Ultrafast Sources of Entangled Photons for Quantum Information Processing by Oktay Onur Kuzucu B.S. Electrical and Electronics Engineering, Middle East Technical University (2001) S.M. Electrical Engineering and Computer Science, Massachusetts Institute of Technology (2003) Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2008 c Massachusetts Institute of Technology 2008. All rights reserved. Author.............................................................. Department of Electrical Engineering and Computer Science June 19, 2008 Certified by. Franco N.C. Wong Senior Research Scientist Thesis Supervisor Accepted by . Terry P. Orlando Chairman, Department Committee on Graduate Students 2 Ultrafast Sources of Entangled Photons for Quantum Information Processing by Oktay Onur Kuzucu Submitted to the Department of Electrical Engineering and Computer Science on June 19, 2008, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract Recent advances in quantum information processing (QIP) have enabled practical applications of quantum mechanics in various fields such as cryptography, computa- tion, and metrology. Most of these applications use photons as carriers of quantum information. Therefore, engineering the quantum state of photons is essential for the realization of novel QIP schemes. A practical and flexible technique to gener- ate high-purity entangled photon pairs is spontaneous parametric downconversion (SPDC) which finds its use in many QIP applications such as quantum key distri- bution (QKD) and linear optics quantum computation. SPDC is often used with ultrafast lasers to generate photon pairs with precise timing and engineered spectral properties. In this thesis, we focused on two photonic QIP applications using ultrafast- pumped SPDC. We first pursued the design and implementation of a pulsed narrow- band polarization-entangled photon pairs at 780 nm for free-space entanglement-based QKD. We built and characterized a compact narrowband ultraviolet pump source and a polarization-entangled photon source based on SPDC in a polarization Sagnac interferometer. We then studied the generation of coincident-frequency entangled photons for Heisenberg-limited quantum metrology. Using extended phase-matching conditions in a periodically-poled KTP crystal, generation of coincident-frequency entanglement was verified and frequency indistinguishability was achieved for broad- band signal and idler photons at ∼1.58 μm. We also developed a novel time domain characterization technique based on time-resolved single-photon upconversion. Us- ing this technique, we measured the joint temporal density of a two-photon state for the first time and observed temporal anti-correlation for the coincident-frequency entangled state as predicted by Fourier duality. This new technique complements ex- isting frequency domain methods for a more complete characterization of two-photon states. Thesis Supervisor: Franco N.C. Wong Title: Senior Research Scientist 3 4 Acknowledgements My long tenure at this ever-stimulating and vibrant institute was an arduous adven- ture, which would not have succeeded without the support of many people. A short two-page acknowledgement would not do justice to my family, friends and colleagues who were always by my side over seven long years. Nevertheless, I still feel obliged to mention their invaluable contribution and support. I am grateful to my advisor, Dr. Franco N. C. Wong, for his mentorship and advising. I have always learned something new from Franco and over the years I came to appreciate his remarkable guidance and support. Our discussions were not limited to physics only, but also covered sports, politics and technology. He was always available for my questions and without his expertise and encouragement this thesis would not have been possible. I would also like to thank my thesis committee members, Prof. Jeffrey H. Shapiro and Prof. Franz X. K¨artner. I have always admired Prof. Shapiro for his excellent teaching and theoretical insight. His superb lectures on quantum optical communications were not only inspirational but also extremely helpful for understanding the theoretical underpinnings of our work. Prof. K¨artner has overseen my first years in graduate school at MIT. I am thankful for his support and advice in ultrafast optics. I am extremely lucky to have collaborated with the other students and post-docs at RLE’s Optical and Quantum Communications Group. My first encounters with experimental quantum optics would not have progressed smoothly without the help of Marco Fiorentino. I am also grateful to Taehyun Kim who always had an open mind for my questions. I always enjoyed our discussions on lab