) plots the ion yield for thetwo charge separation channels in the presence of both XUV and IR laser fields, as a function of

97time delay between them. For the IR field, a 100 µJ pulse was focused to an intensity of ∼6 × 1012
W/cm2 , ensuring that no N2 O+ counts are observed from the IR field alone. When the IR pulse
arrives before the XUV pulse, the relative yield between channels (1) and (2) is approximately
the same as for XUV radiation alone, because the low intensity of our IR pulse does not excite
the molecule. When the IR and XUV pulse coincide temporally, the yields of both channels areenhanced. The time-dependent yields of Figure 7.2 are fit with a convolution of a Gaussian function
and an exponential function. The best fit corresponds to the convolution of a Gaussian function
with a full-width at half-maximum (FWHM) of 41 fs, and an exponential function with decay
constant of 15 fs and 19 fs for channels (1) and (2), respectively. Although the FWHM of theGaussian function is longer than the exponential decay, the asymmetric shape of the trace can beclearly seen. The Gaussian pulse duration is only slightly shorter than the convolution of the 40
fs IR and 10 fs XUV pulses, indicating that only a few IR photons are involved in modulating theyield of the two-step sequential double ionization process.

Figure 7.2: KER of the Coulomb explosion channel N2 O2+ → N2 + + O+ (left) and N2 O2+ → N+
+ NO+ (right) (effusive jet target). The enhancement is larger for the N–O bond-breaking channel,
and consistent with the supersonic jet data.

98
7.1.3

Electronic configurations

The electronic configuration of the ground state of N2 O is(1σ 2 2σ 2 3σ 2 )(4σ 2 5σ 2 )(6σ 2 1π 4 7σ 2 2π 4 ). The first three core-level molecular orbitals correspond to
the 1s orbitals of the three constituent atoms. The (4σ 2 5σ 2 )(6σ 2 1π 4 7σ 2 2π 4 ) molecular orbitals
are delocalized inner- and outer-valence electronic configurations respectively. Photoelectron spectroscopy and dipole (e,2e) spectroscopy studies can easily identify the four outer-valence ionizedstates X 2 Π(2π −1 ), A2 Σ+ (7σ −1 ), B 2 Π(π −1 ) and C 2 Σ+ (6σ −1 ) as discrete sharp peaks, with corresponding binding energies of 12.9, 16.4, 18.2 and 20.1 eV, respectively [137]. However, for innervalence ionization with binding energies between 20 and 40 eV, the photoelectron spectrum isbroad, and it is no longer possible to associate a cation state with a one-hole configuration, whichcorresponds to removal of one electron from a neutral configuration with other electrons unaffected,
in a one-to-one fashion. Generally speaking, the molecular orbital picture breaks down owing toelectron-correlation-mediated mixing of inner-valence one-hole configurations (4σ −1 and 5σ −1 ) andouter-valence shake-up two-hole-one-particle configurations [138, 139], with two outer valence holes
and another excited electron in the previous unoccupied molecular orbital, as shown in Figure
7.3(a). The intensity of the main lines (4σ −1 and 5σ −1 with binding energies of 38 and 40 eV,
respectively) redistributes to many lines corresponding to satellite states, and it is not possible todistinguish between them. The broad photoelectron spectrum between 30 and 40 eV (taken fromprevious photoelectron measurements [137]) is illustrated in Figure 7.3(b). Theoretical calculations
have been able to reproduce the general features of these photoelectron and (e,2e) spectroscopy
data [138, 139], and also show that non-Rydberg type doubly excited electronic configurations giverise to most of these satellite lines. These excited states are major channels contributing to the IR
field enhancement of the double ionization yield.

99

Figure 7.3: Illustration of the coupled electronnuclear ionization dynamics. (a) An illustration of
possible electronic configuration changes during ionization of N2 O+∗ in the presence of XUV and
IR fields, involving multiple electron transitions. (b) Continuous electron spectrum of the innervalence ionizing states measured at 60 eV photon energy. Reproduced from [137]. (c) Schematic
representation of the N2 O+∗ cation (black) and dication (red) potential energy curve along one
bond stretch direction. The two major competing decay pathways of N2 O+∗ are also labelled.

7.1.4

Ionization Yield and KER

The exponential decay of the ion yield signals in Figure 7.4(a) shows that IR field enhances
double ionization through a two-step sequential process during which the molecule is first ionizedby the XUV pulse, and the resulting cation N2 O+ state is then further ionized by the IR pulse.
This conclusion is supported by the fact that instantaneous IR and XUV (two photon) process

100such as IR-assisted shake-off and knock-out of the second electron have small cross sections [43],and the densely distributed N2 O+∗ potential energy surfaces provide many possible intermediateresonances. As mentioned in the main text, all of the N2 O2+ cations fragment into two ions before
they can reach the detector. Therefore, the enhancement of the double ionization yield must comefrom the interaction of the IR pulse with intermediate states such as an excited neutral (N2 O∗∗ )or cation state (N2 O+∗ ).
For doubly-excited neutral states above the double ionization threshold, subsequent dissociation and autoionization are both possible. Dissociation into two neutral atoms has been observedin fluorescence experiments for small molecules [140]. However, since our excitation photon energy
is well above the first ionization threshold, the cross section for creating doubly-excited neutrals is
small [141].

