Extracting the Chern number from the dynamics of a Fermi gas: Implementing a quantum Hall bar for cold atoms

TL;DR

This paper presents a method to measure the Chern number in a cold atom Fermi gas by observing the center of mass dynamics under a constant force, providing a direct link to topological invariants.

Contribution

It introduces a novel scheme to extract the Chern number from atomic cloud dynamics, bridging topological physics and cold atom experiments.

Findings

Center of mass displacement correlates with the Chern number.

Strong driving forces are necessary for measurable displacements.

Qualitative semi-classical analysis explains cloud shape dynamics.

Abstract

We propose a scheme to measure the quantized Hall conductivity of an ultracold Fermi gas initially prepared in a topological (Chern) insulating phase, and driven by a constant force. We show that the time evolution of the center of mass, after releasing the cloud, provides a direct and clear signature of the topologically invariant Chern number. We discuss the validity of this scheme, highlighting the importance of driving the system with a sufficiently strong force to displace the cloud over measurable distances while avoiding band-mixing effects. The unusual shapes of the driven atomic cloud are qualitatively discussed in terms of a semi-classical approach.