The giant vortex state for a Bose-Einstein condensate in a rotating anharmonic trap : extreme rotation regimes

TL;DR

This paper investigates the extreme rotation regimes of a Bose-Einstein condensate in an anharmonic trap, revealing the emergence of a giant vortex state characterized by a central hole and irrotational flow.

Contribution

It introduces a rigorous analysis of the giant vortex state formation in rapidly rotating BECs within anharmonic traps, deriving energy asymptotics and identifying the vortex structure.

Findings

Giant vortex state appears at high rotation speeds.

Energy and density asymptotics are derived from a simplified model.

The vortex state features a central low-density hole with macroscopic phase circulation.

Abstract

We study the fast rotation limit for a Bose-Einstein condensate in a quadratic plus quartic confining potential within the framework of the two dimensional Gross-Pitaevskii energy functional. As the rotation speed tends to infinity with a proper scaling of the other parameters in the model, a linear limit problem appears for which we are able to derive precise energy estimates. We prove that the energy and density asymptotics of the problem can be obtained by minimizing a simplified one dimensional energy functional. In the case of a fixed coupling constant we also prove that a giant vortex state appears. It is an annulus with pure irrotational flow encircling a central low-density hole around which there is a macroscopic phase circulation.