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Photonic Entanglement for a Quantum Repeater

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Photonic Entanglement for a Quantum Repeater UNIVERSITY OF CALGARY Photonic Entanglement for a Quantum Repeater by Jeongwan Jin A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF PHYSICS AND ASTRONOMY CALGARY, ALBERTA JULY, 2014 c Jeongwan Jin 2014 Abstract Quantum Key Distribution (QKD) has opened a new avenue for secure communication, by allowing one to distribute a random secret key between two users that are connected through a public channel without revealing information to unauthorized parties. If a mes- sage is encrypted with the one time pad (a well-known crytography algorithm) using secret keys created by QKD, then the ciphertext is information-theoretically secure and thus un- breakable for adversaries. Despite its unprecedented security, loss in the physical channel has prevented QKD from being used over distances beyond a few hundred kilometers. Fortu- nately, quantum repeaters have opened a path for long-distance QKD by providing a means to establish entanglement between distant users. The goal of this thesis has been to develop a source of entangled photon pairs that is suit- able for quantum repeaters and then use it to test some of the fundamental building blocks of a quantum repeater : the heralded creation of entangled photons by means of entan- glement swapping with properties that allow interfacing with optical quantum memories; the reversible mapping of quantum states from members of entangled photon pairs in and out of solid-state quantum memories; two-photon interference and a Bell state measurement with photons recalled from separate quantum memories. The demonstration of these key ingredients of a quantum repeater constitutes a significant step towards the establishment of entanglement over hundreds of kilometer distance, and hence long-distance QKD. i List of published papers, papers under review, and papers to be submitted 1. \Entanglement swapping with quantum-memory compatible photons", J. Jin, M. G. Pui- gibert, L. Giner, J. A. Slater, M. R. E. Lamont, V. B. Verma, M. B. Shaw, F. Marsili, S. W. Nam, D. Oblak and W. Tittel, To be submitted. 2. \Quantum storage of entangled telecom-wavelength photons in an erbium-doped optical fibre”, E. Saglamyurek, J. Jin, V. B. Verma, M. B. Shaw, F. Marsili, S. W. Nam, D. Oblak, and W. Tittel, Submitted. 3. \Two-photon interference of weak coherent laser pulses recalled from separate solid-state quantum memories", J. Jin, J. A. Slater, E. Saglamyurek, N. Sinclair, D. Oblak, M. George, R. Ricken, W. Sohler and W. Tittel, Nature Communications 4, 2386 (2013). 4. \Conditional detection of pure quantum states of light after storage in a Tm-doped waveg- uide", E. Saglamyurek, N. Sinclair, J. Jin, J. A. Slater, D. Oblak, F. Bussi`eres,M. George, R. Ricken, W. Sohler and W. Tittel, Physical Review Letters, 108, 083602 (2012). 5. \Broadband waveguide quantum memory for entangled photons", E. Saglamyurek, N. Sinclair, J. Jin, J. A. Slater, D. Oblak, F. Bussi`eres,M. George, R. Ricken, W. Sohler and W. Tittel, Nature, 469 512 (2011). 6. \Testing nonlocality over 12.4 km of underground fiber with universal time-bin qubit analyzers", F. Bussi`eres,J. A. Slater, J. Jin, N. Godbout and W. Tittel, Physical Review A, 81 052106 (2010). ii Table of Contents Abstract ........................................ i List of published papers, papers under review, and papers to be submitted ii Table of Contents . iii List of Tables . v List of Figures . vi List of Symbols . viii 1 Overview ..................................... 1 1.1 Long-Distance Quantum Communication . 3 1.2 Quantum Repeater . 4 Bibliography . 8 2 Quantum Communication Components . 10 2.1 Quantum Entanglement . 11 2.1.1 Qubit . 11 2.1.2 Entanglement and Entangled Qubits . 12 2.1.3 Photon-Pair Source . 14 2.1.4 Entanglement Verification Tools . 21 2.2 Quantum Memory . 30 2.2.1 Storage Materials and Protocols . 