Annular Bose-Einstein Condensates in the Lowest Landau Level

Abstract

A rotating superuid such as a Bose-Einstein condensate is usually described by the GrossPitaevskii (GP) model. An important issue is to determine from this model the properties of the quantized vortices that a superuid 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 minimization to the LowestLandau-Level, that is the rst 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 nd that they lie on a distorted lattice and that multiple quantized vortices appear in the central hole of low matter density.