Vortex patterns in a fast rotating Bose-Einstein condensate

TL;DR

This paper analyzes vortex lattice structures in rapidly rotating Bose-Einstein condensates, revealing distortions and energy minimization patterns using analytical and numerical methods within the Lowest Landau Level approximation.

Contribution

It introduces a method to compute and optimize vortex lattice distortions in rotating condensates, extending to various trapping potentials.

Findings

Distorted vortex lattice minimizes energy in fast rotating condensates

Analytical expressions for lattice energies are derived

Optimal distortions relate to wave function decay patterns

Abstract

For a fast rotating condensate in a harmonic trap, we investigate the structure of the vortex lattice using wave functions minimizing the Gross Pitaveskii energy in the Lowest Landau Level. We find that the minimizer of the energy in the rotating frame has a distorted vortex lattice for which we plot the typical distribution. We compute analytically the energy of an infinite regular lattice and of a class of distorted lattices. We find the optimal distortion and relate it to the decay of the wave function. Finally, we generalize our method to other trapping potentials.