Open Quantum Dynamics of Mesoscopic Bose-Einstein ... - Physics

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Contents1 Condensation ‘without forces’ 141.1 An historical introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.2 Underlying themes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.3 Thesis rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.4 Thesis structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17I Quantum dynamics of monitored Bose-Einstein condensates 192 Properties of an atomic Bose condensate in a double-well potential 202.1 Condensate model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2 Semiclassical dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.2.1 Two-mode semiclassical analysis . . . . . . . . . . . . . . . . . . . . 242.2.2 The Gross-Pitaevskii equation . . . . . . . . . . . . . . . . . . . . . 322.3 Quantum dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.3.1 Energy eigenstates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.3.2 Transition temperature . . . . . . . . . . . . . . . . . . . . . . . . . 462.3.3 Coherence properties of the ground state . . . . . . . . . . . . . . . 492.3.4 A condensate in a noisy potential . . . . . . . . . . . . . . . . . . . . 533 Homodyne measurements on a Bose-Einstein condensate 593.1 Symmetry-breaking measurements . . . . . . . . . . . . . . . . . . . . . . . 593.2 Homodyne detection scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.3 Stochastic trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.5 Before we move on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765
CONTENTS4 Continuously monitored Bose condensates: quasiprobability distributions 784.1 Introduction - conditional master equation . . . . . . . . . . . . . . . . . . . 784.2 Stochastic Gross-Pitaevskii equation . . . . . . . . . . . . . . . . . . . . . . 794.3 Atomic Q function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.3.1 Definition in terms of Bloch states . . . . . . . . . . . . . . . . . . . 814.3.2 Numerical simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 834.4 Quasiprobability distributions using optical coherent states . . . . . . . . . 934.5 A semiclassical probability distribution . . . . . . . . . . . . . . . . . . . . . 994.6 Quasiprobability distributions using atomic coherent states . . . . . . . . . 1025 Weak force detection using a double Bose-Einstein condensate 1065.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065.2 Two-mode system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.3 Measurement scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.4 Measurement readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.5 Phase errors and phase diffusion . . . . . . . . . . . . . . . . . . . . . . . . 1135.6 Mean-field limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1165.7 Coherent states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1175.8 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1205.9 Les adieux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121II Quantum evolution of a Bose gas during evaporative cooling 1226 Quantum effects in optical fibre communications systems 1236.1 Multimode simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1236.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1236.3 Phase-space methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1266.4 Modified nonlinear Shrödinger equation . . . . . . . . . . . . . . . . . . . . 1276.5 Perturbation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.5.1 Bright solitons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.5.2 Dark solitons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1336.6 Summary of noise scaling properties . . . . . . . . . . . . . . . . . . . . . . 1346.7 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1376
Page 1 and 2: Open Quantum Dynamics of Mesoscopic
Page 3 and 4: AcknowledgementsMy thanks must firs
Page 5: AbstractThe properties of an atomic
Page 9 and 10: List of Figures2.1 Two-mode approxi
Page 11 and 12: LIST OF FIGURES7.5 Angular momentum
Page 14 and 15: LIST OF ABBREVIATIONS AND SYMBOLSI{
Page 17 and 18: 1. Condensation ‘without forces
Page 19 and 20: 1. Condensation ‘without forces
Page 21 and 22: Chapter 2Properties of an atomic Bo
Page 23 and 24: 2. Properties of an atomic Bose con
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2. Properties of an atomic Bose con
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2. Properties of an atomic Bose con
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3. Homodyne measurements on a Bose-
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Chapter 4Continuously monitored con
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4. Continuously monitored Bose cond
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Chapter 5Weak force detection using
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5. Weak force detection using a dou
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Part IIQuantum evolution of a Bose
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6. Quantum effects in optical fibre
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Chapter 7Quantum simulations of eva
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7. Quantum simulations of evaporati
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A. Stochastic calculus in outlineco
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Appendix BQuasiprobability distribu
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B. Quasiprobability distributions u
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Bibliography[1] Agrawal, G. P. Nonl
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BIBLIOGRAPHY[22] Carter,S.J.Quantum
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BIBLIOGRAPHY[45] Drummond, P. D., C
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BIBLIOGRAPHY[68] Gordon,D.,andSavag
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BIBLIOGRAPHY[92] Jaksch,D.,Gardiner
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BIBLIOGRAPHY[114] Marshall, R. J.,
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BIBLIOGRAPHY[135] Naraschewski, M.,
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BIBLIOGRAPHY[158] Shelby, R. M., Le
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BIBLIOGRAPHY[179] Wiseman, H. M. Qu
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. . . but this book is already too
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