Quantum simulations with optical lattices: avalanche thermalization and fractional quantum Hall states

Quantum simulations with optical lattices offer the unique opportunity to experimentally address outstanding problems in many-body quantum physics. Quantum gas microscopy brings this effort to the ultimate level of single particle control. I will talk about our recent work on two topics: First, I will report on the observation of quantum avalanches, which have been predicted as the leading instability of the many-body localized phase. Second, I will present our results on the realization of a fractional quantum Hall state, which we prepare through adiabatic quantum state engineering within the interacting Harper Hofstadter model. Our work gives new insights to non-equilibrium dynamics in disordered systems, and it provides a starting point for exploring other entangled topological matter with ultracold atoms.