7.2

Dissociation Mechanisms
We can divide excited N2 O+∗ states into two classes. The first class are molecular Rydberg

states with a high n Rydberg electron and a vibrationally or electronically excited core. Howeverthese states follow similar potential energy surfaces to the lower lying states of N2 O2+ and converge
to the same dissociation limits [142]. Moreover, Rydberg electrons can be easily ionized by the IR
field, therefore any enhancement from these molecular Rydberg states should persist longer, atleast for a few hundred femtoseconds. Therefore, Rydberg type N2 O+∗ states are not a major
contribution to the enhancement in double ionization near time zero. However, together with the
doubly-excited neutrals, they could be responsible for the enhancement of double ionization at
longer time delays after the transient at time zero, (which is a relatively small contribution to ourdata). The second class of N2 O+∗ states are non-Rydberg type electronically excited states. From
our data and theoretical calculations, these states are major contributors to the IR enhancementof the double ionization yield.
There are two major competing decay processes for XUV excited N2 O+∗ states, as illustrated
in Figure 7.3(c): molecular autoionization by ejecting a second electron (N2 O+∗ → N2 O2+ + e− )

101Figure 7.4: Time-dependent ionization yield and kinetic energy release of Coulomb explosion fragments. (a) Ionization yield as a function of time delay for the two double ionization channels alongwith a fit to a convolution of a Gaussian function and an exponential decay function. (b) The
time-dependent ionization yield for both channels shown in (a) are normalized to the yield at -60 fs(IR before XUV), illustrating the different enhancements of the two channels. (c,d) Kinetic energy
release as function of time delay between the XUV and IR for channels N2 O2+ → N2 + + O+ andN2 O2+ → N+ + NO+ respectively. The dashed black contour line is to guide the eye to make theKER change for N2 O2+ → N2 + + O+ channel more visible.

accompanied by Coulomb explosion, or dissociation of the ion into a neutral fragment and a singly
charged ion. Autoionization of N2 O+∗ to low-lying electronic states of the doubly ionized moleculecan only happen if the molecule is excited by photon energies above the double photoionizationthreshold (35.5 eV). N2 O+∗ provides an interesting scenario because a portion of the XUV-excitedstate is above the double photoionization threshold of 35.5 eV and forms a super-excited molecular

102
ion, as shown in Figure 7.3(b). This situation is impossible for atoms and many small molecules,
such as N2 , H2 O or CO. However, it is much more common in weakly-bound dimers, because the
distribution of two holes on different atomic or molecular sites in dimers lowers the double ionizationthreshold. This can result in an autoionizing process called inter-molecular Coulomb decay (ICD),
which is an extremely efficient process with decay times between a few femtoseconds and a few
hundred femtoseconds [129, 130]. The inner-valence ionized cation states of dimer molecules areusually well above the dication potential energy surface, which makes ICD the dominant decay
process. This will be discussed further in Chapter 8.
For super-excited N2 O+∗ , the timescale of molecular autoionization (N2 O+∗ → N2 O2+ + e− )varies with the electronic configurations. Non-Rydberg type electronically doubly excited configurations usually autoionize in a few femtoseconds [143]. However, in contrast to ICD, the dense
adiabatic potential energy surfaces (calculated using the Born-Oppenheimer approximation) of
these N2 O+∗ are strongly repulsive, and can quickly drop below the potential energy surfaces of thelower lying dication states, thus reducing the probability of autoionization. If the rates of nuclear
dissociation into a neutral fragment and a singly charged ion are comparable to the average electronic decay rates, competition between dissociation and autoionization is possible, as illustrated
in Figure 7.3(c). The large number of potential energy surface intersections and fast nuclear motion lead to extreme non-Born-Oppenheimer dynamics, and prevent theoretical treatments such asa diabatic representation of strong non-adiabatic coupling at a conical intersection between two
adiabatic potential energy surfaces.
The addition of a weak IR field can couple the excited molecular cation state to other states
or dication continuum states via single or multiphoton transitions. For excited states below the
double ionization threshold, normally energetically forbidden double ionization is made possible in
the presence of an IR field. For excited states above the double ionization threshold, the branchingratio between autoionization and dissociation can be altered [144]. Because of the strong electron
correlation in this region, the IR induced ionization process represents a laser-induced multielectron
process, which from an energetic point of view is preferred over direct ionization of the most loosely-

103bound electron. A schematic of this ionization process involving multiple electrons is illustrated in
Figure 7.3(a).
In the Born-Oppenheimer approximation, autoionization is instantaneous (or at least much
faster compared with nuclear motion), and all excited states above the double ionization thresholdshould autoionize. In this case, the enhancement of double ionization would result from the promotion of N2 O+∗ population from below to above threshold. However, considering that the areaof the photoelectron spectrum below the double ionization threshold is less than that above, as
shown in Figure 7.3(b), this mechanism cannot explain the ×2 enhancement in double ion yield weobserve. Therefore, for the first time, we use a time-resolved measurement to reveal the competition
between dissociation and autoionization in a highly excited molecular ion, and the breakdown of
the Born-Oppenheimer approximation.
The 20 fs decay time of the double ionization enhancement transient indicates the timescale ofultrafast dissociation in excited N2 O+∗ states. During this time, electronic excitation is converted
into kinetic energy of the fragments through complicated electron-nuclear dynamics, which can bethought of as hopping between different adiabatic potential energy surfaces. At a certain point inthis ultrafast dissociation process, the IR intensity used becomes less effective in ionizing the second
electron owing to the increasing ionization potential [82]. Furthermore, the competition between
autoionization and dissociation suggests that the cross-section and timescale for dissociation andautoionization must be comparable.

