NONLINEAR WAVE PACKET INTERFEROMETRY

AND MOLECULAR STATE RECONSTRUCTION

by

TRAVIS SELBY HUMBLE

A DISSERTATION

Presented to the Department of Chemistryand the Graduate School of the University of Oregon

in partial fulfillment of the requirementsfor the degree of

Doctor of Philosophy

August 2005

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“Nonlinear Wave Packet Interferometry and Molecular State Reconstruction,” a

dissertation prepared by Travis Selby Humble in partial fulfillment of the requirements

for the Doctor of Philosophy degree in the Department of Chemistry. This dissertation

has been approved and accepted by:

_________________________________________________________________Dr. Marina Guenza, Chair of the Examining Committee

____________________________________________Date

Committee in Charge: Dr. Marina Guenza, ChairDr. Jeffrey CinaDr. Geraldine RichmondDr. David TylerDr. Michael Raymer

Accepted by:

_____________________________________________________________________Dean of the Graduate School

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© 2005 Travis Selby Humble

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An Abstract of the Dissertation of

Travis Selby Humble for the degree of Doctor of Philosophy

in the Department of Chemistry to be taken August 2005

Title: NONLINEAR WAVE PACKET INTERFEROMETRY AND

MOLECULAR STATE RECONSTRUCTION

Approved:_______________________________________________Dr. Jeffrey Cina, Advisor

Nonlinear wave packet interferometry (WPI) uses two phase-locked pulse-pairs to

excite a molecular electronic population and measures those contributions arising from a

one-pulse nuclear wave packet overlapping with a three-pulse nuclear wave packet. The

interferogram quantifies the wave-packet interference at the probability-amplitude level

and, with knowledge of the three-pulse (reference) wave packets, enables reconstruction

of the one-pulse (target) wave packet.

In one-color nonlinear WPI, both pulse-pairs resonate with the same electronic

transition and the interferogram measures a sum of wave-packet overlaps. Experimental

conditions often minimize mixing of these overlaps and hence permit molecular state

reconstruction, as demonstrated by numerical calculations for model harmonic and

photodissociative systems. Yet, a one-color reconstruction technique requires information

about the Hamiltonian under which the target and reference states propagate. The latter

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knowledge obviates the practical need for experimental state determination, since

computational methods are then a viable, alternative solution.

Two-color nonlinear WPI, in which the pulse-pairs drive different electronic

transitions, circumvents the need for information about the target-state Hamiltonian by

using an auxiliary electronic level for preparing the reference states. Furthermore, in a

two-color experiment, the interferogram measures a single wave-packet overlap,

definitely identifying the information necessary for molecular state reconstruction. These

features suggest two-color nonlinear WPI could serve as a diagnostic tool for identifying

optically-controlled, yet unknown, molecular dynamics. Simulations for model systems

and the lithium dimer demonstrate that target states can be reconstructed in the presence

of signal noise, thermal mixtures, and rovibrational coupling and in the absence of

information about the target-state Hamiltonian.

In the presence of electronic-energy transfer, the interferogram reveals changes in

the probability amplitude first-order in the inter-chromophore scalar coupling J.

Controlling the polarization of the pulse-pairs enables selective excitation of the

components in a model dimer complex and isolation of the overlap between a three-pulse

reference wave packet, independent of J, and a one-pulse target wave packet, whose

electronic and nuclear degrees of freedom are entangled. The processes underlying

coherent energy transfer are identified by interpreting the interferogram with the help of

quasi-classical phase-space diagrams.

This dissertation includes both my previously published and my co-authored

materials.

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CURRICULUM VITAE

NAME OF AUTHOR: Travis Selby Humble

GRADUATE AND UNDERGARDUATE SCHOOLS ATTENDED:

University of Oregon University of North Carolina at Wilmington

DEGREES AWARDED:

Doctor of Philosophy in Chemistry, 2005, University of Oregon Master of Science in Chemistry, 2000, University of Oregon Bachelor of Science in Chemistry, 1998, University of North Carolina at Wilmington

AREAS OF SPECIAL INTEREST:

Nonlinear optical spectroscopy Quantum state reconstruction

PROFESSIONAL EXPERIENCE:

Graduate Research Assistant, Department of Chemistry, University of Oregon, 1998-2005

Research Assistant, Los Alamos National Laboratory, Summer 2001

Research Assistant, Department of Chemistry, University of North Carolina at Wilmington, 1997-1998

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PUBLICATIONS:

[1] T. S. Humble and J. A. Cina, “Nonlinear wave packet interferometry and molecular for a rotating and vibrating diatomic molecule,” submitted to J. Chem. Phys.

[2] T. S. Humble and J. A. Cina, “Molecular state reconstruction using nonlinear wave packet interferometry,” Ultrafast Phenomena XIV (Springer Verlag, Berlin, 2005).

