Vortex structures in rotating Bose-Einstein condensates

TL;DR

This paper provides an exact analytical solution for vortex lattices in rapidly rotating Bose-Einstein condensates, exploring density deviations, geometrical effects, and phase transitions with varying interaction and rotation parameters.

Contribution

It introduces an exact analytical solution for vortex structures in rotating BECs in the lowest Landau level, including phase diagrams and transition orders for different geometries.

Findings

Exact solution for vortex lattice in rotating BECs

Identification of phase transitions between vortex row states

Analysis of density deviations from Thomas-Fermi profile

Abstract

We present an analytical solution for the vortex lattice in a rapidly rotating trapped Bose-Einstein condensate (BEC) in the lowest Landau level and discuss deviations from the Thomas-Fermi density profile. This solution is exact in the limit of a large number of vortices and is obtained for the cases of circularly symmetric and narrow channel geometries. The latter is realized when the trapping frequencies in the plane perpendicular to the rotation axis are different from each other and the rotation frequency is equal to the smallest of them. This leads to the cancelation of the trapping potential in the direction of the weaker confinement and makes the system infinitely elongated in this direction. For this case we calculate the phase diagram as a function of the interaction strength and rotation frequency and identify the order of quantum phase transitions between the states with a different number of vortex rows.