Abstract
In this talk, I will describe experiments where an ultracold Fermi gas is strongly coupled to light in optical resonators. In such a system, virtual photon exchanges between atoms yield a long-range, all-to-all interaction leading to a number of emergent phenomena. I will describe how it induces charge-density wave ordering, and the observation of this transition in real time and with high spatial resolution. I will also discuss extensions of this physics to photon-pair interactions in a superfluid, and show first evidences for pair-density wave ordering in this case. II will then outline the perspectives opened by the convergence of cavity QED with complex quantum matter, in particular the possibility of programming cavity-mediated interactions, and the application of these ideas to quantum simulation of exotic quantum matter such as the SYK model.