work, life after Ph.D. and I also truly appreciate his generosity and friendship. I would like to thank other members of our group for their fellowship and support: Marius Albota, Barı¸sErkmen, PavelGorelik,Ra´ul Garc´ıa-Patr´on S´anchez, Saikat Guha, Chris Kuklewicz, Dmitry Kolker, Julien Le Gou¨et, Mohsen Razavi and Dheera Venkatraman. I came to think that the city of Boston happened to be a landmark in many aspiring scholars’ career. In that respect, I had the privilege of meeting with many 5 great friends in Boston, some of whom have already moved on to other destinations. S¸¨ukr¨uC¸ ınar, Umur C¸ ubuk¸cu, G¨okhan Do˘gan, Barı¸sD¨olek, O˘guz G¨une¸s, Ekrem Esmen, Emre K¨oksal, Volkan Muslu, G¨oksel Tenekecio˘glu, Alp S¸im¸sek, and Barı¸s Y¨uksel were truly remarkable friends and I will always value their companionship. I would also like to express my most sincere appreciation and admiration for Cansu Tunca. If all the hardship I endured for all these years was worth one thing, that would be her coming into my life. My last three years were very special and I look forward to our future moments together. I would not have come this far without the love and support of my family, S¸ahika, Sermet, Ay¸seg¨ul and Eren. This endeavour was only possible with their continuous encouragement and selfless sacrifice. I cannot express my gratitude for their support and perseverance. This thesis is dedicated to them. This work was supported by Advanced Research and Development Activity, Dis- ruptive Technologies Office and Hewlett-Packard Research Laboratories. 6 Contents 1 Introduction 23 2 Preliminaries 37 2.1Introduction................................ 37 2.2SpontaneousParametricDownconversion................ 37 2.3Single-PhotonUpconversionbySum-FrequencyGeneration...... 44 3 Pulsed Sagnac Source of Narrowband Polarization Entangled Pho- tons 53 3.1Introduction................................ 53 3.1.1 BB84QuantumKeyDistributionProtocol........... 54 3.1.2 Entanglement-BasedQuantumKeyDistribution........ 55 3.1.3 ExperimentalRealizations.................... 57 3.2DesignConsiderationsforaFree-SpaceeQKDSource......... 58 3.3PumpSourceDesignandCharacterization............... 60 3.3.1 Master Oscillator ......................... 63 3.3.2 Polarization-MaintainingEDFA................. 69 3.3.3 FirstSHGStagewithMgO:PPLN................ 72 3.3.4 SecondSHGStagewithPPKTP................ 76 3.3.5 FutureDesignConsiderations.................. 80 3.4 Polarization Sagnac Interferometer for Pulsed Entangled Photon Source 81 3.4.1 ExperimentalSetup........................ 84 3.5Low-FluxCharacterizationofthePSISource.............. 89 7 3.5.1 Quantum-Interference Visibility ................. 90 3.5.2 CHSH S-ParameterMeasurements............... 93 3.5.3 QuantumStateTomography................... 95 3.6High-FluxCharacteristics........................ 96 3.6.1 AccidentalCoincidences..................... 97 3.6.2 Multiple-PairGeneration..................... 100 3.7Summary................................. 107 4 Coincident-Frequency Entanglement with Extended Phase-Matching109 4.1Introduction................................ 109 4.2ExtendedPhase-MatchingConditionsforPPKTP........... 112 4.3ExperimentalSetupandInitialResults................. 117 4.4 Improved Two-Photon HOM Interference with Extended Phase-Matched PPKTP.................................. 122 4.4.1 Difference-FrequencyGenerationwithPPKTP......... 126 4.4.2 OptimizedHOMInterference.................. 131 4.5Summary................................. 137 5 Time-Resolved Characterization of Two-Photon State by Upconver- sion 139 5.1Introduction................................ 139 5.2Single-PhotonUpconversion....................... 143 5.3Time-ResolvedPhotodetectionwithUpconversion........... 144 5.4ExperimentalSetup............................ 150 5.4.1 PPMgSLT Characterization with Sum-Frequency Generation . 154 5.4.2 Time-ResolvedSingle-PhotonUpconversion.......... 155 5.4.3 JointTemporalDensityMeasurement.............. 167 5.5QuantifyingContinuous-VariableEntanglement............ 171 5.6Summary................................. 178 6 Conclusions 181 8 A Evaluation of the Bipartite Trace Operation 189 9 10 List of Figures 1-1 Combination of two type-II SPDC outputs generating orthogonally polarized signal and idler photons at a polarizing beam-splitter (PBS), resulting in the polarization-entangled signal and idler photons being deterministicallyseparatedattheoutput,seeRef.[1]. ........ 26 1-2 Hong-Ou-Mandel interferometer, which measures fourth order corre- lation for two incoming photons interfering at a 50–50 beam-splitter [2]. For indistinguishable photons arriving at the beam-splitter simul- taneously,