7.3

Selective Bond Breaking
It is also interesting to compare the dynamics of the two bond-breaking channels of N2 O2+(that is, breaking the N–N bond or breaking the N–O bond), which might shed light on the laserinduced nonadiabatic multielectron dynamics. First, we notice in Figure 7.4(a) that the relative
enhancements of the two bond-breaking channels by the IR laser are different. To emphasize this,
we normalize the time-dependent yield of each channel by the yield in the presence of the XUVpulse alone, as shown in Figure 7.4(b). With the addition of the IR pulse, the less dominant channel

104

Figure 7.5: Momentum distribution of the Coulomb explosion fragments. (a,b) For the N2 + ion
from Coulomb explosion with the IR pulse well before the XUV pulse (a), and with the two pulses
temporally overlapped (b). (c,d) Similar to a and b, but for the NO+ ion. The outer momentum
ring structure from molecular double ionization is separated by dashed yellow lines from the timedelayed autoionization in (b) and (d). The ratio of the integrated outer-momentum ring (direct
double ionization) of N2 + in (b) and (a) are plotted in (e), and the ratio of the integrated outermomentum ring (direct double ionization) of NO+ in (d) and (c) are plotted in (f). The red andblue arrows in (e) and (f) show the direction of the laser and XUV polarization. These data aretaken with an effusive jet.

(breaking the N–O bond) is enhanced more (∼2.6 times) compared with breaking the N–N bond (∼2times). Therefore, the relative difference between the two channels is smaller in the presence of theIR field. Selective bond breaking is an interesting topic, which has been studied both in the context
of single-photon weak-field ionization of core [145] and inner-valence levels [146], as well as in thecontext of multiphoton intense-field ionization [78,132]. Here, control is achieved by combining these
two approaches through a transient intermediate resonance in a highly excited short-lived N2 O+∗
state. Previous photoelectron-photoion coincidence studies [146] show that dissociation of highly
excited N2 O+∗ states in the binding energy region between 30 and 40 eV has a strong preference
for the N–N bond-breaking channel, resulting in N+ + NO or N + NO+ fragments. Therefore, it

105
is surprising that we observe a large enhancement in N–O bond breaking in the presence of theIR field, which is probably a signature of laser-induced multielectron dynamics. Nonresonant light
dressing of the molecular potential could also play a role. In the absence of advanced theory, it
is difficult to understand the detailed mechanism for how the IR field preferentially enhances one
bond-breaking channel.
As the IR laser field interrupts the dissociation of N2 O+∗ and promotes it to an N2 O2+
dication state, there should be a corresponding change in the kinetic energy release (KER, sumof the kinetic energy of the two fragments) of the fragments due to the difference in the potential
energy surfaces of N2 O+∗ and N2 O2+ . Figure 7.4(c),(d) plots the KER of both channels as afunction of XUV-IR relative time delay, where the KER counts are normalized to the maximum
for each time delay to show the shift of the KER more clearly. The KER peak for breaking the
N–O bond is broader than the KER for breaking the N–N bond. The KER are centered at 5 and
6 eV respectively, which agrees with previous work [135]. At time zero, we observe a slight shift
towards higher KER for breaking the N–O bond, whereas the KER for the N–N bond-breaking
channel does not change. However, the observed KER changes for both channels are very small
compared with what was observed previously for diatomic molecules [14, 68, 125]. The most likely
explanation is that for triatomic molecules in a strongly-coupled non-Born-Oppenheimer regime,
any further energy can be efficiently transferred into internal excitation of the molecular fragment
species, instead of into kinetic energy of the fragments.

7.4

Angular Distribution of N2 O2+ fragments
Figure 7.5(a)-(d) plots the angular distribution of the ion fragments both with and without theIR field, for both bond-breaking channels. The angular distribution of the ion fragments is related
to the symmetry of the initial and final electronic orbitals, and can show signatures of electronic
configuration interaction. These data were taken using the effusive jet with much longer dataacquisition times, at two fixed time delays between XUV and IR pulses, namely when the IR pulse
arrives 200 fs before the XUV pulse, and when both pulses are overlapped in time. The former is

