Topological effects in Floquet-engineered ultracold matter

Ultracold atoms in optical lattices constitute a versatile platform to study the fascinating phenomena of gauge fields and topological matter. Periodic driving can induce topological band structures with non-trivial Chern number of the effective Floquet Hamiltonian and paradigmatic models, such as the Haldane model on the honeycomb latticce, can be directly engineered. In this talk, I will report on our recent experiments, in which we realized new approaches for measuring the Chern number in this system and map out the Haldane phase diagram. This includes time-resolved Bloch-state tomography allowing for the observation of a dynamical linking number after a quench as well as the application of machine learning techniques to analyse experimental data. In the future, the combination of gauge fields with a quantum gas microscope will allow accessing new regimes such as fractional Chern insulators.