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High Speed Homodyne Detector for Gaussian-Modulated Coherent-State Quantum Key Distribution High Speed Homodyne Detector for Gaussian-Modulated Coherent-State Quantum Key Distribution by Yuemeng Chi A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Electrical and Computer Engineering University of Toronto Copyright © 2009 by Yuemeng Chi Abstract High Speed Homodyne Detector for Gaussian-Modulated Coherent-State Quantum Key Distribution Yuemeng Chi Master of Applied Science Graduate Department of Electrical and Computer Engineering University of Toronto 2009 We developed a high speed homodyne detector in the telecommunication wavelength re- gion for a Gaussian-modulated coherent-state quantum key distribution experiment. We are able to achieve a 100 MHz bandwidth, ultra-low electronic noise and pulse-resolved homodyne detector. The bandwidth of this homodyne detector has reached the same order of magnitude of the best homodyne detectors reported. By overcoming photodiode response functions mismatch, choosing proper laser sources, ensuring the homodyne de- tector linearity and stabilizing the homodyne detection system, we demonstrate that the homodyne detector has a 10 dB shot-noise-to-electronic-noise ratio in the time domain at a local oscillator of 5.4108 photons/pulse at a laser repetition rate of 10 MHz. With this homodyne detector, we expect to increase our GMCS QKD experiment speed by 100 times, which will improve the key generation rate by 1-2 orders of magnitude. ii Dedication First and foremost I owe my deepest gratitude to my supervisors, Professor Hoi- Kwong Lo and Professor Li Qian, who have supported me thoughout my research with their patience and knowledge. I attribute my master work to their encouragement and e®ort. Without their support, this thesis would not have been completed. It is an honor for me to work with them during my last two years' study. One simply could not wish for a better or friendlier supervisor. I am also deeply appreciate the help and advice received from Doctor Bing Qi, who essentially teaches me everything in an optical and electrical lab. I am grateful to Doctor Bing Qi for his knowledge and many useful discussions that motivated me. Special thanks are extended to Professor J. Stewart Aitchison, Professor Lacra Pavel, and Professor Joyce Poon for their time, advice, and willingness to serve on the commit- tee. I would like to show my gratitude to Professor Alex Lvovsky at University of Calgray for generously providing the homodyne detector electronic design and printed circuit board layout. I also thank Professor SunHyun Youn and Nitin Jain for their kind help in building the homodyne detector circuit and sharing a lot of construction experience. I would also extend my thanks to Liang Tian, who has helped a lot in tuning the homodyne detector circuit. I also would like to acknowledge Professor Namdar Saniei and Doctor Wen Zhu for helpful discussions. It is a pleasure to thank a friendly and cheerful group of fellow students, Viacheslav Burenkov, Wei Cui, Chi-Hang Fred Fung, Junbo Han, Wolfram Helwig, Kenny Ho, Dongpeng Kang, Xiongfeng Ma, Jason Ng, Wing-Chau Ng, Chris Sapiano, Peyman Sarra¯, Gigi Wong, Fei Ye, Jiawen Zhang, Lijun Zhang, and Eric Zhu for their support and friendship. I also thank 3GMetalWorx Inc. for providing a professional shielding metal box for the homodyne detector circuit. Furthermore, I would like to thank Ms. Diane Silva and Ms. Linda Liu for their e±cient and professional administrative work. iii Finally and most importantly, this thesis would not have been possible without the endless love and support from my family. This thesis is dedicated to my husband and my parents. iv Contents 1 Introduction 1 1.1 Background . 1 1.2 Motivation: high speed homodyne detector . 6 1.3 Objective . 7 1.4 Organization . 8 2 Review of GMCS QKD and Homodyne Detection 9 2.1 Gaussian-modulated coherent-state quantum key distribution . 9 2.1.1 Protocol . 9 2.1.2 State of the art . 12 2.2 Homodyne detection . 14 2.2.1 Introduction . 14 2.2.2 State of the art . 19 2.3 Summary . 21 3 GMCS QKD over 20 km Fiber 22 3.1 Experimental setup . 22 3.2 Secure key rate formula . 24 3.3 Results . 27 3.4 Discussions . 33 3.5 Summary . 36 v 4 High Speed Homodyne Detector 37 4.1 Requirement of a homodyne detector in GMCS QKD . 37 4.2 High speed homodyne detector design . 38 4.2.1 Homodyne detector optical setup in ¯ber . 38 4.2.2 Homodyne detector electrical circuit . 39 4.3 Challenges . 40 4.3.1 Low electronic noise . 41 4.3.2 Di®erent photodiode response functions . 42 4.3.3 Linearity . 