106
equivalent to irradiation by the XUV pulse alone. In the momentum distribution after excitation by
the XUV pulse alone, the anisotropy in the angular distribution is clearly visible. The anisotropyof ion fragments from double ionization is not trivial to understand, because two electrons are
involved [147]. Focusing on the IR enhancement of direct molecular double photoionization, Figure
7.5(e),(f) plots the angle-dependent IR enhancement of double photoionization by integrating thecounts in the outer momentum ring along different angles. The enhancement of the N+ + NO+
channel is almost isotropic whereas the enhancement of the N2 + + O+ channel favours the directionof the laser polarization.
As shown in Figure 7.5, for both channels there are two separate momentum rings. The outer
momentum ring in Figure 7.5 corresponds to the major KER peak in Figure 7.2, while the inner
momentum ring in Figure 7.5 corresponds to the low KER peak shown in Figure 7.2. Although afull four-body (two electrons plus two ion fragments) momentum map is not possible with our countrates, we can still assign the small momentum ring counts as due to time-delayed autoionization,and the larger momentum ring as molecular double ionization, according to previous studies on CO
and H2 O [125, 148].

7.5

Autoionization Pathway
In the case of time-delayed autoionization, some of the dissociating potential energy surfacesof N2 O+∗ will end up above the dissociation limit of the dication. In this case, the excited atomic ormolecular species such as N∗ , O∗ , N2 ∗ and NO∗ , will proceed to autoionize. For N2 O, the presenceof time-delayed atomic autoionization has been confirmed by the atomic-like autoionization linesof N∗ and O∗ atomic species presented in previous photoion-photoelectron-photoelectron triple
coincidence measurements [128]. However, N2 ∗ and NO∗ autoionization have not been isolated
this way because of the broad autoionization lines. Time-delayed autoionization processes can evenhappen for excitation below the double ionization threshold, as low as 34 eV [128]. Using an effusive
jet, we have more counts with low KER than for the case of supersonic jet data for both channels,
which is probably due to the increased statistics and a slight red shift of the XUV spectrum

107(about 0.5eV), which could increase time-delayed autoionization. Apparently autoionization of O∗
or N2 ∗ is more prominent than autoionization of N∗ or NO∗ . The angular distribution of the small
momentum ring related to N∗ or NO∗ autoionization channel is oriented perpendicular to the laser
polarization direction, while the orientation of the O∗ or N2 ∗ autoionization channels and direct
double ionization channels are along the direction of the laser polarization.
Past work has shown that atomic autoionization is the dominant double ionization mechanism
for O2 even above the double ionization threshold. A time-resolved XUV pump IR probe experimentconfirmed that autoionization of O∗ does not happen until a few hundred femtoseconds after the
XUV pulse [68]. However, the time delayed autoionization is not our focus in this paper and it
is minor channel for the enhanced double ionization of N2 O by IR: when the IR pulse is applied
near time zero, the autoionization channels remain almost unchanged, while the direct molecular
double ionization channels are strongly enhanced, which is obvious in the energy-dependent KER
enhancement shown in Figure 7.2.
To fully understand the observed dynamic evolution of N2 O+∗ , with or without the presence of the IR field, will require more advanced theory. However, the strong electron–electron
and electron–nuclear coupling make reliable quantum chemistry calculations very challenging. Further experiments using shorter duration XUV and IR pulses could measure these timescales more
precisely. With photoelectron or photoelectron-photoion coincidence measurements, it should bepossible to extract valuable information about laser-induced electronic reorganization from theangular distribution of electrons.
In summary, few-femtosecond XUV pulses can produce highly-excited inner-valence ionized
N2 O+∗ molecular ions which rapidly dissociate or autoionize in ∼20 fs. Using moderate intensity
IR fields, surprisingly it is possible to enhance and to change the branching ratios for selectively
breaking the N–N or N–O bond. The short timescale over which enhancement is possible reveals
the competition between fast dissociation and autoionization processes in N2 O+∗ , and highlights
the role of non-Born-Oppenheimer strongly-coupled dynamics. The ability to control the branchingratio for bond breaking provides evidence of laser-induced multielectron processes. The observed

108
competition between dissociation and emission of a second electron is relevant to many physicalprocesses with strongly coupled electron and nuclear dynamics.

Chapter 8

Complex Systems

Because of COLTRIMS’s ability to measure the momenta of both electrons and ions incoincidence, much of the previous work has focused on atomic and diatomic experiments where
the complete system can be best be theoretically modeled [14, 23, 42, 43, 63, 68, 82]. Applying
similar techniques to larger and more complicated molecules allows for the exploration into a wider
area of physical chemistry. As discussed in Chapter 7, even a triatomic system can provide many,often unexpected, complexities. Both molecules examined here, ethylene and ozone, have enormous
impact on better understanding important processes like the chemical reaction responsible for vision
and allowing for more accurate atmospheric models relating to climate change as well as many otherapplications. Additionally, the argon dimer, while a diatomic system, provides a useful system tostudy because of the weak bonding and simpler electronic structure.

