Transition to the Giant Vortex State in an Harmonic Plus Quartic Trap

TL;DR

This paper investigates the transition from a vortex lattice to a giant vortex state in a rapidly rotating Bose-Einstein condensate confined in a harmonic plus quartic trap, using variational analysis and numerical solutions.

Contribution

It provides a detailed phase diagram of the transition between vortex lattice and giant vortex states based on variational and numerical methods.

Findings

Phase boundary mapped as a function of rotation rate and trap parameters

Good qualitative agreement between variational and numerical results

Identification of conditions favoring the giant vortex state

Abstract

We consider a rapidly rotating Bose-condensed gas in an harmonic plus quartic trap. At sufficiently high rotation rates the condensate acquires an annular geometry with the superposition of a vortex lattice. With increasing rotation rate the lattice evolves into a single ring of vortices. Of interest is the transition from this state to the giant vortex state in which the circulation is carried by only a central vortex. By analyzing the Gross-Pitaevskii energy functional variationally, we have been able to map out the phase boundary between these two states as a function of the rotation rate and the various trapped gas parameters. The variational results are in good qualitative agreement with those obtained by means of a direct numerical solution of the Gross-Pitaevskii equation.