Measurement of Chern numbers through center-of-mass responses
  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. 
H. M. Price, O. Zilberberg, T. Ozawa, I. Carusotto and N. Goldman
cond-mat.quant-gas cond-mat.mes-hall