[3] T. S. Humble and J. A. Cina, “Molecular state reconstruction by nonlinear wave packet interferometry,” Phys. Rev. Lett. 93, 060402 (2004).

[4] T. S. Humble and J. A. Cina, “Towards the reconstruction of time-dependent vibronic state from nonlinear wavepacket interferometry signal,” Bull. Kor. Chem. Soc. 24, 1111 (2004); Correction, ibid., 25, 584 (2004).

[5] J. A. Cina, D. Kilin, and T. S. Humble, “Wave packet interferometry for short-time electronic energy transfer: Multidimensional optical spectroscopy in the time domain,” J. Chem. Phys. 118, 46 (2003).

[6] J. A. Cina and T. S. Humble, “Molecular wavepacket decomposition by nonlinear interferometry,” Bull. Chem. Soc. Jpn. 75, 1135 (2002).

[7] T. S. Humble, C. J. Halkides, J. D. Keltner, and M. Messina, “A theoretical study of intra-molecular vibrational effects on the fractionation factor in molecules with low-barrier hydrogen bonds,” Chem. Phys. Lett. 289, 90 (1998).

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ACKNOWLEDGEMENTS

The long process of thought and deliberation leading to this dissertation has been

encouraged by many around me. I wish to thank all of them. Special mention must be

made of my advisor Jeff Cina, who not only provided great insight into wave packet

interferometry but showed extraordinary patience in teaching me fundamental science.

Also I extend special thanks to: Mary Rohrdanz, Dmitri Kilin, Yu-Chen Shen, and the

other scientist who comprised the Cina group during my time here, for their enlightening

conversations on science and everything else; the whole of the wave packet

interferometry group, for our shared interest in novel theories and experiments; and the

“Landau and Lifshiftz” reading group, for sharing laughter in the face of fear.

And I thank my wife, for understanding what I was doing, even when I did not.

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This one goes out to the one I love.

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TABLE OF CONTENTSChapter Page

I. INTRODUCTION ........................................................................................................1Multidimensional Electronic Spectroscopy ...........................................................1Wave Packet Interferometry ...................................................................................3Previous State Reconstruction Schemes .................................................................6Outline of the Dissertation ......................................................................................7Notes ....................................................................................................................10

II. LINEAR WAVE PACKET INTERFEROMETRY ................................................13Theory ...................................................................................................................14Molecular State Reconstruction ............................................................................23Model Harmonic System ......................................................................................28Remarks..................................................................................................................38Notes ....................................................................................................................40

III. ONE-COLOR NONLINEAR WAVE PACKET INTERFEROMETRY ............42Theory ...................................................................................................................43Molecular State Reconstruction ............................................................................59Model Harmonic System ......................................................................................63Model Photodissociative System ..........................................................................76Remarks..................................................................................................................80Notes ....................................................................................................................84

IV. TWO-COLOR NONLINEAR WAVE PACKET INTERFEROMETRY ...........85Theory ...................................................................................................................86Molecular State Reconstruction ............................................................................99Model Harmonic System ....................................................................................102Model Photodissociative System ........................................................................113Rovibrational Wave Packets: The Lithium Dimer .............................................124Remarks................................................................................................................147Notes ..................................................................................................................151

V. WAVE PACKET INTERFEROMETRY AND ELECTRONIC ENERGYTRANSFER.......................................................................................................153

Introduction ..........................................................................................................153Basic Theory .......................................................................................................156Case Study............................................................................................................160

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Chapter Page

Energy-transfer Wave Packet Dynamics ............................................................164Discussion ............................................................................................................173Notes ..................................................................................................................183

VI. CONCLUDING REMARKS..................................................................................190Notes ..................................................................................................................195

APPENDIXA. THE DISPLACEMENT OPERATOR....................................................................196B. MULTIPHOTON WAVE PACKETS.....................................................................202C. POPULATION AVERAGING................................................................................205D. ALTERNATIVE POLARIZATIONS.....................................................................209E. TARGET AND REFERENCE WAVE PACKETS................................................213F. INTERPRETING THE FRINGE STRUCTURE ....................................................215

BIBLIOGRAPHY...............................................................................................................218

