Breathing mode of rapidly rotating Bose-Einstein condensates

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.