Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials

TL;DR

This paper investigates the quantized Hall-like conductivity in cold atom systems with non-Abelian gauge potentials, demonstrating topological robustness and revealing a fractal phase diagram.

Contribution

It extends the understanding of topological quantization to non-Abelian gauge potentials in cold atom systems, showing robustness and explicit calculations.

Findings

Quantized Hall-like conductivity is related to Chern numbers.

Quantization remains robust under non-Abelian potentials.

Fractal phase diagram emerges from specific non-Abelian systems.

Abstract

We study the transport of cold fermionic atoms trapped in optical lattices in the presence of artificial Abelian or non-Abelian gauge potentials. Such external potentials can be created in optical lattices in which atom tunneling is laser assisted and described by commutative or non-commutative tunneling operators. We show that the Hall-like transverse conductivity of such systems is quantized by relating the transverse conductivity to topological invariants known as Chern numbers. We show that this quantization is robust in non-Abelian potentials. The different integer values of this conductivity are explicitly computed for a specific non-Abelian system which leads to a fractal phase diagram.