8.1

C2 D4 isomerization
The molecule rhodopsin has long been known to be the primary photochemical receptor

responsible for the process that allows for vision [149]. Nonradiative relaxation through a conicalintersection allows for the ultrafast transfer of light into chemical energy but the details of theprocess are not well understood [150]. This process is both extremely efficient with its energy
conversion as well as its response time, having dynamics on ultrafast timescales. The isomerizationof the all-trans form in rhodopsin was identified as the main photochemical event in vision, involving
a conical intersection between the potential energy surfaces of the ground and excited electronic

110states [151, 152]. A conical intersection is the non-adiabatic coupling between two potential energy
surfaces. At the these intersections, the Born-Oppenheimer approximation breaks down and theelectronic and nuclear changes are highly coupled. As with other experiments previously discussed,
the nature of these dynamics presents a challenging experimental environment where probing theexciting state necessary to access a conical intersection requires precise spectral control but we muststill have time resolution to probe the reacting molecule which changes on an ultrafast timescale.
The photoisomerization of retinal rhodopsin can be effectively modeled by the twist andstretch of a carbon double bond [153]. The simplest molecule with a carbon double bond is ethylene(C2 H4 ), yet even this “simple” molecule presents numerous experimental and theoretical complexities. Ethylene’s first absorption band is centered at 165 nm [154] making the 5th harmonic of theTi:sapphire laser an ideal pump for this system. This band is dominated by a π → π ∗ transition
where in this excited state the lowest potential energy configuration is no longer planar [155, 156].
Using nomenclature from Mulliken, this is the V state (for valence) and is shown schematically in
Figure 8.1.

Figure 8.1: Potentials and dynamics of C2 H4 adapted from [157], indicating also hydrogen migration(perpendicular to the drawing plane) and the displacement of the conical intersection. φ is the C-C
torsion angle.

111
Some calculations predict that one of the major pathways in which the molecule relaxes
to the ground state is through an ethylidene configuration (HCCH3 ), where one of the hydrogenatoms has migrated across the carbon-carbon bond [157]. This provides an additional coordinate
for relaxation down to the ground state. The ethylidene configuration is predicted to be followed
by a H2 stretch leading to the elimination of neutral or ionized molecular hydrogen [154, 158–161].
Because of this, understanding the asymmetric dissociations of ethylene is an incredibly importantpart to better understand this type of conical intersection.
We use a pump-probe geometry with VUV photons as a pump pulse and a delayed IR pulse
to probe. With experimental conditions similar to what was discussed in Chapter 6 we know wehave signals from 7th, 9th, and 11th harmonic energies. We also believe that the phase matchingcondition and reflectivity of the mirrors allow for the 5th harmonic as well. We also allow a small
intensity of the high harmonic driving IR intensity to copropagate. This driving IR field is locked inphase to the high harmonics and provides a reference for the probing IR field. Having establishedthis a technique on simpler systems [23], we wish to show the ability to induce and control theoutcome of a chemical reaction on an attosecond timescale. We focus mainly on the dissociation
pathways involving D2 + , C2 D2 + and C2 D4 + , however as shown in Figure 8.2, many other ions arepresent.
Figure 8.2 shows the time-of-flight spectrum for C2 D4 irradiated by a VUV pulse train and
IR pulse temporally overlapped. As expected with a strong-field IR pulse as well as with low orderharmonics, a primary signals come from the singly ionized parent ion, C2 D4 + . There is also astrong C2 D2 + signal, but which is sensitive to the VUV pulse.
Additionally, there is a detectable C2 D4 → C2 D2 + D2 + + e− pathway less probable thanC2 D4 → C2 D2 + + D2 + e− . The experiment was performed with the effusive gas jet. An unexpected result was the presence of the ethylene dimer (C4 D8 ) which presents an exciting system totest with future experiments. With the effusive gas jet the ethylene molecules are emitted withmore thermal energy than with the supersonic jet. Typically the atoms or molecules must lose
most of this thermal energy to allow for a measurable level of dimers to be present.

112

Figure 8.2: C2 D4 time-of-flight spectrum, plotted on both linear and logarithmic scales. The parent
ion undergoes many different fragmentation pathways. The single ionization (C2 D4 + ) allows forcomparison against the dissociation pathways (C2 D2 + and D2 + ).

Experiments were performed with both femtosecond and suboptical cycle resolution. Figure
8.3 shows the ionization yields for the C2 D4 + , C2 D2 + , D2 + ions a function of pump-probe delay.
The C2 D2 + and D2 + yields show enhancement with IR overlap; the C2 D4 + peaks 40 fs later.
Previous studies have seen a maximum fragmentation yield attributed to ethylidene isomerization
later at approximately 80 fs and model the isomerization time at approximately 50 fs [154, 159].
The C2 D2 + enhancement at 40 fs is reproduced by scans with a larger step size. This enhancementof the C2 D2 + yield is believed to take place after the D migration allowing for the elimination of D2 .
This measurement could be improved with a shorter probing pulse envelope; however, there is aclear response before what has been previously measured in association with the isomerization [159].
Figure 8.4 shows a zoomed in view of the ion yields at four different regions near pumpprobe overlap. While each ion yield appears to oscillate with the same full optical cycle oscillation
the yields do not oscillate in phase with one another. The difference in the enhancement of eachionization channel cannot be simply explained by the instantaneous strength of the electric field

