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

More documents

Recommendations

Info

2. Properties of an atomic Bose condensate in a double-well potentialthe two cases. For Θ ≤ 1, A0, the solution isx(t) = 1 dn(ΩΘt; k(Θ)) (2.41a)2√k(Θ) = 1 − 1 − 1 Θ 2 . (2.41b)So above the critical value, the solution is again periodic, with period 2K(k)/(ΩΘ), butwith diminishing peak-to-peak amplitude: 1 − √ 1 − k 2 (Fig. 2.3(d)). When Θ ≫ 1, thecondensate remains trapped in one well. Figure 2.2 illustrates the Θ dependence of theperiod and amplitude.Fixed pointsThe fixed points of the system provide an insight into the dynamics of the system forgeneral initial conditions. The fixed points are(x ∞ ,y ∞ ,z ∞ ) 1 = (0, 0, 1 2 ) (2.42a)(x ∞ ,y ∞ ,z ∞ ) 2 = (0, 0, − 1 2 ) (2.42b)(x ∞ ,y ∞ ,z ∞ ) 3 = 1 4 (√ 4Θ 2 − 1, 0, 1)Θ (2.42c)(x ∞ ,y ∞ ,z ∞ ) 4 = 1 √4Θ4 (− 2 − 1, 0, 1)Θ. (2.42d)The stability of these points can be calculated by expanding x = x ∞ + ξ/Ω andy =y ∞ + ψ/Ω, which leads to the linearised equation for X =(ξ,ψ) ′ :⎛Ẋ = ⎝0 −11 − 4Θz ∞ + 4Θx2 ∞ 4Θx ∞y ∞z ∞ z ∞⎞⎠ X. (2.43)29
2. Properties of an atomic Bose condensate in a double-well potentialFigure 2.3: The semiclassical evolution of x(t) for different values of the parameter Θ=κN/Ω.In (a) Θ=0.0, in(b)Θ=0.9, in(c)Θ=1.0, andin(d)Θ=1.1. The dashed line correspondsto all the atoms starting in one well (x 0 = 1 2 , z 0 =0), while the continuous line correspondsto the atoms being initially distributed equally between the wells but with maximum tunnellingmomentum (x 0 =0, z 0 =0). The critical value of Θ is Θ c =1.0.5(a)0.5(b)x(t)0x(t)0x 0= 0x 0= 1/2−0.50 5 10 15 20t/t 0x 0= 0x 0= 1/2−0.50 5 10 15 20t/t 00.5(c)0.5(d)x(t)0x(t)0x 0= 0x 0= 1/2−0.50 5 10 15 20t/t 0x 0= 0x 0= 1/2−0.50 5 10 15 20t/t 030
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 29: 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
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Chapter 5Weak force detection using
Page 109 and 110:
5. Weak force detection using a dou
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Part IIQuantum evolution of a Bose
Page 125 and 126:
6. Quantum effects in optical fibre
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Chapter 7Quantum simulations of eva
Page 143 and 144:
7. Quantum simulations of evaporati
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
A. Stochastic calculus in outlineco
Page 173 and 174:
Appendix BQuasiprobability distribu
Page 175 and 176:
B. Quasiprobability distributions u
Page 177 and 178:
Bibliography[1] Agrawal, G. P. Nonl
Page 179 and 180:
BIBLIOGRAPHY[22] Carter,S.J.Quantum
Page 181 and 182:
BIBLIOGRAPHY[45] Drummond, P. D., C
Page 183 and 184:
BIBLIOGRAPHY[68] Gordon,D.,andSavag
Page 185 and 186:
BIBLIOGRAPHY[92] Jaksch,D.,Gardiner
Page 187 and 188:
BIBLIOGRAPHY[114] Marshall, R. J.,
Page 189 and 190:
BIBLIOGRAPHY[135] Naraschewski, M.,
Page 191 and 192:
BIBLIOGRAPHY[158] Shelby, R. M., Le
Page 193 and 194:
BIBLIOGRAPHY[179] Wiseman, H. M. Qu
Page 195:
. . . but this book is already too
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?