Landau levels and the Thomas-Fermi structure of rapidly rotating Bose-Einstein condensates

TL;DR

This paper demonstrates that rapidly rotating Bose-Einstein condensates exhibit Thomas-Fermi density profiles and explores the structure of their wave functions, showing slight vortex lattice distortions are energetically favorable and consistent with experimental observations.

Contribution

It introduces a variational approach to model vortex lattice distortions in rapidly rotating BECs within the lowest Landau level approximation.

Findings

Thomas-Fermi density profile applies at high vortex densities

Slight vortex lattice distortions are energetically preferred

Predicted distortions align with experimental data

Abstract

We show that, within mean-field theory, the density profile of a rapidly rotating harmonically trapped Bose-Einstein condensate is of the Thomas-Fermi form as long as the number of vortices is much larger than unity. Two forms of the condensate wave function are explored: i) the lowest Landau level (LLL) wave function with a regular lattice of vortices multiplied by a slowly varying envelope function, which gives rise to components in higher Landau levels; ii) the LLL wave function with a nonuniform vortex lattice. From variational calculations we find it most favorable energetically to retain the LLL form of the wave function but to allow the vortices to deviate slightly from a regular lattice. The predicted distortions of the lattice are small, but in accord with recent measurements at lower rates of rotation.