113

Figure 8.3: Pump-probe spectrum of C2 D4 fragmentation yields. Positive delays refer to the VUVpulse train preceding the IR pulse. The ionization yield is enhanced around 0 fs for C2 D4 + andD2 + but the enhancement of C2 D2 + is delayed ∼40 fs. The attosecond scale resolution is shown
above as the yields oscillate with a full optical cycle periodicity.

due to the IR pulse. Figure 8.4 also shows sinusoidal fits for the experimental yields, each plottedwith the same amplitude. The fits clearly show a shift of the phase of the C2 D2 + and D2 + yields
relative to C2 D4 + over the region where the pulses are overlapped.
The delay between the C2 D2 + and C2 D4 + changes from 90 attoseconds to 370 attoseconds.
The interferometric stability limits the ability to see how the transition occurs over the scan but
the change is definite. Further theoretical simulations must be done to fully understand how thisdifference in ionization yield relates to the changing molecular structure. This level of analysis overmeasuring yields on femtosecond timescales moves closer to the factors for inducing and controlling
this and similar reactions.

114

Figure 8.4: Fits for four different overlap regions of C2 D4 fragments. A sinusoidal fit was performed
in four different regions relative to pump-probe time zero. These fits are plotted on the right side
for each region with normalized amplitude. The experimental yields have been shifted here forcomparison purposes.

8.2

Argon dimer Inter-Coulombic Decay
Noble gas dimers are bound by a weak van der Waals potential which results in a substantiallylarger internuclear separation than with covalently bound diatomics. Therefore, while having somemolecular-like properties, the electrons remain more centered at each nucleus. Photoionization of

115
dimers with both XUV and strong-field ionization should probe the electronic properties in such a
way to see both localized structure as well as shared electronic behavior. Complete understandingof intramolecular charge transfer remains a challenge [162], and systems like argon dimer, which
exhibit related processes in a simplified structure. The inner valence states will be ionized with ahigh harmonic photon of sufficient energy and the strong-field will look primarily at the outer-mostshared electrons. As discussed in Chapter 5, changing internuclear spacing dramatically affects the
kinetic energy release (KER) which provides information about the changing molecular orbitals.
The simplified bonding of dimers makes them a preferable system to study similar electronic structure changes.

Figure 8.5: Adapted from [163], schematic potential energy curves of Ar2 2+ and Ar2 + showing
double ionization with a single 36 eV photon and then excitation by strong field IR. The presenceof the IR should affect the localization of the ionization. RCT indicates a radiative charge transfer
that becomes more efficient at small internuclear distances.

A 36 eV XUV photon is an ideal tool to access the double ionization of Ar dimers and then

116
the following Coulomb explosion. It is above the double ionization potential of the argon dimer(35.3 eV) but below the double ionization of atomic argon (43.4 eV). The experiment must be
set up in such a way that focuses on dynamics from the dimer while filtering out counts due tobackground atomic argon. As discussed in Chapter 7, Coulomb explosion provides an excellent way
to filter through ion-ion coincidences. Additionally, Coulomb explosion gives information throughthe KER being inversely proportional to the internuclear spacing to a good approximation. True
ion-ion coincidences exclude any influence from atomic argon ionization.
Cederbaum et al. predicted the decay of excited atoms and molecules through a process theycalled interatomic Coulombic decay (ICD) [164]. The process involves an excited ion with a close
neighbour; this was originally applied to molecular clusters but dimers provide a simpler system.
The excited ion can relax by transferring its excitation energy to this neighbour, causing thatneighbour to emit a lower energy electron. Similar to an Auger decay process, ICD typically occurs
on the order of femtoseconds which is much faster than radiative decay processes [165, 166]. ICD
differs from Auger decay because the energy transfer must involve a neighboring atom or molecule.
Because of the weak bonding and high internuclear spacing in a dimer, the excitation canbe site specific and separated from the nuclear dynamics. This causes an expectation to find a
Coulomb explosion KER after double ionization that corresponds to the equilibrium internuclear
separation of a neutral Ar2 dimer. Previous work has found that in addition to this channel there
are Ar+ ions with a higher kinetic energy release [163]. In order to explain this increase in energy
the dimer must move towards a much smaller internuclear spacing. The process is proposed where
the dimer is initially doubly ionized at a single site (Ar2+ -Ar) or put into a one-site singly charged
excited state (Ar+∗ -Ar), which then may decay by ICD [164, 165, 167].
Figure 8.6 shows the time-of-flight spectrum for the supersonic gas jet seeded with argon andpumped by 36 eV XUV photons with IR temporally overlapped. This provides an indication ofsome of the experimental difficulties as the concentration of the dimer compared to atomic argon in
the jet makes it difficult to achieve good signal-to-noise. Even with a clear source and dissociation
channel photoion-photoion coincidence experiments require long integration times [14, 68]. In this117
experiment, the rarity of Ar2 causes a decrease in the signal by additional orders of magnitude
compared to similar previous Coulomb explosion experiments [14, 168].

