Chern numbers hiding in time-of-flight images

TL;DR

This paper introduces a method to detect Chern numbers, a topological invariant, directly from time-of-flight images of ultra-cold atoms, linking momentum distribution features to topological properties.

Contribution

The authors demonstrate that Chern numbers can be inferred from local maxima in momentum distributions, providing a practical experimental technique for topological state characterization.

Findings

Number of local maxima equals Chern number in certain limits

Local maxima persist across a range of parameters

Method applicable to cold atom experiments for topological detection

Abstract

We present a technique for detecting topological invariants -- Chern numbers -- from time-of-flight images of ultra-cold atoms. We show that the Chern numbers of integer quantum Hall states of lattice fermions leave their fingerprints in the atoms' momentum distribution. We analytically demonstrate that the number of local maxima in the momentum distribution is equal to the Chern number in two limiting cases, for large hopping anisotropy and in the continuum limit. In addition, our numerical simulations beyond these two limits show that these local maxima persist for a range of parameters. Thus, an everyday observable in cold atom experiments can serve as a useful tool to characterize and visualize quantum states with non-trivial topology.