Vortex core structure and global properties of rapidly rotating Bose-Einstein condensates

TL;DR

This paper develops a method to analyze the structure and properties of rapidly rotating Bose-Einstein condensates in harmonic traps, covering a wide range of rotation frequencies and predicting the global density profile.

Contribution

It introduces a new approach to calculate stationary states of rotating BECs, accounting for vortex core structure and global properties across different rotation regimes.

Findings

Vortex structure transitions from isolated vortex to lowest p-wave state as rotation increases.

Global density profile is predicted to be Thomas-Fermi type under typical experimental conditions.

Method applies for arbitrary rotation frequencies, bridging low and high rotation regimes.

Abstract

We develop an approach for calculating stationary states of rotating Bose-Einstein condensates in harmonic traps which is applicable for arbitrary ratios of the rotation frequency to the transverse frequency of the trap $\omega_{\perp}$. Assuming the number of vortices to be large, we write the condensate wave function as the product of a function that describes the structure of individual vortices times an envelope function, varying slowly on the scale of the vortex spacing. By minimizing the energy, we derive Gross-Pitaevskii equations that determine the properties of individual vortices and the global structure of the cloud. For low rotation rates, the structure of a vortex is that of an isolated vortex in a uniform medium, while for rotation rates approaching the frequency of the trap (the mean field quantum Hall regime), the structure is that of the lowest p-wave state of a particle in a harmonic trap with frequency $\omega_{\perp}$. The global structure of the cloud is determined by minimizing the energy with respect to variations of the envelope function; for conditions appropriate to most experimental investigations to date, we predict that the transverse density profile of the cloud will be of the Thomas-Fermi form, rather than the Gaussian structure predicted on the assumption that the wave function consists only of components in the lowest Landau level.