Determination of Chern numbers with a phase retrieval algorithm

Ultracold atoms in optical lattices form a clean quantum simulator platform which can be utilized to examine topological phenomena and test exotic topological materials. Here we propose an experimental scheme to measure the Chern numbers of two-dimensional multiband topological insulators with bosonic atoms. We show how to extract the topological invariants out of a sequence of time-of-flight images by applying a phase retrieval algorithm to matter waves. We illustrate advantages of using bosonic atoms as well as efficiency and robustness of the method with two prominent examples: the Harper-Hofstadter model with an arbitrary commensurate magnetic flux and the Haldane model on a brick-wall lattice.