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Slow and Stored Light Under Conditions of Electromagnetically Induced Transparency and Four Wave Mixing in an Atomic Vapor

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Slow and Stored Light Under Conditions of Electromagnetically Induced Transparency and Four Wave Mixing in an Atomic Vapor SLOW AND STORED LIGHT UNDER CONDITIONS OF ELECTROMAGNETICALLY INDUCED TRANSPARENCY AND FOUR WAVE MIXING IN AN ATOMIC VAPOR Nathaniel Blair Phillips Lancaster, Pennsylvania Master of Science, College of William and Mary, 2006 Bachelor of Arts, Millersville University, Millersville PA, 2004 A Dissertation presented to the Graduate Faculty of the College of William and Mary in Candidacy for the Degree of Doctor of Philosophy Department of Physics The College of William and Mary August 2011 c 2011 Nathaniel Blair Phillips All rights reserved. APPROVAL PAGE This Dissertation is submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Nathaniel Blair Phillips Approved by the Committee, June, 2011 Committee Chair Assistant Professor Irina Novikova, Physics The College of William and Mary Assistant Professor Seth Aubin, Physics The College of William and Mary Professor John Delos, Physics The College of William and Mary Professor Gina Hoatson, Physics The College of William and Mary Eminent Professor Mark Havey, Physics Old Dominion University ABSTRACT PAGE The recent prospect of efficient, reliable, and secure quantum communication relies on the ability to coherently and reversibly map nonclassical states of light onto long-lived atomic states. A promising technique that accomplishes this em- ploys Electromagnetically Induced Transparency (EIT), in which a strong classical control field modifies the optical properties of a weak signal field in such a way that a previously opaque medium becomes transparent to the signal field. The accom- panying steep dispersion in the index of refraction allows for pulses of light to be decelerated, then stored as an atomic excitation, and later retrieved as a photonic mode. This dissertation presents the results of investigations into methods for op- timizing the memory efficiency of this process in an ensemble of hot Rb atoms. We have experimentally demonstrated the effectiveness of two protocols for yielding the best memory efficiency possible at a given atomic density. Improving memory effi- ciency requires operation at higher optical depths, where undesired effects such as four-wave mixing (FWM) become enhanced and can spontaneously produce a new optical mode (Stokes field). We present the results of experimental and theoretical investigations of the FWM-EIT interaction under continuous-wave (cw), slow light, and stored light conditions. In particular, we provide evidence that indicates that while a Stokes field is generated upon retrieval of the signal field, any information originally encoded in a seeded Stokes field is not independently preserved during the storage process. We present a simple model that describes the propagation dynamics and provides an intuitive description of the EIT-FWM process. TABLE OF CONTENTS Page Acknowledgments............................ x ListofTables .............................. xii ListofFigures .............................xiii CHAPTER 1 Introduction ........................... 2 1.1 Opticalquantummemory . 4 1.2 Electromagnetically induced transparency . .... 5 1.3 Performance criteria for optical quantum memory . ... 8 1.4 Experimental demonstrations of EIT . 10 1.5 Progress towards long distance quantum communication using atomicensembles ........................... 12 1.5.1 Experimental demonstration of DLCZ components . 15 1.5.2 Towardsstorageofsinglephotons . 16 1.6 Outlineofthisdissertation . 17 2 Reviewofthetheory . 19 2.1 Maxwell’sEquations . 20 2.2 Generalmodeloftheatomicsystem . 21 2.3 Interaction of a bichromatic electromagnetic field with a three- level Λ system............................. 24 v 2.4 Electromagnetically Induced Transparency . ... 29 2.4.1 A brief aside on two-level atoms in a resonant laser field. 30 2.4.2 Complex refractive index of a three-level Λ system. 32 2.5 DarkstatedescriptionofEIT . 34 2.6 Slowlightandstoredlight . 35 2.7 Dark state polariton description of stored light . ..... 39 2.8 EfficiencyofEIT-basedstorage . 42 2.9 Theeffectsoffour-wavemixing . 43 3 Experimental Arrangements . 50 3.1 Theatoms............................... 50 3.1.1 Zeeman sub-structure and transitions . 53 3.1.2 Vaporcells........................... 55 3.1.3 Neonbuffergas ........................ 57 3.1.4 Diffusiontime ......................... 58 3.1.5 Collisionalbroadening . 60 3.1.6 Dopplerbroadening. 62 3.1.7 Opticalpumping . .. .. 63 3.1.8 Opticaldepth ......................... 65 3.1.9 Rabifrequencyofthecontrolfield . 69 3.2 Experimentaldescription . 69 3.3 Thelightfields ............................ 73 3.3.1 Lightfieldmodulation . 73 3.3.2 Spectral filtering with a temperature-tunable Fabry-Pérot Filter.............................. 76 3.3.3 Vaporcellenclosure. 79 3.3.4 Lightdetection ........................ 79 vi 3.3.5 ControlofAOMandEOMinputs . 81 3.3.6 CalibrationofAOMandEOM. 82 3.3.7 A typical cw (EIT) experiment . 84 3.3.8 A typical slow/stored light experiment . 86 3.3.9 Measuring spin decay time . 89 4 Optimization of memory efficiency . 