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

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[77] M. Cristiani, O. Morsch, N. Malossi, M. Jona-Lasinio, M. Anderlini, E. Courtade, E. Arimondo, Instabilities of a Bose-Einstein condensate in a periodic potential: an experimental investigation, cond-mat/0311160. [78] O. Morsch, J.H. Müller, D. Ciampini, M. Cristiani, P.B. Blakie, C.J. Williams, P.S. Julienne, and E. Arimondo, Decay and revival of phase coherence of a Bose-Einstein condensate in a one-dimensional lattice, Phys. Rev. A 67, 031603 (2003). [79] J.H. Denschlag, J.E. Simsarian, H. Häffner, C. McKenzie, A. Browaeys, D. Cho, K. Helmerson, S.L. Rolston and W.D. Phillips, A Bose-Einstein condensate in an optical lattice, J. Phys. B 35, 3095 (2002). [80] A.S. Mellish, G. Duffy, C. McKenzie, R. Geursen, A.C. Wilson, Nonadiabatic loading of a Bose-Einstein condensate into the ground state of an optical lattice, Phys. Rev. A 68, 051601 (2003). [81] B. Eiermann, P. Treutlein, T. Anker, M. Albiez, M. Taglieber, K.P. Marzlin, M.K. Oberthaler, Dispersion management for atomic matter waves, Phys. Rev. Lett. 91, 060402 (2003). [82] L. Fallani, F.S. Cataliotti, J. Catani, C. Fort, M. Modugno, M. Zawada, M. Inguscio, Optically-induced lensing effect on a Bose-Einstein condensate expanding in a moving lattice, cond-mat/0303626. [83] Th. Anker, M. Albiez, B. Eiermann, M. Taglieber, M.K. Oberthaler, Linear and nonlinear dynamics of matter wave packets in periodic potentials, cond-mat/0401165. [84] B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.P. Marzlin, M.K. Oberthaler, Bright gap solitons of atoms with repulsive interaction, condmat/0402178. [85] S. Burger, F.S. Cataliotti, C. Fort, P. Maddaloni, F. Minardi, M. Inguscio, Quasi-2D Bose-Einstein condensation in an optical lattice, Europhys. Lett. 57, 1 (2002). [86] F. Ferlaino, P. Maddaloni, S. Burger, F.S. Cataliotti, C. Fort, M. Modugno, M. Inguscio, Dynamics of a Bose-Einstein condensate at finite temperature in an atomoptical coherence filter, Phys. Rev. A 66, 011604(R) (2002). [87] M. Greiner, I. Bloch, O. Mandel, T.W. Hänsch, and T. Esslinger, Exploring Phase Coherence in a 2D Lattice of Bose-Einstein Condensates, Phys. Rev. Lett. 87, 160405 (2001). [88] H. Moritz, T. Stöferle, M. Köhl, and T. Esslinger, Exciting Collective Oscillations in a Trapped 1D Gas, Phys. Rev. Lett. 91, 250402 (2003). [89] C. Orzel, A.K. Tuchmann, M.L. Fenselau, M. Yasuda, and M.A. Kasevich, Squeezed States in a Bose-Einstein Condensate, Science 291, 2386 (2001). [90] M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch and I. Bloch, Quantum Phase Transition from a Superfluid to a Mott Insulator in a gas of ultracold atoms, Nature 415, 39 (2002).
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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 and 180: Bibliography [1] L. Pitaevskii and
Page 181 and 182: [31] E. Lundh, C.J. Pethick, and H.
Page 183: [63] B.P. Anderson, P.C. Haljan, C.
Page 187 and 188: [125] E. Taylor and E. Zaremba, Bog
Page 189: [157] R.M. Bradley and S. Doniach,
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