Ultracold atoms in U(2) non-Abelian gauge potentials preserving the Landau levels

TL;DR

This paper investigates how U(2) non-Abelian gauge potentials affect Landau levels in ultracold atoms, classifying conditions for their preservation, and analyzing the resulting deformed quantum Hall states and energy spectra.

Contribution

It classifies conditions under which degenerate Landau levels are preserved in U(2) non-Abelian potentials and explores their physical implementation and effects on quantum Hall states.

Findings

Landau levels are deformed by non-Abelian potentials

Degeneracy of Landau levels can be preserved under specific conditions

Deformed quantum Hall states are characterized for fermions and bosons

Abstract

We study ultracold atoms subjected to U(2) non-Abelian potentials: we consider gauge potentials having, in the Abelian limit, degenerate Landau levels and we then investigate the effect of general homogeneous non-Abelian terms. The conditions under which the structure of degenerate Landau levels is preserved are classified and discussed. The typical gauge potentials preserving the Landau levels are characterized by a fictitious magnetic field and by an effective spin-orbit interaction, e.g. obtained through the rotation of two-dimensional atomic gases coupled with a tripod scheme. The single-particle energy spectrum can be exactly determined for a class of gauge potentials, whose physical implementation is explicitly discussed. The corresponding Landau levels are deformed by the non-Abelian contribution of the potential and their spin degeneracy is split. The related deformed quantum Hall states for fermions and bosons (in the presence of strong intra-species interaction) are determined far from and at the degeneracy points of the Landau levels. A discussion of the effect of the angular momentum is presented, as well as results for U(3) gauge potentials.