Jean-Philippe Brantut

Cavity quantum electrodynamics (QED) is one of the most powerful frameworks to observe and leverage quantum phenomena. While it has been thoroughly studied for simple quantum systems such as two-level systems or harmonic oscillators, it has only recently become available for complex, correlated quantum many-body systems. In the last years, we have developed systems combining cavity QED with cold Fermi gases. In this talk, I will describe these setups, and some of the intriguing consequences of the interplay of strong atom-atom and strong light-matter coupling. I will then present the use of the cavity to induce long-range interactions between, and review some of the spectacular consequences on the state of the gas.  Last, I will outline the perspectives open 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 for condensed matter and high-energy physics.