91 4.1 Signalpulseoptimization . 92 4.2 Controlpulseoptimization . 96 4.3 Dependence of memory efficiency on the optical depth . .. 99 5 Full control over storage and retrieval . 106 6 The effects of four-wave mixing on pulse propagation through anEITmedium ...........................114 6.1 Theoretical description of FWM in the steady-state . .115 6.2 SpectralMeasurements . .119 6.3 SlowLightMeasurements. .122 6.3.1 Case I: δ =2 ∆ ........................125 | R| 6.3.2 Case II: δ =2δs.........................126 6.3.3 Case III: δ =0. ........................126 6.4 FWMunderStoredLightconditions . .127 6.4.1 Coupled propagation of signal and Stokes fields in a double- Λ system............................128 6.4.2 Correspondence between experiment and theory . 129 6.4.3 The effect of four-wave mixing on the spin wave . 132 6.5 Optical depth dependence of the Stokes field . 141 7 Experimental investigations of spin decay mechanisms . 144 7.1 Mechanisms that affect the rate of spin decay . 145 7.1.1 Diffusion and 2d-dependence . .145 vii 7.1.2 Collisions ...........................146 7.1.3 Magneticfields . .. .. .148 7.2 Experimental evidence for spin decay mechanisms . .148 7.2.1 Ω and dependences . .148 Ein 7.3 Possible physical mechanisms . 151 7.3.1 Powerbroadening . .151 7.3.2 Radiation trapping and diffusion effects . 151 7.3.3 TransverseACStarkshifts . .154 7.3.4 Two-photon detuning (δ)dependence . .155 7.3.5 FWMdependence. .158 7.4 Summaryandconclusions . .161 8 Conclusion and Outlook . 162 APPENDIX A Details of control field shaping . 165 APPENDIX B Derivation of Eqs. 6.20, 6.21, 6.29, and 6.30 . 171 Bibliography ..............................178 Vita ...................................191 viii DEDICATION I present this thesis in honor of my AP physics teacher, Mr. Jeffrey A. Way. ix ACKNOWLEDGMENTS I could not have completed this research without the support and guidance of my advisor, Dr. Irina Novikova. I value the patience with which you taught me how to align (and re-align) optics, and am continuously impressed with your knack for creating clever and compact experiments. In addition, much of this work could not have been completed without our theorist collaborator, the inimitable Dr. Alexey Gorshkov, who developed the optimization protocols and provided essential support for the theoretical modeling of the FWM-EIT interaction. It has been a pleasure to work with my lab colleagues, Nathan, Will, Kevin, Gleb, Matt, Travis, Francesca, Quint, Joe, and Eugeniy. I am forever in debt to my good friend, Mr. Jeff Fuhrman, who fostered my interest in science over many trips to Hershey Park, various volunteer adventures involving technology support at concerts, and vital advice when life wasn’t always easy. My interest in science and math stemmed from several awesome teachers that I met in high school. To Dr. Bill Grove, who taught me the importance of memorizing trigonometric values and identities. To my 11th grade Chemistry teacher, Mr. Glen Shaffer, who taught me that I can be a better student if I just studied. To my AP Statistics teacher, Mr. Steve Haldeman, and my AP Calculus teacher, Mr. Mark Rorabaugh, who pushed me to strive for perfection. And especially to my AP Physics teacher and good friend, the late Mr. Jeff Way, who taught me to believe that I was capable of learning something difficult like physics, and whose positive personality inspired many. I would not be at William and Mary if it weren’t for my undergraduate advisor, Dr. Zenaida Uy, who insisted that I apply to at least one graduate school. My life would be incomplete if I had never met Ken, Diane, Jennie, and Trent Keifer, who, with their vast knowledge of all things colonial, suggested that I apply to W&M. Graduate school isn’t always super-fun times. I’d like to thank the people who tried to make it more fun. Thanks to the friends who risked heat stroke to play week- end “touch” football (that is, when they weren’t working on their glamour muscles), played 3-on-3-on-3 softball, philosophized about many mock sports, and played (and even occasionally won) intramural soccer, volleyball, softball, and hockey. Thanks to the Thursday-TV club: Stephen, Carla, Chris, Aidan, and sometimes Doug, with whom I’ve been honored to enjoy a few laughs and a few beers. Finally, no list of acknowledgments would be complete without my family, who has supported me always. Dad, Mom, Melissa, Jonathan, and Adam—I love you guys (and frankly, I’m impressed that you’re reading this). If it were physically x possible, I would to express infinite thanks to my lovely wife and best friend, Kelly, and my two cats, Batman the Cat and the late Gravy, for continuous moral support through this entire process. xi LIST OF TABLES Table Page 3.1 87Rb D (52S 52P ) Clebsch-Gordan coefficients for σ+ tran- 1 1/2 → 1/2 sitions, F =1, m F ′, m ′ = m +1 ............... 56 | F →| F F 3.2 87Rb D (52S 52P ) Clebsch-Gordan coefficients for σ+ tran- 1 1/2 → 1/2 sitions, F =2, m F ′, m ′ = m +1 ............... 56 | F →| F F xii LIST OF FIGURES Figure Page 1.1 (a) Three-level Λ system under EIT conditions. (b) Absorption and (c) refractive index seen by the signal field . 6 1.2 A schematic of the (a) entanglement creation, and (b) entanglement swappingstagesoftheDLCZprotocol.
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