Bose-Einstein Condensation from a Rotating Thermal Cloud: Vortex Nucleation and Lattice Formation

TL;DR

This paper develops a stochastic Gross-Pitaevskii theory to study vortex nucleation and lattice formation in a rotating Bose-Einstein condensate, revealing how vortices enter, organize, and melt in thermal equilibrium.

Contribution

It introduces a new theoretical framework for modeling vortex dynamics and lattice formation in rotating Bose gases quenched through condensation.

Findings

Vortices are trapped en masse during condensate formation.

Vortices organize into an Abrikosov lattice at low temperatures.

Lattice melting occurs with increasing temperature, reducing vortex correlations.

Abstract

We develop a stochastic Gross-Pitaveskii theory suitable for the study of Bose-Einstein condensation in a {\em rotating} dilute Bose gas. The theory is used to model the dynamical and equilibrium properties of a rapidly rotating Bose gas quenched through the critical point for condensation, as in the experiment of Haljan et al. [Phys. Rev. Lett., 87, 21043 (2001)]. In contrast to stirring a vortex-free condensate, where topological constraints require that vortices enter from the edge of the condensate, we find that phase defects in the initial non-condensed cloud are trapped en masse in the emerging condensate. Bose-stimulated condensate growth proceeds into a disordered vortex configuration. At sufficiently low temperature the vortices then order into a regular Abrikosov lattice in thermal equilibrium with the rotating cloud. We calculate the effect of thermal fluctuations on vortex ordering in the final gas at different temperatures, and find that the BEC transition is accompanied by lattice melting associated with diminishing long range correlations between vortices across the system.