Lowest Landau-level description of a Bose-Einstein condensate in a rapidly rotating anisotropic trap

TL;DR

This paper extends the lowest Landau-level description of rapidly rotating Bose-Einstein condensates to anisotropic traps, deriving the wave function form and analyzing vortex arrangements and density profiles.

Contribution

It introduces a generalized wave function form for anisotropic traps, incorporating a complex variable and phase, and analyzes vortex distribution and density profiles within this framework.

Findings

Wave function includes an anisotropic Gaussian and an analytic function P(zeta)

Vortex positions are determined by zeros of P(zeta)

Density profile is anisotropic and parabolic, minimizing energy at zero temperature

Abstract

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional trap can be described with the lowest Landau-level set of states. In this case, the condensate wave function psi(x,y) is a Gaussian function of r^2 = x^2 + y^2, multiplied by an analytic function P(z) of the single complex variable z= x+ i y; the zeros of P(z) denote the positions of the vortices. Here, a similar description is used for a rapidly rotating anisotropic two-dimensional trap with arbitrary anisotropy (omega_x/omega_y le 1). The corresponding condensate wave function psi(x,y) has the form of a complex anisotropic Gaussian with a phase proportional to xy, multiplied by an analytic function P(zeta), where zeta is proportional to x + i beta_- y and 0 le beta_- le 1 is a real parameter that depends on the trap anisotropy and the rotation frequency. The zeros of P(zeta) again fix the locations of the vortices. Within the set of lowest Landau-level states at zero temperature, an anisotropic parabolic density profile provides an absolute minimum for the energy, with the vortex density decreasing slowly and anisotropically away from the trap center.