Breathing Modes in Rotating Bose-Condensed Gas: An Exact Diagonalization Study

TL;DR

This study uses exact diagonalization to analyze breathing mode excitations in a rotating Bose-Einstein condensate, revealing how interactions and angular momentum influence collective excitations and symmetry breaking.

Contribution

It provides a detailed analysis of breathing modes in rotating BECs using exact diagonalization, including effects of interactions and angular momentum in a quasi-two-dimensional system.

Findings

Breathing mode frequency increases for L=0 and N with stronger interactions.

Breathing mode frequency decreases for intermediate L states as interactions grow.

First breathing mode position remains stable across a wide range of interaction strengths.

Abstract

We present an exact diagonalization study of the breathing mode collective excitations for a rotating Bose-Einstein condensate of $N=10$ spinless bosons interacting via repulsive finite-range Gaussian potential and harmonically confined in quasi-two-dimension. The yrast state and the low-lying excited states are variationally obtained in given subspaces of the quantized total angular momentum $L$ employing the beyond lowest Landau level approximation in slowly rotating regime with $0 \le L < 2N$. For a given $L$, the low-energy eigenspectra (bands) are obtained in weakly to moderately interacting regime. Further, for a given interaction, the split in low-lying eigenenergies with increasing $L$ is the precursor to spontaneous symmetry breaking of the axisymmetry associated with the entry of the first vortex. With increase in repulsive interaction, the value of the first breathing mode increases for stable total angular momentum states $L=0~\mbox{and}~N$, but decreases for intermediate $0<L<N$ metastable states. The position of the observed first breathing modes in the eigenspectrum remains unchanged as the interaction is varied over several orders of magnitude.