Figure 8.6: Time-of-flight spectrum for argon in the supersonic gas jet probed with 36 eV XUVphotons and IR. The signal will be dominated by Ar+ as well as include a clear indicator of theAr2+ ion. Visible on a semi-log plot is the Ar2 + . The small concentration of Ar2 in the jet causes
an experimental challenge. Also visible in the plot are peaks due to a small concentration of H2 O,
N2 , and O2 present due to a small amount of atmosphere present from the input to the gas jet.

Figure 8.7 shows a photoion-photoion coincidence plot for argon dimer counts. Because Ar
is much more prevalent than Ar2 there is a high frequency of false coincidences. There will bemany events with a Ar+ count arriving at the detector first and an second Ar+ count arriving later
due to multiple ionization events in different parts of the gas jet or ionization in the backgroundgas. The double ionization of an argon dimer will result in two positively charged nuclei in close
proximity. The Coulomb force on the two ions will cause them to have large repulsive velocities.
This Coulomb explosion has a definite center of mass and the particles will show a conservation of
momentum. Because of this true coincidence counts have a time-of-flight relationship where if one
ion has an initial momentum in the +z direction then the other ion will have momentum in the

118−z direction. Center of mass and conversation of momentum provide two features that allow forfiltering on coincidence counts.

Figure 8.7: Coincidence counts are highlighted within the white oval. Conservation of momentum
between each Ar+ ion from the same original dimer allows for filtering. Plot density shown on alogarithmic scale.

Figure 8.8 shows the KER for the photoion-photoion coincidence channel shown in Figure 8.7.
There is a clear KER peak at 3.8 eV that is consistent with previous results [163, 169]. This KER
peak shows enhancement when IR is overlapped with the XUV and this enhancement continues for
positive delays. Ar dimer has an equilibrium internuclear distance of approximately 7.13 Å [170].
The KER calculated for this distance is 3.82 eV and matches the experimental results exactly [163].
This 3.8 eV Coulomb explosion channel comes from creating single ionization on both argon nuclei
on the same dimer.
Figure 8.9 is the KER at 50 fs and clearly shows the peaks at 3.8 eV and around 5 eV, labeled(a) and (b), respectively. A direct two-site double ionization of Ar2 is unable to explain this higher

119

Figure 8.8: Time resolved kinetic energy release of Ar+ + Ar+ coincidence channel from Ar2 2+ .
KER of ∼4 eV is consistent with previous results [163,169]. The left panel shows total KER counts
integrated over the scan and the upper panels shows total counts versus delay.

KER peak (b). It requires an internuclear distance smaller than the equilibrium separation. The
ionization of each atom in the dimer will result in a Coulomb explosion at the equilibrium distance.
If a single atom of the dimer is doubly ionized there are two possible mechanisms that will allow
for Coulomb explosion [163]. One mechanism is through a virtual photon which will happen at theequilibrium internuclear spacing and will appear at the 3.8 eV peak. The higher KER peak can
be explained by a single site double ionization channel. A 36 eV photon with the IR is enough to
put a single argon atom about its double ionization threshold (43.4 eV).This radiative mechanism
has a considerable probability to happen even at large internuclear separation. Its rate follows an120
inverse power law as a function of the internuclear separation R [171]. The dimer decreases theinternuclear spacing in order to relax and allow for ICD.

Figure 8.9: Kinetic energy release of Ar+ + Ar+ coincidence channel at 50 fs. The KER peaks at
3.8 eV, labeled peak (a), and 5 eV, labeld peak (b), are consistent with previous results [163, 169].
While

8.3

Laser-Induced Ultrafast dynamics of Ozone Double Photoionization
Ozone is of tremendous importance in the Earth’s upper atmosphere and its dynamics are

significant in atmospheric modeling. Being very absorptive in parts of ultraviolet spectrum a
relatively small amount is responsible the protection against DNA damage from solar radiation[172,173]. Parts of the dissociation dynamics and possible reformation of ozone are not well known
and the improved understanding has many implications related to climate change [174].
By irradiating ozone molecules with few-femtosecond XUV pulses and probing the fragmentation pathways, we find that the excess energy is rapidly and efficiently transferred into internal
excitation of the triatomic molecule similar to the discussion in Chapter 7. Using a high energy
photon to access the double cation of ozone, we probe the excited state using a strong field IR
pulse. Photon energies at 43 eV put ozone well about its double ionization threshold (∼34 eV).
Figure 8.10 shows a schematic of exciting ozone to a doubly ionized state and the expected KER.
Figure 8.11 shows the ion time-of-flight spectrum for an ozone sample. Part of the experimen-

121

Figure 8.10: Schematic of exciting ozone to a doubly excited state with a single 43 eV photon andprobing with IR. Figure adapted from [175].

tal difficulty is producing a clean ozone source with enough pressure to seed a jet in COLTRIMS.
Once created, ozone will naturally degrade, with a half life on the order of hours, and the process iscatalyzed with interaction with metals such as copper. Creating a pure sample of ozone is important
to distinguish the presence of O2 from the dissociation process compared to that from backgroundO2 due to the atmospheric contamination as well as natural degradation. Some background N2
and O2 is visible in the figure.
The preparation process for ozone make it better suited for the effusive gas jet. Because
ozone naturally degrades creating a stable sample with the greatest concentration of O3 to O2
required improvements with the preparation and deliver to the gas jet. Once generated, ozone on
the porous surface in a silica gel “trap”. Figure 8.12 shows the ozone trap when fully charged. Ahigh concentration of color is indicated by the blue color (where ozone is less absorptive). Dry ice

