Annular Bose-Einstein Condensates in the Lowest Landau Level

A rotating superfluid such as a Bose–Einstein condensate (BEC) 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 BEC. In a certain limit, it is physically relevant to restrict the minimization 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 multiple quantized vortices appear in the central hole of low matter density.