Simulating quantum Hall physics in ultracold atomic gases: prospects and challenges

This proceedings presents recent advancements in the realization of topological states of matter using ultracold atomic gases. We focus on the simulation of the quantum Hall effect, originally discovered in two-dimensional electron gases subjected to a magnetic field. Given that ultracold atoms are neutral, simulating the effect of a magnetic field requires an ad-hoc technique. We review various methods developed for this purpose, highlighting their respective advantages and limitations. Furthermore, we explore the extension of these techniques to interacting quantum gases within topological bands, aiming to create analogs of fractional quantum Hall states. These many-body states are distinguished by their topological order, which is characterized by long-range entanglement among particles and the emergence of low-lying excitations exhibiting fractional quantum statistics. The discussion will encompass the current state of research and potential future directions in the field.