Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy

TL;DR

This paper explores how ultracold Fermi gases in non-Abelian gauge fields exhibit quantum Hall effects, topological quantization, and fractal spectra, revealing new phases and anomalous Hall phenomena in neutral atomic systems.

Contribution

It demonstrates the persistence of quantum Hall effects and fractal spectra in ultracold atoms under non-Abelian gauge potentials with a constant Wilson loop, highlighting novel topological phases.

Findings

Quantized transverse conductivity related to topological invariants.

Presence of a fractal energy spectrum with large gaps.

Observation 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 \emph{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.