Commensurability and hysteretic evolution of vortex configurations in rotating optical lattices

TL;DR

This paper theoretically investigates vortex behavior in a rotating Bose-Einstein condensate within an optical lattice, revealing complex energy landscapes, hysteresis, and configuration patterns dependent on commensurability, with implications for imaging vortex structures.

Contribution

It introduces a detailed theoretical model of vortex configurations in rotating optical lattices, highlighting the effects of commensurability and hysteresis on vortex arrangements.

Findings

Vortex configurations depend on the commensurability between vortex and site densities.

Hysteretic evolution of vortex states due to complex energy landscapes.

Vortices are more observable in time-of-flight images than in-situ.

Abstract

We present a theoretical study of vortices within a harmonically trapped Bose-Einstein condensate in a rotating optical lattice. Due to the competition between vortex-vortex interactions and pinning to the optical lattice we find a very complicated energy landscape, which leads to hysteretic evolution. The qualitative structure of the vortex configurations depends on the commensurability between the vortex density and the site density -- with regular lattices when these are commensurate, and concentric rings when they are not. We model the imaging of these structures by calculating time-of-flight column densities. As in the absence of the optical lattice, the vortices are much more easily observed in a time-of-flight image than \emph{in-situ}.