Vortex Rings in Fast Rotating Bose-Einstein Condensates

TL;DR

This paper rigorously confirms the transition threshold to the giant vortex phase in fast rotating Bose-Einstein condensates by analyzing vortex distribution and energy bounds, showing vortices gather along a specific circle below the critical speed.

Contribution

It proves the optimality of the critical rotation speed for the giant vortex transition and describes vortex arrangements near this threshold.

Findings

Vortices gather along a specific circle below the critical speed.

The critical speed for the transition is confirmed to be optimal.

New energy bounds are established to support the analysis.

Abstract

When Bose-Eintein condensates are rotated sufficiently fast, a giant vortex phase appears, that is the condensate becomes annular with no vortices in the bulk but a macroscopic phase circulation around the central hole. In a former paper [M. Correggi, N. Rougerie, J. Yngvason, {\it arXiv:1005.0686}] we have studied this phenomenon by minimizing the two dimensional Gross-Pitaevskii energy on the unit disc. In particular we computed an upper bound to the critical speed for the transition to the giant vortex phase. In this paper we confirm that this upper bound is optimal by proving that if the rotation speed is taken slightly below the threshold there are vortices in the condensate. We prove that they gather along a particular circle on which they are evenly distributed. This is done by providing new upper and lower bounds to the GP energy.