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

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4. Continuously monitored Bose condensates: quasiprobability distributionsThis completes our exploration of alternative ways to analyse a condensate undergoinga homodyne measurement scheme. The numerical calculations of the Q functions in Sec.4.3.2 complement the simulations of Ch. 3, while other sections have paved the way fora semiclassical analysis. These kinds of quasiprobability distributions will be used againin the second part of the thesis to map quantum equations of motion onto stochasticcomplex-number equations, for numerical simulations of multimode systems.105
Chapter 5Weak force detection using a doubleBose-Einstein condensate5.1 IntroductionWe shall conclude this part of the thesis by studying a possible application of the Bose-Einstein condensate in precision measurement. Tentative steps have been taken in thisdirection already, with the realisation of a Bose-Einstein atomic clock in the laboratory,based on persistent tunnelling oscillations between two coupled condensates[3, 16, 35].Although inspired by this attempt, this chapter, as the title suggests, deals not withprecision clocks, but with precision force measurements. Although the scheme presentedhere uses tunnelling oscillations, the essence of the measurement lies in generating quantumentanglement in this mesoscopic system. The use of maximal quantum entanglement ofa large number of particles has been suggested before[13, 86], in the context of making afrequency-standard measurement with an array of two-level or spin-half systems[178, 177],such as cold, trapped ions[13, 86]. Here we shall apply these ideas to the Bose condensate,and find an improvement in precision that is proportional to the number of atoms N inthe condensate.106
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Open Quantum Dynamics of Mesoscopic
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AcknowledgementsMy thanks must firs
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AbstractThe properties of an atomic
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CONTENTS4 Continuously monitored Bo
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List of Figures2.1 Two-mode approxi
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LIST OF FIGURES7.5 Angular momentum
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LIST OF ABBREVIATIONS AND SYMBOLSI{
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1. Condensation ‘without forces
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1. Condensation ‘without forces
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Chapter 2Properties of an atomic Bo
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2. Properties of an atomic Bose con
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Page 123 and 124: Part IIQuantum evolution of a Bose
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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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