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

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154 Sound propagation in presence of a one-dimensional optical lattice n φ / π 0.8 −200 −100 0 100 200 n φ / π 1.2 1 1 0.5 0 0.5 −1 −200 −100 0 100 200 1.2 1 1 0.5 0 0.5 x / d 0.8 −200 −100 0 100 200 −1 −200 −100 0 100 200 x / d Figure 11.9: Sound signals in the saturation regime at an early (t = 16¯h/ER; upper two panels) and a late stage (t = 200¯h/ER; lower two panels) for a deep lattice with δ/U ≪ 1/3. Firstand third panel from top: Relative density nℓ(t)/nℓ(t =0)obtained from the DNLS-simulation. Second and forth panel from top: Relative phase (11.11) obtained from the DNLS-simulation.
∆ n ( U / δ ) 1/2 1 0.8 0.6 0.4 0.2 11.3 Nonlinear propagation of sound signals 155 0 0 3 6 9 12 15 T p b / w ∆ φ / π 0.25 0 0 3 6 9 12 15 T p b / w Figure 11.10: Results for the density and relative signal amplitudes ∆n and ∆φ obtained from DNLS simulations for varying barrier parameters TP ,b,w(see Eq.(11.1)), tunnel coupling δ and on-site interaction U (see Eq.(11.8)) with δ ≪ U/3. This is in agreement with the behavior we find for ∆n in the first (linear) and even in the second (shockwave) regime as summarized in Fig. 11.10. The first order approximation to sin(φℓ±1/2) in φℓ±1/2 is valid for ∆φ
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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
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 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 155 and 156: 11.3 Nonlinear propagation of sound
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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 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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Bose-Einstein Condensates in Rotating Traps and Optical ... - BEC

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