Fluctuations and correlations in rotating Bose-Einstein condensates

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.

Added a paragraph to Section III; Revised arguments in Section III.A, results unchanged; Added references

References in corpus (4)

• Rapidly Rotating Atomic Gases
• Quantum Hall physics in rotating Bose-Einstein condensates
• Competing Compressible and Incompressible Phases in Rotating Atomic Bose Gases at Filling Factor $\nu =2$
• Dislocation-Mediated Melting in Superfluid Vortex Lattices

Cited by in corpus (7)

• Landau critical velocity in weakly interacting Bose gases
• Bose-Einstein condensates in toroidal traps: instabilities, swallow-tail loops, and self-trapping
• Collective modes and generation of a new vortex in a trapped Bose gas at finite temperature
• Vortices in Bose-Einstein condensates - finite-size effects and the thermodynamic limit
• Vortex patterns in moderately rotating Bose-condensed gas
• Novel phases in rotating Bose-condensed gas: vortices and quantum correlation
• Correlations in lowest Landau level vortex states