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

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126 Macroscopic Dynamics breathing mode is found to be 2ω⊥ independent of the lattice depth. This is in agreement with the theory described above. The respective experimental data is presented in Fig. 9.4.
9.5 Small amplitude collective oscillations in the presence of harmonic trapping 127 ω/2πHz 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 Figure 9.1: Frequency of the small amplitude center-of-mass oscillation as a function of lattice depth s for the experimental setting [73]. The circles display the experimental data reported in [73]. The solid line refers to the theoretical prediction (9.51). quadrupole (Hz) 14 13 12 11 10 s 6.5 7.0 7.5 8.0 8.5 9.0 dipole (Hz) Figure 9.2: Frequency of the axial quadrupole mode of an elongated condensate trapped in the combined potential of harmonic magnetic trap and 1D optical lattice as a function of the axial dipole mode frequency measured for different values of the optical lattice depth from 0ER to 4.1ER in the experiment [75]. The line represents a linear fit with a slope of 1.57 ± 0.01. Figure taken from [75].
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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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Page 79 and 80: 6.2 Tight binding regime 75 conside
Page 81 and 82: 6.2 Tight binding regime 77 Compari
Page 83 and 84: 6.2 Tight binding regime 79 2m¯v/q
Page 85 and 86: 6.2 Tight binding regime 81 The lea
Page 87 and 88: Chapter 7 Bogoliubov excitations of
Page 89 and 90: 7.2 Bogoliubov bands and Bogoliubov
Page 97 and 98: 7.3 Tight binding regime of the low
Page 99 and 100: 7.3 Tight binding regime of the low
Page 101 and 102: 7.4 Velocity of sound 97 d|bjql| 2
Page 103 and 104: 7.4 Velocity of sound 99 c(s)/c(s=0
Page 105 and 106: Chapter 8 Linear response - Probing
Page 107 and 108: 8.1 Dynamic structure factor 103 wi
Page 109 and 110: 8.1 Dynamic structure factor 105 Th
Page 111 and 112: 8.1 Dynamic structure factor 107 Th
Page 113 and 114: 8.2 Static structure factor and sum
Page 119 and 120: Chapter 9 Macroscopic Dynamics In t
Page 121 and 122: 9.1 Macroscopic density and macrosc
Page 123 and 124: 9.2 Hydrodynamic equations for smal
Page 125 and 126: 9.4 Sound Waves 121 9.4 Sound Waves
Page 127 and 128: 9.5 Small amplitude collective osci
Page 129: 9.5 Small amplitude collective osci
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
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[31] E. Lundh, C.J. Pethick, and H.
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[63] B.P. Anderson, P.C. Haljan, C.
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[91] T. Stöferle, H. Moritz, C. Sc
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[125] E. Taylor and E. Zaremba, Bog
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[157] R.M. Bradley and S. Doniach,
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Bose-Einstein Condensates in Rotating Traps and Optical ... - BEC

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