Bose-Einstein Condensates in Rotating Traps and Optical ... - BEC

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[14] G. Hechenblaikner, E. Hodby, S.A. Hopkins, O.M. Maragò, and C.J. Foot, Direct Observation of Irrotational Flow and Evidence of Superfluidity in a Rotating Bose-Einstein Condensate, Phys. Rev. Lett. 88, 070406 (2002). [15] C.J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Bose Gases (Cambridge University Press, 2002). [16] A. Recati, F. Zambelli, and S. Stringari, Overcritical Rotation of a Trapped Bose-Einstein Condensate, Phys. Rev. Lett. 86, 377 (2000). [17] S. Sinha and Y. Castin, Dynamic Instability of a Rotating Bose-Einstein Condensate, Phys. Rev. Lett. 87, 190402 (2001). [18] J. Garcia-Ripoll and V. Pérez-Garcia, Anomalous rotational properties of Bose-Einstein condensates in asymmetric traps, Phys. Rev. A 64, 013602 (2001). [19] E.M. Lifshitz and L.P. Pitaevskii, Statistical Physics (Butterworth-Heinemann, Oxford, 1999). [20] L. Onsager, Nuovo Cimento 6, suppl. 2, 249 (1949) (observation concerning C.J. Gorter, The two fluid model for Helium II, Nuovo Cimento 6, suppl. 2, 245 (1949)). [21] R.P. Feynman, Application of Quantum Mechanics to liquid Helium, in Progress in Low Temperature Physics, Vol. I, ed. C.J. Gorter (North-Holland, Amsterdam, 1955). [22] A.A. Abrikosov, On the Magnetic Properties of Superconductors of the Second Group, JETP 5, 1174 (1957). [23] V.K. Tkachenko, On Vortex Lattices, JETP 22, 1282 (1966). [24] D. Butts and D. Rokshar, Predicted signatures of rotating Bose-Einstein condensates, Nature 397, 327 (1999). [25] Y. Castin and R. Dum, Bose-Einstein condensates with vortices in rotating traps, Eur. Phys. J. D 7, 399 (1999). [26] D.L. Feder, C.W. Clark, and B.I. Schneider, Vortex Stability of Interacting Bose-Einstein Condensates Confined in Anisotropic Harmonic Traps, Phys. Rev. Lett. 82, 4956 (1999). [27] A.L. Fetter and A.A. Svidzinsky, Vortices in a trapped dilute Bose-Einstein condensate, J. Phys.: Condens. Matter 13, R135 (2001). [28] M.R. Matthews, B.P. Anderson, P.C. Haljan, D.S. Hall, C.E. Wieman, and E.A. Cornell, Vortices in a Bose-Einstein Condensate, Phys. Rev. Lett. 83, 2498 (1999). [29] P.C. Haljan, B.P. Anderson, I. Coddington, and E.A. Cornell, Use of Surface-Wave Spectroscopy to Characterize Tilt Modes of a Vortex in a Bose-Einstein Condensate, Phys. Rev. Lett. 86, 2922 (2001). [30] P.C. Haljan, I. Coddington, P. Engels, and E.A. Cornell, Driving Bose-Einstein-Condensate Vorticity with a Rotating Normal Cloud, Phys. Rev. Lett. 87, 210403 (2001).
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Università degli Studi di Trento F
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7 Bogoliubov excitations of Bloch s
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Chapter 1 Introduction Superfluids
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The second class of stationary solu
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Chapter 2 Vortex nucleation The pro
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2.1 Single vortex line configuratio
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2.2 Role of Quadrupole deformations
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2.2 Role of Quadrupole deformations
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2.3 Critical angular velocity for v
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2.3 Critical angular velocity for v
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2.4 Stability of a vortex-configura
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Chapter 3 Introduction Since the ac
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The order parameter’s temporal ev
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and spectroscopy were described in
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the external probe generates a dens
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Chapter 4 Single particle in a peri
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4.1 Solution of the Schrödinger eq
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4.2 Tight binding regime 43 describ
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4.2 Tight binding regime 45 paramet
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Chapter 5 Groundstate of a BEC in a
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5.1 Density profile, energy and che
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5.1 Density profile, energy and che
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5.2 Compressibility and effective c
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5.4 Effects of harmonic trapping 55
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Chapter 6 Stationary states of a BE
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6.1 Bloch states and Bloch bands 65
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6.2 Tight binding regime 75 conside
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6.2 Tight binding regime 77 Compari
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6.2 Tight binding regime 79 2m¯v/q
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6.2 Tight binding regime 81 The lea
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Chapter 7 Bogoliubov excitations of
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7.2 Bogoliubov bands and Bogoliubov
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7.3 Tight binding regime of the low
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7.3 Tight binding regime of the low
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7.4 Velocity of sound 97 d|bjql| 2
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7.4 Velocity of sound 99 c(s)/c(s=0
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Chapter 8 Linear response - Probing
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8.1 Dynamic structure factor 103 wi
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8.1 Dynamic structure factor 105 Th
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8.1 Dynamic structure factor 107 Th
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8.2 Static structure factor and sum
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Chapter 9 Macroscopic Dynamics In t
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9.1 Macroscopic density and macrosc
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9.2 Hydrodynamic equations for smal
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9.4 Sound Waves 121 9.4 Sound Waves
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9.5 Small amplitude collective osci
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Page 133 and 134: 9.6 Center-of-mass motion: Linear a
Page 135 and 136: 9.6 Center-of-mass motion: Linear a
Page 137 and 138: Chapter 10 Array of Josephson junct
Page 139 and 140: 10.1 Current-phase dynamics in the
Page 141 and 142: 10.2 Lowest Bogoliubov band 137 µ
Page 143 and 144: 10.3 Josephson Hamiltonian 139 wher
Page 145 and 146: 10.3 Josephson Hamiltonian 141 For
Page 147 and 148: Chapter 11 Sound propagation in pre
Page 149 and 150: 11.2 Current-Phase dynamics 145 [14
Page 151 and 152: 11.3 Nonlinear propagation of sound
Page 153 and 154: n(x, t)/n(x, t=0) 11.3 Nonlinear pr
Page 159 and 160: ∆ n ( U / δ ) 1/2 1 0.8 0.6 0.4
Page 161 and 162: 11.4 Experimental observability 157
Page 163 and 164: Chapter 12 Condensate fraction The
Page 165 and 166: 12.2 Uniform case 161 The Bogoliubo
Page 167 and 168: 12.2 Uniform case 163 The solution
Page 169 and 170: 12.3 Shallow lattice 165 12.3 Shall
Page 171 and 172: 12.4 Tight binding regime 167 3D th
Page 173 and 174: 12.4 Tight binding regime 169 direc
Page 175 and 176: 12.4 Tight binding regime 171 Quant
Page 179: Bibliography [1] L. Pitaevskii and
Page 183 and 184: [63] B.P. Anderson, P.C. Haljan, C.
Page 185 and 186: [91] T. Stöferle, H. Moritz, C. Sc
Page 187 and 188: [125] E. Taylor and E. Zaremba, Bog
Page 189: [157] R.M. Bradley and S. Doniach,
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