Vortices in a rotating Bose-Einstein condensate: Critical angular velocities and energy diagrams in the Thomas-Fermi regime

By Amandine Aftalion, Qiang Du. 2001

155 citations recorded by the source corpus.

For a Bose-Einstein condensate placed in a rotating trap and strongly confined along the z axis, we set a framework of study for the Gross-Pitaevskii energy in the Thomas-Fermi regime for an effective twodimensional ~2D! situation in the x-y plane. We investigate an asymptotic expansion of the energy, the critical angular velocities of nucleation of vortices with respect to a small parameter «, and the location of vortices. The limit « going to zero corresponds to the Thomas-Fermi regime. The nondimensionalized energy is similar to the Ginzburg-Landau energy for superconductors in the high-k high-field limit and our estimates rely on techniques developed for this latter problem. We also take advantage of this similarity to develop a numerical algorithm for computing the Bose-Einstein vortices. Numerical results and energy diagrams are presented.

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Citations in the corpus

Angular Momentum and Vortex Formation in Bose-Einstein-Condensed Cold Dark Matter Haloes (2011, methodology): “A similar splitting was deduced in Aftalion & Du (2001) and Rindler-Daller (2008) for laboratory BECs in the ThomasFermi regime R/ξ ≫ 1.”
Numerical solution of the Gross--Pitaevskii equation for Bose--Einstein condensation (2003, methodology): “o t= 5π(after constant stirring, i.e. W s(t) = W f for π≤ t≤ 4π) and the condensate is left to evolve freely after t= 5π. We recall that 2-dim and 3-dim vortices simulations were already performed in [14, 15, 3], here we present this example in order to put our numerical method to an important physi”
Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases (2005, background): “In general, the non-uniqueness of the GP minimizer stems from the appearance of quantized vortices, which break the axial symmetry, and hence lead to a whole continuum of GP minimizers [21, 22, 2, 3, 8, 7, 1].”
Ground-state solution of Bose--Einstein condensate by directly minimizing the energy functional (2003, methodology): “onnegative ground state solution φg(x) >0 for x∈ Rd [32]. In physical literatures, the minimizer of (3.6) was obtained by either the Runge-Kutta type method [21, 2, 3] or the imaginary time method [6, 16, 14]. Here we present a method by directly minimizing the energy functional Eκ(φ) through the”
Computing the Ground State Solution of Bose-Einstein Condensates by a Normalized Gradient Flow (2003, methodology): “9) The non-rotating Bose-Einstein condensate ground state solution φ g(x) is a real nonnegative function found by minimizing the energy E β(φ) under the constraint (1.8) [32]. In physical literatures [3, 13, 15], this minimizer was obtained by applying an imaginary time (i.e. t→ −it) in (1.1) and ev”
Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap (2009, methodology): “Some used specifically the imaginarytime propagation method [6,31,44,45].”
Ground, Symmetric and Central Vortex States in Rotating Bose-Einstein Condensates (2005, methodology): “where β2≈β 2 =β √ γz/2π and V2(x,y)= 12 ( γ(2) xx 2 +γ(2) yy 2 ) [1, 7, 8].”
Mathematical Models and Numerical Methods for Bose-Einstein Condensation (2012, methodology): “Furthermore, for the above CNGF, as observed in [5,27,91], the solution of (3.”