Spatial patterns in optical lattices submitted to gauge potentials

TL;DR

This paper investigates vortex formation in optical lattices under artificial gauge potentials, analyzing superfluid density and vortex rules for Abelian and non-Abelian cases, with implications for experimental observation.

Contribution

It introduces a mean-field approach to compute superfluid density and derives a rule for vortex number dependence on magnetic flux in optical lattices.

Findings

Superfluid density exhibits a rich dependence on magnetic flux.

A simple rule relates vortex number to effective magnetic flux.

Predictions are relevant for experimental optical lattice setups.

Abstract

We study the vortex formation in optical lattices submitted to artificial gauge potentials. We compute the superfluid density for Abelian and non-Abelian gauge potentials with a mean-field approach of the Bose-Hubbard model and we determine the rule describing the number of vortices as a function of the effective magnetic flux. This simple rule is represented by a remarkably rich figure that represents the superfluid density as a function of the flux. The phenomena which emanate from this work should be observed experimentally in optical lattices within which atom tunneling is laser-assisted and described by commutative or non-commutative tunneling operators.