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Quantum Information Science and Quantum Metrology: Novel Systems and Applications Quantum Information Science and Quantum Metrology: Novel Systems and Applications A dissertation presented by P´eterK´om´ar to The Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Physics Harvard University Cambridge, Massachusetts December 2015 c 2015 - P´eterK´om´ar All rights reserved. Thesis advisor Author Mikhail D. Lukin P´eterK´om´ar Quantum Information Science and Quantum Metrology: Novel Systems and Applications Abstract The current frontier of our understanding of the physical universe is dominated by quantum phenomena. Uncovering the prospects and limitations of acquiring and processing information using quantum effects is an outstanding challenge in physical science. This thesis presents an analysis of several new model systems and applications for quantum information processing and metrology. First, we analyze quantum optomechanical systems exhibiting quantum phenom- ena in both optical and mechanical degrees of freedom. We investigate the strength of non-classical correlations in a model system of two optical and one mechanical mode. We propose and analyze experimental protocols that exploit these correlations for quantum computation. We then turn our attention to atom-cavity systems involving strong coupling of atoms with optical photons, and investigate the possibility of using them to store information robustly and as relay nodes. We present a scheme for a robust two-qubit quantum gate with inherent error-detection capabilities. We consider several remote entanglement protocols employing this robust gate, and we use these systems to study the performance of the gate in practical applications. iii Abstract Finally, we present a new protocol for running multiple, remote atomic clocks in quantum unison. We show that by creating a cascade of independent Greenberger- Horne-Zeilinger states distributed across the network, the scheme asymptotically reaches the Heisenberg limit, the fundamental limit of measurement accuracy. We propose an experimental realization of such a network consisting of neutral atom clocks, and analyze the practical performance of such a system. iv Contents Title Page . .i Abstract . iii Table of Contents . .v List of Figures . xi List of Tables . xiii Citations to Previously Published Work . xiv Acknowledgments . xv Dedication . xvii 1 Introduction and Motivation 1 1.1 Overview and Structure . .1 1.2 Optomechanical Systems . .3 1.3 Atom-Cavity Systems . .4 1.4 Quantum Repeaters . .5 1.5 Atomic Clocks and Quantum Metrology . .6 1.6 Rydberg Blockade . .9 2 Single-photon nonlinearities in two-mode optomechanics 11 2.1 Introduction . 11 2.2 Multimode optomechanics . 14 2.3 Equal-time correlations . 17 2.3.1 Average transmission and reflection . 17 2.3.2 Intensity correlations . 20 2.3.3 Absence of two-photon resonance at ∆ = 0 . 23 2.3.4 Finite temperature . 25 2.4 Delayed coincidence and single phonon states . 30 2.4.1 Driven mode . 31 2.4.2 Heralded single phonon states . 34 2.5 Reaching strong coupling . 37 2.6 Conclusions . 38 v Contents 3 Optomechanical quantum information processing 40 3.1 Introduction . 40 3.2 Model . 42 3.3 Resonant strong-coupling optomechanics . 43 3.4 An OM single-photon source . 46 3.5 Single-phonon single-photon transistor . 47 3.6 Phonon-phonon interactions . 49 3.7 Conclusions . 51 4 Heralded Quantum Gates with Integrated Error Detection 52 4.1 Introduction . 52 4.2 Heralding gate . 54 4.3 Performance . 56 4.3.1 Model . 56 4.3.2 Effective Hamiltonian . 57 4.3.3 Success probability . 58 4.3.4 Gate time . 59 4.4 Additional errors . 60 4.5 Possible implementation . 62 4.6 Application . 63 4.7 Conclusion . 64 5 Remote entanglement distribution using individual atoms in cavities 65 5.1 Introduction . 65 5.2 High-fidelity quantum repeater . 68 5.2.1 Secret key rate . 74 5.2.2 Repeater architecture . 76 5.3 Other cavity based repeaters . 78 5.3.1 Single-photon entanglement creation . 78 5.3.2 Initial purification . 80 5.3.3 CNOT gates . 82 5.4 Numerical optimization . 84 5.5 Conclusion . 94 6 Heisenberg-Limited Atom Clocks Based on Entangled Qubits 97 6.1 Introduction . 97 6.2 Feedback loop . 103 6.3 Spectroscopic noises . 104 6.3.1 Phase estimation with multiple GHZ groups . 105 6.3.2 Optimization . 106 6.4 Comparison with other schemes . 107 vi Contents 7 A quantum network of clocks 111 7.1 Introduction . 111 7.2 The concept of quantum clock network . 113 7.3 Preparation of network-wide entangled states . 116 7.4 Interrogation . 118 7.5 Feedback . 120 7.6 Stability analysis . 121 7.7 Security . 125 7.8 Outlook . 126 8 Quantum network of neutral atom clocks 130 8.1 Introduction . 130 8.2 Description of the protocol . 132 8.2.1 Collective excitations . 133 8.2.2 Non-local connection . 133 8.2.3 Local connection . 135 8.2.4 Local GHZ growing . 136 8.3 Implementation . 138 8.4 Clock network optimization . 140 8.5 Conclusion . 143 A Appendices for Chapter 2 144 A.1 Derivation of reflected mode operator . 144 A.2 Analytic model . 145 B Appendices for Chapter 3 148 B.1 Phonon nonlinearities . 148 B.1.1 Model . 148 B.1.2 Displaced frame . 149 B.1.3 Hybridized modes . 150 B.1.4 Adiabatic elimination of the cavity mode . 152 B.1.5 Simple perturbation theory . 153 B.1.6 Corrections . 154 B.1.7 Numerical simulation . 155 B.2 Phonon-phonon interactions . 157 C Appendices for Chapter 4 160 C.1 Perturbation theory . 160 C.1.1 Success probability and fidelity . 165 C.1.2 N-qubit Toffoli gate . 165 C.1.3 CZ-gate . 167 C.1.4 Two-photon driving . 169 vii Contents C.2 Gate time . 172 C.3 Numerical simulation . 174 C.4 Additional errors . 177 D Appendices for Chapter 5 181 D.1 Error analysis of the single-photon scheme . 181 D.2 Error analysis of the two-photon scheme . 183 D.3 Deterministic CNOT gate . 184 D.4 Rate analysis . 186 D.4.1 Deterministic gates . 189 D.4.2 Probabilistic gates . 192 E Appendices for Chapter 6 196 E.1 Figure of merit: Allan-variance . 196 E.2 Single-step Uncorrelated ensemble . 198 E.2.1 Sub-ensembles and projection noise . 198 E.2.2 Effects of laser fluctuations: Phase slip errors . 199 E.2.3 Optimal Ramsey time . ..
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