Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop

TL;DR

This paper explores the properties of ultracold Fermi gases in non-Abelian gauge potentials with constant Wilson loops, revealing a robust band structure, quantized transverse conductivity, and fractal phase diagrams akin to quantum Hall effects.

Contribution

It demonstrates the existence of a quantized Hall effect and fractal energy spectra in ultracold atoms under non-Abelian gauge potentials with constant Wilson loops, a novel insight in the field.

Findings

Robust band structure with large gaps and fractal patterns.

Quantized transverse conductivity related to topological invariants.

Presence of an anomalous Hall effect similar to graphene.

Abstract

Nowadays it is experimentally feasible to create artificial, and in particular, non-Abelian gauge potentials for ultracold atoms trapped in optical lattices. Motivated by this fact, we investigate the fundamental properties of an ultracold Fermi gas in a non-Abelian U(2) gauge potential characterized by a constant Wilson loop. Under this specific condition, the energy spectrum exhibits a robust band structure with large gaps and reveals a new fractal figure. The transverse conductivity is related to topological invariants and is shown to be quantized when the Fermi energy lies inside a gap of the spectrum. We demonstrate that the analogue of the integer quantum Hall effect for neutral atoms survives the non-Abelian coupling and leads to a striking fractal phase diagram. Moreover, this coupling induces an anomalous Hall effect as observed in graphene.