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Travis Dissertation Experimental Generation and Manipulation of Quantum Squeezed Vacuum via Polarization Self-Rotation in Rb Vapor Travis Scott Horrom Scaggsville, MD Master of Science, College of William and Mary, 2010 Bachelor of Arts, St. Mary’s College of Maryland, 2008 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 May 2013 c 2013 Travis Scott Horrom All rights reserved. APPROVAL PAGE This Dissertation is submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Travis Scott Horrom Approved by the Committee, March, 2013 Committee Chair Research Assistant Professor Eugeniy E. Mikhailov, Physics The College of William and Mary Associate Professor Irina Novikova, Physics The College of William and Mary Assistant Professor Seth Aubin, Physics The College of William and Mary Professor John B. Delos, Physics The College of William and Mary Professor and Eminent Scholar Mark D. Havey, Physics Old Dominion University ABSTRACT Nonclassical states of light are of increasing interest due to their applications in the emerging field of quantum information processing and communication. Squeezed light is such a state of the electromagnetic field in which the quantum noise properties are altered compared with those of coherent light. Squeezed light and squeezed vacuum states are potentially useful for quantum information protocols as well as optical measurements, where sensitivities can be limited by quantum noise. We experimentally study a source of squeezed vacuum resulting from the interaction of near-resonant light with both cold and hot Rb atoms via the nonlinear polarization self-rotation effect (PSR). We investigate the optimal conditions for noise reduction in the resulting squeezed states, reaching quadrature squeezing levels of up to 2.6 dB below shot noise, as well as observing noise reduction for a broad range of detection frequencies, from tens of kHz to several MHz. We use this source of squeezed vacuum at 795 nm to further study the noise properties of these states and how they are affected by resonant atomic interactions. This includes the use of a squeezed light probe to give a quantum enhancement to an optical magnetometer, as well as studying the propagation of squeezed vacuum in an atomic medium under conditions of electromagnetically induced transparency (EIT). We also investigate the propagation of pulses of quantum squeezed light through a dispersive atomic medium, where we examine the possibilities for quantum noise signals traveling at subluminal and superluminal velocities. The interaction of squeezed light with resonant atomic vapors finds various potential applications in both quantum measurements and continuous variable quantum memories. TABLE OF CONTENTS Page Acknowledgments..................................... v Dedication......................................... vi ListofTables....................................... vii ListofFigures ...................................... viii CHAPTER 1 Introduction.................................... 2 1.1 Quantumnoiseandsqueezedlight. 2 1.2 Developmentofsqueezingresearch. ... 5 1.3 Applicationsofsqueezedlight . 7 1.3.1 Opticalmeasurements . 7 1.3.2 Optical communications and quantum information . .... 8 1.3.3 Quantummemory.......................... 10 1.3.4 Quantumsensingandimaging . 11 1.4 Squeezingwithresonantatoms. 12 1.5 Dissertationoutline . 15 2 Squeezedlightstates ............................... 17 2.1 TheWaveequation ............................. 17 2.2 Electromagneticwavesinfreespace . ... 18 2.3 Fieldquantization.............................. 19 2.3.1 Creationandannihilationoperators . .. 20 2.3.2 Quadratureoperators. 21 2.3.3 Electricfieldoperator. 22 i 2.4 Coherentstates ............................... 23 2.5 Squeezedcoherentstates . 26 2.6 Nonlinearprocessesinatoms. 30 2.7 Sideband model of squeezing and two-photon formalism . ....... 31 3 Nonlinear polarization self-rotation effect . ........ 34 3.1 Polarizationself-rotation . ... 34 3.1.1 PSReffectinatomicvapor. 34 3.1.2 PSRsqueezing............................ 35 3.1.3 Polarizationsqueezing . 39 3.2 Theoreticalsqueezinglevels . .. 41 3.3 Limitationsforsqueezinggeneration . .... 42 4 Resonantlight-atominteractions. ..... 45 4.1 Alkali atoms and 87Rb ........................... 45 4.2 Density matrix and slowly varying envelope approximation ....... 47 4.3 Three-levelatomΛsystem . 49 4.4 Nonlinearmagneto-opticalrotation . ... 54 4.5 Polarization self-rotation g parameter................... 58 4.6 Dark states and electromagnetically-induced transparency........ 60 4.7 Quantumnoiseoperators. 64 5 Quadraturenoisedetection. .. 67 5.1 Homodynedetection ............................ 67 5.2 Spectrumanalysis.............................. 