Oscillations of a Bose-Einstein condensate rotating in a harmonic plus quartic trap

TL;DR

This paper analyzes the collective excitations of a rotating Bose-Einstein condensate in a combined harmonic and quartic trap, providing analytical predictions validated by numerical simulations, especially at high angular velocities.

Contribution

It offers new analytical predictions for collective mode frequencies of a rotating BEC in complex traps, extending understanding into the giant vortex regime.

Findings

Predicted excitation frequencies at high rotation speeds.

Confirmed analytical results with numerical simulations.

Identified modes in the giant vortex regime.

Abstract

We study the normal modes of a two-dimensional rotating Bose-Einstein condensate confined in a quadratic plus quartic trap. Hydrodynamic theory and sum rules are used to derive analytical predictions for the collective frequencies in the limit of high angular velocities, $\Omega$, where the vortex lattice produced by the rotation exhibits an annular structure. We predict a class of excitations with frequency $\sqrt{6} \Omega$ in the rotating frame, irrespective of the mode multipolarity $m$, as well as a class of low energy modes with frequency proportional to $|m|/\Omega$. The predictions are in good agreement with results of numerical simulations based on the 2D Gross-Pitaevskii equation. The same analysis is also carried out at even higher angular velocities, where the system enters the giant vortex regime.