# Determination of Chern numbers with a phase retrieval algorithm

## TL;DR

This paper introduces a novel phase retrieval algorithm to measure Chern numbers in 2D topological insulators using ultracold bosonic atoms, enabling efficient and robust topological invariant detection via time-of-flight imaging.

## Contribution

It presents a new experimental scheme combining phase retrieval with ultracold atoms to determine Chern numbers in topological insulators, improving measurement robustness.

## Key findings

- Effective extraction of Chern numbers from time-of-flight images.
- Demonstrated method's robustness with Harper-Hofstadter and Haldane models.
- Applicable to multiband topological systems with bosonic atoms.

## Abstract

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.