Cavity quantum electrodynamics (QED) is one of the most powerful framework 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 five years, we have developed systems combining cavity QED with ultra-cold Fermi gases [1]. In this talk, I will describe several intriguing consequences of the interplay of strong atom-atom and strong light-matter coupling, such as the onset of coherent excitations mixing Fermion-pairs and photons, pair-polaritons [2] or the coupling of density fluctuations with light [3]. I will then present the use of the cavity to induce long-range interactions in a strongly-interacting Fermi gas, leading to density-wave order, a system of direct relevance to condensed matter physics. Last I will outline the perspectives open by the convergence of cavity QED with Fermionic quantum matter, in particular the possibility of programming cavity-mediated interactions at will between atoms.
[1] K. Roux, H. Konishi, V. Helson and J.P. Brantut, Nature Communications 11 2074 (2020)
[2] H. Konishi, K. Roux, V. Helson and J.P. Brantut, Nature 596 509 (2021)
[3] V. Helson, T. Zwettler, K. Roux, H. Konishi, S. Uchino and J.P. Brantut arXiv:2111.02931 (2021)