Non-equilibrium dynamics of strongly interacting Bose-Fermi mixtures

We develop a conserving dynamical theory of a degenerate Bose-Fermi mixture near an interspecies Feshbach resonance. In contrast to the typical Hartree-Fock-Bogoliubov approximation, our beyond Gaussian theory correctly embeds the microscopic two-body physics in the gas, which is enhanced by the competing influences of the Fermi sea and the Bose-Einstein condensate. We benchmark our theory by studying atom-pair coherence near the Feshbach resonance, where our results show excellent agreement with analytical predictions. Next, we apply our theory to a deep quench of the gas to the unitary regime, characterizing the resulting depletion of the condensate, the deformation of the Fermi surface, and the production of molecules. We furthermore discuss how our theory can be extended to include boson-boson interactions mediated by the fermionic cloud, which were recently observed in experiments.