Quantum kinetics of ultracold fermions coupled to an optical resonator

We study the far-from-equilibrium statistical mechanics of periodically driven fermionic atoms in a lossy optical resonator. We show that the interplay of the Fermi surface with cavity losses leads to subnatural cavity linewidth narrowing, squeezed light, and nonthermal quantum statistics of the atoms. Adapting the Keldysh approach, we set up and solve a quantum kinetic Boltzmann equation in a systematic 1/N expansion with N the number of atoms. In the strict thermodynamic limit N, V ->infinity, N/V = const. we find that the atoms (fermions or bosons) remain immune against cavity-induced heating or cooling. At next-to-leading order in 1/N, we find a one-way thermalization of the atoms determined by cavity decay. In absence of an equilibrium fluctuation-dissipation relation, the long-time limit Delta t -> infinity does not commute with the thermodynamic limit N -> infinity, such that for the physically relevant case of large but finite N, the dynamics ultimately becomes strongly coupled, especially close to the superradiance phase transition.