122

Figure 8.11: Time-of-flight spectrum for a typical data set with ozone sent through the effusive jet.
The relative size of the O3 + peak shows it to be a clean sample but the distribution of the O+ andO2+ peaks indicate they originate from dissociation pathways.

was used to control the vapor pressure as well as prevent possible spontaneous combustion. Even
with a carrier gas used to seed the supersonic jet, the necessary decay time before the jet would
result in a significant level of degeneration.
We found it necessary to evacuate the device to 10 mtorr or lower to remove an appreciablebackground signal, although the data still contain a significant amount of background caused byresidual atmosphere in the device. Because of the background, compared to pure targets that areeasier to prepare, relying on photoelectron is challenging without a coincidence photoion to indicate
the photoelectron’s source.
Figure 8.13 shows the advantage COLTRIMS presents in being able to filter O3 from background signals. Even with an ideal ozone source there will still be a measurable concentration ofmolecular oxygen (O2 ) present in the gas jet. Using coincidence techniques we can distinguish O+
fragments that originate from O3 rather than O2 . Using a 43 eV photon as a probe causing themolecule to reach a double ionizing state it will result in Coulomb explosion and force the molecule
to a clear O2 + + O+ signal. Additionally, this photon energy excites an auto-ionizing state in O2
resulting in a O+ + O+ coincidence channel [14]. Because the information of the molecular oxygen
Coulomb explosion is taken simultaneously and well known it is an excellent calibration for better
understanding the ozone Coulomb explosion.

123

Figure 8.12: Photograph of the ozone trap. Silica gel provides a porous surface and provides ameans to trap generated ozone. The dark blue color indicates a high concentration. The trap isstored with dry ice to produce a lower vapor pressure as well as to prevent spontaneous combustion.

By comparing the O3 + and O2 + ion fragmentation yields and their kinetic energies as afunction of time delay between the XUV pump and IR probe, we find that the triatomic ozone
molecule shows an ability to absorb any excess energy internally rather than emerging as kinetic
energy released by the Coulomb exploding fragments as observed in other triatomic molecules [168].
This internal conversion of energy in a triatomic molecule before explosion is very different fromthe case of diatomic molecular oxygen [14] which we can record simultaneously with the ozone

124

Figure 8.13: Photoion-Photoion coincidence (PIPICO) spectrum showing both O2 + + O+ and O++ O+ coincidence channels. Both channels can be filtered using conservation of momentum andcenter of mass filters. Plot density is on a logarithmic scale.

dissociation.
In addition to probing the double ionization we attempted to observe dynamics in the main
absorption band in the UV, the Hartley band. On the blue side of this band, at wavelengths
shorter than 243 nm, some O2 dissociation products are created with a large amount of internalenergy [174, 176]. Characterization of this process is important to a thorough understanding ofthese atmospherically relevant conical intersection dynamics. These dynamics would be probed bynegative time delays in the above scans, using three photon absorption to pump to the Hartley
band, and probing the states with an XUV photon (providing a clear photoelectron signal). These
dynamics happen quickly and are difficult to capture with a 30 fs pulse. Additionally, the IR pulse
pumps to other dissociating channels. Future improvements using a ultrafast 3ω harmonic of the
IR should allow for resolution of these dynamics.

125

Figure 8.14: Time resolved kinetic energy release of ozone. KER of ∼7.5eV is consistent with our
expected results [175].

Chapter 9

Conclusion

In conclusion, this thesis describes the the advancement in understanding of XUV induced
atomic and molecular dynamics including the visualization of the dissociation process, the interaction of nuclear and electronic wavepackets and optically controlling ionizing pathways. It
demonstrates important progress in the field of atomic and molecular physics, but also calls for abetter understanding of known systems and push towards the more complex.
With argon, the understanding of ionizing pathway was better understood including theoretical support. The ability to induce full electro-magnetic transparency in an atom was demonstrated
with helium. In diatomic systems the dissociation of bromine helped probe the fundamental timescales of the changing orbital structure in such a process and hydrogen provided a simple system
for the interaction of nuclear and electronic dynamics in the non-Born-Oppenheimer regime. With
N2 O the ability to optically affect the dissociation process of a triatomic molecule demonstrated a
new degree of coherent control.
This work can also be extended to a broad range of systems as demonstrated by the resultswith more complicated systems. The argon dimer presents a simpler electronic structure, and ozone
provides a chance to provide a great deal of understanding to the chemical processes in the upper
atmosphere. Ethylene shows many complex dynamics and has the potential for a great deal of future
work. While these more complex systems present a challenge different than atomic or diatomic
targets, it is only with the ability to resolve attosecond scale electronic and nuclear dynamics thatsuch processes will be well understood. Ultimately it will require further advancement in not only

127
the high harmonic source and detection but through sample preparation that will allow for new
systems.

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