Topological many-body states with ultracold rydberg atoms
Understanding and controlling quantum matter is a key challenge for basic research and for the development of applications. The richness of quantum physics is notoriously difficult to handle for strong interactions, usually leading to massive entanglement between particles, especially when it is associated with a nontrivial topology of the Hamiltonian. The realization of well-controlled experiments probing strongly correlated quantum matter is thus a major objective to explore these perspectives.  In this project, I will investigate many-body states of quantum matter in- and out-of-equilibrium. I will study the interplay between topology and interactions in tailored model systems and explore new quantum phases of matter. I will focus on two main objectives: (i) The study of dynamical properties of strongly interacting 1D Bose gases using quantum transport experiments. (ii) The realization of fractional Chern insulator states in topological lattices. These objectives will be achieved thanks to ultracold gases of Rydberg atoms, where the excellent control of quantum gases is extended thanks to the strong interactions between Rydberg particles.