Interferometric detection of Chern numbers of Haldane model on bosonic optical lattices

Abstract

Topological states of matter emerge as a new type of quantum phases, which can be distinguished by their associated topological invariants, e.g., Chern numbers. Currently, there has been increasing interest toward the physical detection of the new predicted topological phases. Here, we propose an interferometric approach to directly measure the Chern number of the topological Haldane model in bosonic optical lattices via detecting the associated Zak phases. We show that this interferometric approach can distinguish Zak phases of from 0 in the first Brillouin zone, and thus it provides a new tool to directly detect the Chern number of topological systems. In addition, we demonstrate that this method is feasible under realistic experimental conditions and may generalize to detect topological systems with higher Chern numbers.