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LIST OF FIGURES

Figure Page

2.1 A Timeline of the Pulse Pair Used ...........................................................................15

2.2 A Schematic Illustration of the Molecular System...................................................19

2.3 The Two Harmonic Potential Surfaces.....................................................................28

2.4 The Linear WPI Signal for a Harmonic Oscillator System .....................................34

2.5 Phase-space Diagrams for the One-pulse Wave Packets..........................................36

2.6. Target and Reconstructed Wave Packets for the Model Harmonic System...........37

3.1 The Sequence of Four Pulses Used in a Nonlinear WPI Experiment......................44

3.2 The Wave Packets 1( ) f and 432( ) f in a One-color Experiment ........................52

3.3 The Wave Packets 2( ) f and 431( ) f in a One-color Experiment ........................52

3.4 The Wave Packets 3( ) f and 421( ) f in a One-color Experiment .......................53

3.5 The Wave Packets 4( ) f and 321( ) f in a One-color Experiment .......................53

3.6 The Two Harmonic Potential Surfaces ....................................................................65

3.7 One-color 432( ) f 1( ) f Contribution for a Model Harmonic System ....................69

3.8 One-color 431( ) f 2( ) f Contribution for a Model Harmonic System. ...................70

3.9 One-color 421( ) f 3( ) f Contribution for a Model Harmonic System. ...................71

3.10 One-color 321( ) f 4( ) f Contribution for a Model Harmonic System..................72

3.11 Phase-Space Trajectory Diagrams for 1( ) f and 432( ) f ....................................74

3.12 Phase-Space Trajectory Diagrams for 4( ) f and 321( ) f ...................................74

3.13 Phase-Space Trajectory Diagrams for 2( ) f and 431( ) f ....................................75

3.14 Phase-Space Trajectory Diagrams for 3( ) f and 421( ) f ....................................75

3.15 The Model Dissociative Potential ...........................................................................77

3.16 The Real and Imaginary Components of p−1,1 .........................................................78

3.17 The Target and Reconstructed States for the Dissociative System........................80

3.18 A Target State Returns ............................................................................................82

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Figure Page

4.1 The Sequence of Four Pulses ....................................................................................87

4.2 A Sketch of the Power Spectra..................................................................................87

4.3 The Wave Packets 3( ) f and 421( ) f in a Two-color Experiment .......................95

4.4 The wave packets 4( ) f and 321( ) f in a Two-color Experiment. .......................95

4.5 A Three-level Model Harmonic System.................................................................104

4.6 Two-color 421( ) f 3( ) f Contribution for a Model Harmonic System .................107

4.7 Two-color 321( ) f 4( ) f Contribution for a Model Harmonic System. ................108

4.8 Phase-space Trajectories of the 3( ) f and 421( ) f Wave Packets .......................109

4.9 Phase-space Trajectories of the 4( ) f and 321( ) f Wave Packets ......................110

4.10 Reconstruction of the Target for the Harmonic System.......................................111

4.11 Noisy Reconstruction of the Target for the Harmonic System............................112

4.12 Target State Shaped by a Positively Chirped Pulse..............................................116

4.13 Target State Shaped by a Negatively Chirped Pulse ............................................117

4.14 The Interferogram with a Positively Chirped Third Pulse ...................................118

4.15 The Interferogram with a Negatively Chirped Third Pulse .................................118

4.16 Reconstruction of the Positively Chirped Target State ........................................119

4.17 Reconstruction of the Negatively Chirped Target State......................................119

4.18 Interferogram for a Mixed-state System at 298 K................................................121

4.19 Reconstruction of the Target States Contributing to the Mixed-state Signal ......121

4.20 Reconstruction of the Unchirped Target State......................................................123

4.21 Potential Energy Surfaces of the Lithium Dimer .................................................125

4.22 Schematic Preparation of the Target and Reference States..................................126

4.23 The Reflection Principle and the Electronic Difference Potentials .....................135

4.24 The Vibrational Components of the Target State.................................................136

4.25 A Phase-space Diagram of the Target-state Vibrational Components ................138

4.26 Real and Imaginary Components of the Interferogram........................................140

4.27 The Amplitude (Solid Lines) and Phase (Dashed Lines)...........................................

of the Target (Fine Lines) and Reconstructed (Bold Lines) Wave Packets ...141

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Figure Page

4.28 The Amplitude (Solid Lines) and Phase (Dashed Lines)...........................................

of the Target (Fine Lines) and Reconstructed (Bold Lines) Wave Packets ...144

4.29 The Actual E ← A Transition Dipole Moment Function.....................................145

4.30 The Amplitude (Solid Lines) and Phase (Dashed Lines)...........................................

of the Target (Fine Lines) and Reconstructed (Bold Lines) Wave Packets ...146

4.31 The Amplitude (Solid Lines) and Phase (Dashed Lines)...........................................

of the Target (Fine Lines) and Reconstructed (Bold Lines) Wave Packets ...147

4.32 Calculated Potentials Using the Time-dependent Target States ..........................150

5.1 Schematic Contour Plots of Potential Energy Surfaces .........................................157

5.2 Phase-space Trajectories for the a-mode and b-mode............................................165

5.3 Phase-space Trajectories for the a-mode and b-mode............................................166

5.4 Calculated Interferogram for the Case of Equal Site Energies ..............................168

5.5 Calculated Interferogram for the Case of Downhill Energy Transfer ...................169

5.6 Real and Imaginary Parts of the Target Wave Packet............................................170

5.7 Real and Imaginary Parts of the Reference Wave Packet ......................................170

5.8 Same as Fig. 5.6, but for the Downhill Case ..........................................................171

5.9 Real Part, Imaginary Part, and Absolute Value of the Reference Wave Packet ...171