Fluctuations and correlations in rotating Bose-Einstein condensates

TL;DR

This paper studies how correlations affect the ground state of rotating Bose-Einstein condensates, revealing energy lowering, vortex displacement, and unstable modes, and constructs vortex states with critical rotation frequencies.

Contribution

It introduces Bogoliubov fluctuations to mean-field states, showing their impact on energy, vortex positioning, and stability in rotating Bose gases.

Findings

Correlations lower the ground state energy.

Vortex core shifts outward due to fluctuations.

Unstable modes appear at slow rotation speeds.

Abstract

We investigate the effects of correlations on the properties of the ground state of the rotating harmonically-trapped Bose gas by adding Bogoliubov fluctuations to the mean-field ground state of an $N$-particle single-vortex system. We demonstrate that the fluctuation-induced correlations lower the energy compared to that of the mean-field ground state, that the vortex core is pushed slightly away from the center of the trap, and that an unstable mode with negative energy (for rotations slower than a critical frequency) emerges in the energy spectrum, thus, pointing to a better state for slow rotation. We construct mean-field ground states of 0-, 1-, and 2-vortex states as a function of rotation rate and determine the critical frequencies for transitions between these states, as well as the critical frequency for appearance of a metastable state with an off-center vortex and its image vortex in the evanescent tail of the cloud.