Energy of a rotating Bose-Einstein condensate in a harmonic trap

TL;DR

This paper analyzes the energy and vortex structure of a rotating Bose-Einstein condensate in a harmonic trap, focusing on the Thomas-Fermi regime with high rotation speeds and providing leading order energy estimates and vortex locations.

Contribution

It introduces a detailed analysis of the ground state energy and vortex distribution for a rotating BEC in the Thomas-Fermi regime, highlighting the effects of high rotation speeds.

Findings

Leading order estimate of the ground state energy.

Location of vortices in the condensate bulk.

Shape deformation of the condensate with increasing rotation.

Abstract

The state of a rotating Bose-Einstein condensate in a harmonic trap is modeled by a wave function that minimizes the Gross-Pitaevskii functional. The resulting minimization problem has two new features compared to other similar functionals arising in condensed matter physics, such as the Ginzburg-Landau functional. Namely, the wave function is defined in all the plane and is normalized relative to the $L^2$-norm. This paper deals with the situation when the coupling constant tends to $0$ (Thomas-Fermi regime) and the rotation speed is large compared with the first critical speed. It is given the leading order estimate of the ground state energy together with the location of the vortices of the minimizing wave function in the bulk of the condensate. When the rotation speed is inversely proportional to the coupling constant, the condensate is confined in an elliptical region whose conjugate diameter shrinks and whose transverse diameter expands as the rotation speed increases.