Thomas-Fermi profile of a fast rotating Bose-Einstein condensate

TL;DR

This paper derives an effective Thomas-Fermi model for a rapidly rotating Bose-Einstein condensate, linking vortex lattice formation to the energy expansion of a homogeneous gas in a magnetic trap.

Contribution

It introduces a new effective model capturing the condensate's behavior in the fast rotation limit, connecting vortex lattice emergence to the energy of a homogeneous gas.

Findings

Derived a Thomas-Fermi-like model for fast rotating BECs

Linked vortex lattice formation to the energy expansion of a homogeneous gas

Provided a mathematical framework for the lowest Landau level states

Abstract

We study the minimizers of a magnetic 2D non-linear Schr\"odinger energy functional in a quadratic trapping potential, describing a rotating Bose-Einstein condensate. We derive an effective Thomas-Fermi-like model in the rapidly rotating limit where the centrifugal force compensates the confinement, and available states are restricted to the lowest Landau level. The coupling constant of the effective Thomas-Fermi functional is linked to the emergence of vortex lattices (the Abrikosov problem). We define it via a low density expansion of the energy of the corresponding homogeneous gas in the thermodynamic limit.