Dynamics of rapidly rotating Bose-Einstein condensates in a harmonic plus quartic trap

TL;DR

This paper investigates the behavior and vortex states of a rapidly rotating Bose-Einstein condensate in a combined harmonic and quartic trap, revealing transitions to giant vortex states through variational analysis.

Contribution

It introduces a variational approach to analyze vortex configurations and transitions in a rotating BEC with a combined trap potential, highlighting the conditions for giant vortex formation.

Findings

Identification of a critical rotation speed for central hole formation

Observation of a transition to a giant vortex state at higher rotation speeds

Analysis of the stability of vortex rings in the condensate

Abstract

A two-dimensional rapidly rotating Bose-Einstein condensate in a harmonic plus quartic trap is expected to have unusual vortex states that do not occur in a pure harmonic trap. At a critical rotation speed $\Omega_h$, a central hole appears in the condensate, and at some faster rotation speed $\Omega_g$, the system undergoes a transition to a giant vortex state with pure irrotational flow. Using a time-dependent variational analysis, we study the behavior of an annular condensate with a single concentric ring of vortices. The transition to a giant vortex state is investigated by comparing the energy of the two equilibrium states (the ring of vortices and the giant vortex) and also by studying the dynamical stability of small excitation modes of the ring of vortices.