Energy and Vorticity in Fast Rotating Bose-Einstein Condensates

TL;DR

This paper analyzes the ground state energy of a rapidly rotating Bose-Einstein condensate in a finite trap, revealing the vortex lattice structure and energy contributions in a specific strong coupling regime.

Contribution

It provides an exact evaluation of the next-to-leading order energy contribution in the strong coupling limit, including vortex lattice effects, within a precise parameter regime.

Findings

Exact next-to-leading order energy in the strong coupling limit.

Vortex lattice density proportional to rotational velocity.

Energy contributions include centrifugal forces and vortex effects.

Abstract

We study a rapidly rotating Bose-Einstein condensate confined to a finite trap in the framework of two-dimensional Gross-Pitaevskii theory in the strong coupling (Thomas-Fermi) limit. Denoting the coupling parameter by $1/\eps^2$ and the rotational velocity by $\Omega$, we evaluate exactly the next to leading order contribution to the ground state energy in the parameter regime $|\log\eps|\ll \Omega\ll 1/(\eps^2|\log\eps|)$ with $\eps\to 0$. While the TF energy includes only the contribution of the centrifugal forces the next order corresponds to a lattice of vortices whose density is proportional to the rotational velocity.