45 4.3.4 Laser source . 47 4.3.5 Optical stability . 52 4.4 Summary . 54 5 Performance of the Homodyne Detector 55 5.1 Experimental plan . 56 5.2 Measurement with CW light . 56 5.2.1 Experimental setup . 57 5.2.2 Noise measurement in the time domain . 58 5.2.3 Noise measurement in the frequency domain . 60 5.3 Measurement with pulsed light . 62 5.3.1 Pulsed laser source . 62 5.3.2 Noise measurement in the time domain . 63 5.3.3 Noise measurement in the frequency domain . 73 5.4 Conclusions and discussions . 77 6 Conclusion and Future Work 81 6.1 Signi¯cance and contribution . 81 6.2 Future work . 83 vi List of Tables 1.1 Secure key rate (bit) per pulse for GMCS [1], decoy state [2] and DPS [3] protocols over 5-km telecommunication ¯ber. Secure key rates for de- coy state and DPS protocols are simulation results based on experimental conditions. 5 3.1 Parameters used in the key rate simulation , from Ref. [1]. The length of the ¯ber is 5 km. 31 3.2 20-km GMCS QKD parameters and results (e: experimental result; c: calculated result) . 33 3.3 Secure key rate in our GMCS QKD experiment and in Ref. [4] over 20-km ¯ber. rep. :repetition . 33 4.1 Speci¯cations of FGA04 InGaAs photodiode (typical values). 39 4.2 Speci¯cations of the two lasers used in photodiode linearity test . 49 5.1 Parameters in the key rate simulation (given in Ref. [1]). Here we assume ²A and Nleak are the same for high-speed and low-speed GMCS QKD experiments. 71 6.1 HD peformance comparison between our group and Ref. [5] . 82 vii List of Figures 1.1 One-time-pad scheme . 2 1.2 Alice prepares four photons with arbitrary polarizations. Eve taps them from the channel and uses her basis (horizontal and vertical basis) to measure them. The polarization of those photons will collapse to Eve's basis. Thus, Eve cannot perfectly duplicate those states. 3 2.1 GMCS QKD protocol. 11 2.2 Schematic of a homodyne detection. BS: beam splitter; SIG: signal; LO: local oscillator; PD: photodiode; Á: introducing a phase between the signal and the LO; Black line: optical path; Blue line: electrical path; Dashed box: homodyne detector . 15 2.3 LO and signal states in the phasor space. 16 2.4 Scheme of a photocurrent subtraction. PD: photodiode . 19 3.1 Schematic of the GMCS QKD system. L: 1550 nm CW ¯ber laser, PC1−5: polarization controllers; PBS1−3: polarization beam splitters or combiners; AM0−1: amplitude modulators; PM1−2: phase modulators; SW1−2:optical switches; AOM+(AOM−): upshift(downshift) acousto-optic modulators; VOA1−2: variable optical attenuators; ISO: isolator; C: ¯ber coupler; HOM: homodyne detector [1, 6, 7] . 23 viii 3.2 Quadrature variances prepared by Alice, quadrature variances measured by Bob, and equivalent input noise Â. Quadrature variance prepared by Alice, and equivalent input noise  are referred to the input. Noise on Bob's side is referred to the output. 25 3.3 QKD experimental results. The equivalent input noise has been deter- mined experimentally to be  = 6:13[6, 7]. 28 3.4 Determine ± by using a high modulation variance VA 40000 and a weak LO (105 photon/pulse). The result is ± = 0:0049 . 29 3.5 Noise of the balanced HD as a function of LO power. With a LO of 1.2107 photons/pulse, the electronic noise is 6.8 dB below the shot noise (plot with raw data obtained from [1]) . 30 3.6 Secure key rate as a function of the electronic noise (in shot noise unit) under the \general model". Parameters in this simulation are in Table 3.1 . 31 3.7 The leakage from LO to signal. LO: local oscillator; SIG: signal; LE: leakage; PBS: polarization beam splitter; LO is 5-6 orders of magnitude higher than signal. The leakage from signal to LO is negligible. Arrowed lines indicate the polarization of the beam . 32 3.8 Key rate simulation when ultra-low loss ¯ber and standard ¯ber are used in the GMCS QKD experiment. Parameters are based on Table 3.2 under the \realistic model" when ¯ = 0.898 . 34 3.9 Key rate simulation with excess noise and in the absence of excess noise. Parameters are based on Table 3.2 under the \realistic model" when ¯ = 0.898 . 35 4.1 Homodyne detection setup in the telecommunication wavelength. LO: local oscillator; OVD: optical variable delay; FC: 50:50 ¯ber coupler; VOA: variable optical attenuator; PD: photodiode; AMP: electronic ampli¯ers. 39 ix 4.2 A simpli¯ed homodyne detector circuit. PD: photodiode (Thorlabs,FGA04); OPA847: operational ampli¯er (Texas Instrument) . 40 4.3 Photo of the circuit board of the homodyne detector. Two FGA04 photo- diodes are in the upper left corner. 42 4.4 Customized metal box for shielding, constructed by 3GMetalWorx Inc.
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