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

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LIST OF ABBREVIATIONS AND SYMBOLSI{···} imaginary part of ···Ĵ x , Ĵ y , Ĵ z angular momentum operatorsk B Boltzmann’s constant (1.380 658 × 10 −23 JK −1 )κL···〉∣ µ〈〉n(k)n(k)〈〉n(j)NΩPatom collision strengthfirst-order differential operatoratomic coherent state, or Bloch stateobserved momentum distributionsingle-trajectory momentum distributionangular momentum distributionnumber of condensed atomstunnelling frequencyGlauber-Sudarshan P functionPr{···} probability of ···ˆΨphoton-field annihilation operatorΦ Nˆψ † , ˆψ〉∣ Ψ ∣ ˜Ψ〉∣ 〉∣Ψ ccondensate mean fieldbosonic many-body creation and annihilation operators for atomssystem ket vectorunnormalised system ket vectorconditional system ket vector±q 0 positions of well minimaQQ(µ)quantum optics Q functionatomic Q functionR{···} real part of ···ρˆρˆρ cΘU 0u 1 , u 2V···(r)W , dWground-state spatial density distributiondensity operator for the condensateconditional density operator for the condensatenormalised atom collision strength (κN/Ω)two-body interaction strengthlocal ground-state modes of the double-well potentialtrapping potentialWiener process and increment13
Chapter 1Condensation ‘without forces’The theory is pretty, but is there some truth in it?-A.Einstein 1 .1.1 An historical introductionWhat is now known as Bose-Einstein condensation was predicted by Albert Einstein in1924[139]. Einstein’s contribution to statistical mechanics was but a brief interlude inhis life as a physicist, but this alone, without relativity or his contributions to the earlyquantum theory would have guaranteed him fame, at least in scientific circles.Beforeany quantum theory had been fully developed, Einstein was investigating the quantumstatistical properties of massive particles.He generalised the work of Bose, who hadonly dealt with the statistical properties of photons, and in the process predicted a new,quantum state of matter.In deriving an equilibrium distribution of radiation, Bose had treated light as a quantumgas 2 of photons[14]. Einstein reasoned that if quanta of light could be treated in thisway, then so could particles of matter, and derived the properties of a quantum gas of‘molecules’. This was the beginning of quantum statistical mechanics.Among Einstein’s predictions was that below a certain temperature, part of the gasmust condense into the quantum state of lowest energy, thus creating a macroscopic occupationof a single quantum state[54]. For some years, the existence of this phenomenonwas treated with some skepticism, with Einstein himself wondering if the effect could be1 From a letter to Ehrenfest in December 1924, quoted on page 432 of [139].2 A quantum gas in the sense that its constituent particles are indistinguishable.14
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 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 62 and 63: 3. Homodyne measurements on a Bose-
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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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