Annular Bose-Einstein Condensates in the Lowest Landau Level
arXiv:1009.1968
Abstract
A rotating superfluid such as a Bose-Einstein condensate is usually described by the Gross-Pitaevskii (GP) model. An important issue is to determine from this model the properties of the quantized vortices that a superfluid nucleates when set into rotation. In this paper we address the minimization of a two dimensional GP energy functional describing a rotating annular Bose-Einstein condensate. In a certain limit it is physically relevant to restrict the minimimization to the Lowest-Landau-Level, that is the first eigenspace of the Ginzburg-Landau operator. Taking the particular structure of this space into account we obtain theoretical results concerning the vortices of the condensate. We also compute the vortices' locations by a numerical minimization procedure. We find that they lie on a distorted lattice and that multiply quantized vortices appear in the central hole of low matter density.
21 pages, 4 figures. To appear in Applied Mathematic Research Express. This is an expanded and upgraded version of [X.Blanc, N.Rougerie, Lowest-Landau-Level vortex structure of a Bose-Einstein condensate rotating in a harmonic plus quartic trap, arXiv:0801.3571, Phys. Rev. A 77 (2008)]
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