Bose–Fermi mixtures near an interspecies Feshbach resonance: testing a non-equilibrium approach

We test a non-equilibrium approach to study the behaviour of a Bose–Fermi mixture of alkali atoms in the presence of a Feshbach resonance between bosons and fermions. To this end we derive the Hartree–Fock–Bogoliubov (HFB) equations of motion for the interacting system. This approach has proven very successful in the study of resonant systems composed of Bose particles and Fermi particles. However, when applied to a Bose–Fermi mixture, the HFB theory fails to identify even the correct binding energy of molecules in the appropriate limit. Through a more rigorous analysis we are able to ascribe this difference to the peculiar role that noncondensed bosons play in the Bose–Fermi pair correlation, which is the mechanism through which molecules are formed. We therefore conclude that molecular formation in Bose–Fermi mixtures is driven by three-point and higher-order correlations in the gas.