30 2.2.2 Figures of Merit . 33 2.3 Two-Photon Measurement . 39 2.3.1 Two-Photon Interference . 39 2.3.2 Bell-State Measurement . 41 Bibliography . 44 3 Real-World Entanglement .......................... 50 3.1 Introduction . 52 3.2 Experiment . 54 3.3 Measurements and Results . 59 3.4 Conclusion and Discussion . 62 Bibliography . 65 4 Entanglement Swapping with Quantum-Memory Compatible Photons 68 4.1 Introduction . 71 4.2 Experiment . 72 4.3 Measurements and Results . 76 4.4 Conclusion and Discussion . 77 Bibliography . 78 5 Storage of Quantum Bits ........................... 81 5.1 Introduction . 83 5.2 Experiment . 84 5.3 Measurements and Results . 89 5.4 Conclusion and Discussion . 91 Bibliography . 94 6 Storage of Entangled Photons at 795 nm . 96 iii 6.1 Introduction . 98 6.2 Experiment . 100 6.3 Measurements and Results . 105 6.4 Conclusion and Discussion . 108 Bibliography . 109 7 Storage of Entangled Photons at Telecom Wavelength . 112 7.1 Introduction . 114 7.2 Experiment . 115 7.3 Measurements and Results . 120 7.4 Conclusion and Discussion . 124 Bibliography . 126 8 Bell-State Measurement with Photons Recalled from Memories . 129 8.1 Introduction . 132 8.2 Experiment . 134 8.3 Measurement and Results . 137 8.4 Conclusion and Discussion . 148 Bibliography . 150 9 Summary and Outlook ............................ 154 Bibliography . 158 A Supplementary Information for Chapter 6 . 159 Bibliography . 166 B Supplementary Information for Chapter 7 . 168 Bibliography . 175 C Supplementary Information for Chapter 8 . 178 Bibliography . 201 iv List of Tables 2.1 Summary of experimental Bell tests with a closed loophole . 25 3.1 Results of the CHSH inequality violations with the four different configurations 61 6.1 Entanglement measures, purities and fidelities . 107 7.1 Characterization of the two-photon state . 123 8.1 Experimental two-photon interference visibilities for different degrees of freedom138 A.1 Joint-detection probabilities for density matrix reconstruction . 164 A.2 Correlation coefficients for Bell-inequality tests . 165 B.1 Joint-detection probabilities for density matrix reconstruction . 172 B.2 Measurement settings and correlation coefficients for Bell-inequality tests . 173 v List of Figures and Illustrations 1.1 A schematic diagram of quantum repeater . 5 1.2 Elementary links of quantum repeater and their connection . 7 2.1 Qubit representation . 12 2.2 Generation of a time-bin qubits . 13 2.3 Spontaneous parametric down-conversion . 15 2.4 SPDC efficiency comparison . 17 2.5 Generation of photon pairs . 18 2.6 Generation of photonic time-bin entanglement . 19 2.7 Measurement setups for SPDC-source characterization . 20 2.8 A measurement setup for time-bin entangled photons . 22 2.9 Experimentally measured joint detections . 28 2.10 Property of the Werner state in terms of entanglement visibility . 29 2.11 Picuture of quantum memories . 31 2.12 Atomic frequency comb . 32 2.13 Two-photon interference . 39 2.14 A photonic Bell-state measurement . 42 3.1 Sources of time-bin and hybrid entangled qubits . 53 3.2 Universal Time-Bin Qubit Analyzers . 56 3.3 Experimental setup for CHSH inequality test . 57 3.4 Entanglement visibility measurements . 63 3.5 The four configurations used to vioate the CHSH inequality . 64 4.1 A schematic diagram of entanglement swapping . 69 4.2 Picture of the experimental setup for entanglement swapping . 70 4.3 Schematics of of our setup. 73 4.4 Coincidence count rate as a function of the delay of one photon . 75 4.5 Density matrix characterizing the joint state of the two 795 nm photons . 76 5.1 Photon pair source and quantum memory setup . 85 5.2 Waveguide geometry (a) and simplified energy diagram of Tm atoms (b) . 88 5.3 Storage of early and late time-bin qubit states in the AFC memory . 90 5.4 Retrieval of qubits created in a superposition of early and late temporal modes: 92 6.1 Storage and retrieval of photonic entanglement . 97 6.2 Schematics of the experimental setup for the storage of.
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