Vortex lattices for ultracold bosonic atoms in a non-Abelian gauge potential

TL;DR

This paper investigates how non-Abelian gauge fields influence vortex lattice structures in ultracold bosonic gases, revealing significant ground state changes and effective interaction modifications, with implications for quantum Hall states.

Contribution

It introduces a model of bosonic atoms coupled to a U(2) non-Abelian gauge field and analyzes its impact on vortex lattice phases using mean-field theory.

Findings

Non-Abelian gauge fields cause dramatic changes in vortex lattice structures.

The gauge field effects mimic effective interactions with non-zero range.

Implications for strongly correlated fractional quantum Hall states are discussed.

Abstract

The use of coherent optical dressing of atomic levels allows the coupling of ultracold atoms to effective gauge fields. These can be used to generate effective magnetic fields, and have the potential to generate non-Abelian gauge fields. We consider a model of a gas of bosonic atoms coupled to a gauge field with U(2) symmetry, and with constant effective magnetic field. We include the effects of weak contact interactions by applying Gross-Pitaevskii mean-field theory. We study the effects of a U(2) non-Abelian gauge field on the vortex lattice phase induced by a uniform effective magnetic field, generated by an Abelian gauge field or, equivalently, by rotation of the gas. We show that, with increasing non-Abelian gauge field, the nature of the groundstate changes dramatically, with structural changes of the vortex lattice. We show that the effect of the non-Abelian gauge field is equivalent to the introduction of effective interactions with non-zero range. We also comment on the consequences of the non-Abelian gauge field for strongly correlated fractional quantum Hall states.