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 sub-natural cavity linewidth narrowing, squeezed light, and out-of-equilibrium 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→ infty, N/V=const. we find 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. We argue that, in absence of an equilibrium fluctuation-dissipation relation, the long-time limit Δt → infty does not commute with the thermodynamic limit N→ infty, 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.