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

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2. Properties of an atomic Bose condensate in a double-well potentialan upper bound. Equation (2.64) becomesN =z ∞ 1 − z + ∑z l −lβΩ 1 − e−lNβΩe . (2.65)1 − e−lβΩ l=1A high temperature approximation, in which βΩ ≪ 1, gives the approximate result 4 :()N =z1 − z + k BTΩ ln 1 − ze −(N+ 1 2 )Ω/(k BT ). (2.66)1 − z(1 − Ω/(2k B T ))The critical temperature T c can be determined as the minimum temperature that satisfiesthe above equation when N 0 = 0. This is easily done by taking z → 1, to give()N = k BT cΩ ln 1 − e −(N+ 1 2 )Ω/(k BT ), (2.67)Ω/(2k B T c )and a condensate fraction when T
2. Properties of an atomic Bose condensate in a double-well potentialFigure 2.14: The condensate fraction versus temperature (scaled by Ω/k B )forN = 100 anddifferent values of the atom-interaction strength. In (a) Θ=0,in(b)Θ=0.5, in(c)Θ=2,in(d)Θ=20,in(e)Θ = 100 and in (f) Θ = 500.1(a)1(b)0.80.8N 0/N0.60.4ExactApproximateN 0/N0.60.40.2T c= 26.10.2T c= 35.400 10 20 30 40 50Temperature T10.8(c)00 10 20 30 40 50 60 70Temperature T10.8(d)N 0/N0.60.4N 0/N0.60.40.2T c= 54.30.2T c= 154.200 20 40 60 80 100Temperature T10.8(e)00 50 100 150 200 250 300Temperature T10.8(f)N 0/N0.60.4N 0/N0.60.40.2T c= 353.70.2T c= 854.000 100 200 300 400 500 600 700Temperature T00 500 1000 1500Temperature T48
Page 1 and 2: Open Quantum Dynamics of Mesoscopic
Page 3 and 4: AcknowledgementsMy thanks must firs
Page 5 and 6: AbstractThe properties of an atomic
Page 7 and 8: CONTENTS4 Continuously monitored Bo
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
Page 47: 2. Properties of an atomic Bose con
Page 62 and 63: 3. Homodyne measurements on a Bose-
Page 70: 3. Homodyne measurements on a Bose-
Page 79 and 80: Chapter 4Continuously monitored con
Page 81 and 82: 4. Continuously monitored Bose cond
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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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