Breathing mode of rapidly rotating Bose-Einstein condensates

TL;DR

This paper models the breathing mode of rapidly rotating Bose-Einstein condensates using a generalized wave function, deriving a mode frequency of twice the trap frequency, consistent with experimental observations.

Contribution

It introduces a generalized LLL wave function with variable oscillator length to analyze the breathing mode in rotating BECs, extending understanding beyond linear oscillations.

Findings

Breathing mode frequency is 2 times the trap frequency in 2D.

The mode frequency matches experimental data in 3D cases.

Large-amplitude oscillations do not alter the fundamental frequency result.

Abstract

We show that the breathing mode of a rapidly-rotating, harmonically-trapped Bose-Einstein condensate may be described by a generalized lowest Landau level (LLL) wave function, in which the oscillator length is treated as a variable. Using this wave function in a variational Lagrangian formalism, we show that the frequency of the breathing mode for a two-dimensional cloud is $2\omega_{\perp}$, where $\omega_{\perp}$ is the trap frequency. We also study large-amplitude oscillations and confirm that the above result is not limited to linear oscillations. The resulting mode frequency can be understood in terms of orbits of a single particle in a harmonic trap. The mode frequency is also calculated for a cloud in three dimensions and the result for the axial breathing mode frequency agrees with recent experimental data in the rapid rotation regime.