Measurement of Chern numbers through center-of-mass responses

TL;DR

This paper demonstrates that center-of-mass responses in ultracold atomic systems can reveal richer topological information than traditional methods, by depending on both current density and particle density, with implications for quantum Hall effect measurements.

Contribution

It introduces a semiclassical framework showing how center-of-mass responses depend on topological invariants beyond current density, including particle density effects.

Findings

Center-of-mass response depends on both current and particle density.

The approach applies to 2D and 4D quantum Hall effects.

Numerical simulations support the theoretical predictions.

Abstract

Probing the center-of-mass of an ultracold atomic cloud can be used to measure Chern numbers, the topological invariants underlying the quantum Hall effects. In this work, we show how such center-of-mass observables can have a much richer dependence on topological invariants than previously discussed. In fact, the response of the center of mass depends not only on the current density, typically measured in a solid-state system, but also on the particle density, which itself can be sensitive to the topology of the band structure. We apply a semiclassical approach, supported by numerical simulations, to highlight the key differences between center-of-mass responses and more standard conductivity measurements. We illustrate this by analyzing both the two- and the four-dimensional quantum Hall effects. These results have important implications for experiments in engineered topological systems, such as ultracold gases and photonics.