Trapped Fermi Gases in Rotating Optical Lattices: Realization and Detection of the Topological Hofstadter Insulator

TL;DR

This paper proposes a cold atom setup with rotating optical lattices to realize the topological Hofstadter insulator, demonstrating how density profiles reveal spectral gaps and quantized Hall conductance.

Contribution

It introduces a method to realize and detect the Hofstadter insulator in cold atom systems using density profile measurements.

Findings

Density profiles show quantized plateaus corresponding to Hofstadter gaps.

Quantized Hall conductance can be inferred from density measurements.

Conditions for realizing the Hofstadter insulator in cold atoms are outlined.

Abstract

We consider a gas of non-interacting spinless fermions in a rotating optical lattice and calculate the density profile of the gas in an external confinement potential. The density profile exhibits distinct plateaus, which correspond to gaps in the single particle spectrum known as the Hofstadter butterfly. The plateaus result from insulating behavior whenever the Fermi energy lies within a gap. We discuss the necessary conditions to realize the Hofstadter insulator in a cold atom setup and show how the quantized Hall conductance can be measured from density profiles using the St\v{r}eda formula.