70 5.3 Experimentaldetectionschemes . .. 71 5.3.1 Detectionscheme#1: Interferometric . .. 72 5.3.2 Detectionscheme#2: Copropagating . 74 6 Squeezed vacuum generation and optimization in hot atomic vapor ..... 78 6.1 Squeezing generation experimental setup . ..... 79 ii 6.2 Pumplaserfocusing............................. 80 6.3 Vaporcellselection ............................. 81 6.4 Detectoralignment ............................. 82 6.5 Limitationsduetoclassicallasernoise . ..... 83 6.6 Detuningdependence ............................ 85 6.7 Temperaturedependence . 87 6.8 Powerdependence.............................. 90 6.9 Bestsqueezingresults. 92 6.10 Effectofmagneticfieldonsqueezing . .. 93 6.11 Squeezinggenerationsummary. .. 98 7 Pulsedsqueezinggeneration . .. 99 7.1 Quantum information application for pulsed squeezed light ....... 100 7.2 Quadraturenoisepulseshaping . 102 8 Quantumenhancedmagnetometer. 106 8.1 Magnetometersetup ............................ 107 8.2 Experimentalobservations . 109 8.3 Magnetometersummary . 115 9 Slowandfastsqueezedlightstudies . 117 9.1 Introduction................................. 117 9.2 Dispersion .................................. 117 9.3 Experimentalsetup ............................. 118 9.4 Pulsedelay/advancementmeasurements . 124 9.5 Chaptersummary.............................. 127 10 EITnoisefilteringexperiments . 129 10.1Introduction................................. 129 10.2Theory.................................... 131 10.3ZeemanEIT................................. 133 iii 10.3.1 Zeemanexperimentalsetup . 134 10.3.2 Filteringobservations. 137 10.4HyperfineEIT................................ 142 10.4.1 Hyperfineexperimentalsetup . 143 10.4.2 Undesirable excess phase-dependent noise . 144 10.4.3 Hyperfinefilteringobservations . 147 10.4.4 NoninvasiveEITprobe . 149 10.5 EITnoisefilteringsummary . 151 11 PSR and quadrature noise studies in cold atomic vapor . ........ 154 11.1 Polarization rotation in cold 87Rbatoms ................. 154 11.1.1 Experimentalsetup . 155 11.1.2 Experimentalresults . 157 11.1.3 Self-rotation and Faraday rotation . 160 11.2 Quadrature noise of light interacting with a cold atomicgas ...... 170 11.2.1 Experimentalsetup . 171 11.2.2 Experimentalresults . 172 11.3 Summaryandfutureimprovements . 174 12 Conclusionsandoutlook . 178 APPENDIX A Cavityvsfree-spacemodes. 181 APPENDIX B Descriptionofnumericalsimulations . ...... 183 APPENDIX C Listofelectronicsused . 185 APPENDIX D Permissions ...................................... 187 Bibliography ....................................... 189 Vita ............................................ 206 iv ACKNOWLEDGMENTS There are many people I wish to thank for their involvement in the completion of this dissertation work, as well as for their guidance and support throughout my academic career. First, thank you to my adviser Dr. Eugeniy E. Mikhailov, for patiently guiding me through this work and for continually expanding my knowledge and motivating me to become a better scientist. Also, a very special thanks to Dr. Irina Novikova, for always being available to explain a concept, and always knowing the next step to take in an experiment. I would like to thank the other members of our lab group at William & Mary. It has been a pleasure working alongside Nate Phillips, Matt Simons, Gleb Romanov, Ellie Radue, and Mi Zhang. Thanks especially to Gleb, who carried out much of this research with me, and Nate who assisted with the preparation of this manuscript. I am very grateful to our collaborators Robinjeet Singh, Salim Balik, Mark D. Havey, Arturo Lezama, and John P. Dowling. I would also like to thank my entering graduate class, for accompanying me on this journey known as grad school, and for helping to make my time here enjoyable and fulfilling. I appreciate the welcoming and knowledgeable community that encompasses the physics department here at William & Mary. Thanks to those who played volleyball, football, or put it all on the line and helped to win those t-shirts in floor hockey. I would also like thank my respectable office mates, Josh and Alena Devan. I acknowledge those who got me started down this path, and would like to thank Prof. Charles Adler whose enthusiasm for physics and teaching helped spark my interest in the field, Prof. Josh Grossman for helpful advice and guidance, and Dr. Frank Narducci who has always been generous with his time and support. I also thank my college roommate Grady, for tossing around a football with me while working on quantum mechanics homework. Lastly, I wish to express my great appreciation to my family for their constant support and love. Thank you Doug, Diane, Alex, Tristan, Susannah, and especially
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