Generalized mean-field approach to a resonant Bose-Fermi mixture

We formulate a generalized mean-field theory of a mixture of fermionic and bosonic atoms, in which the fermion-boson interaction can be controlled by a Feshbach resonance. The theory correctly accounts for molecular binding energies of the molecules in the two-body limit, in contrast to the most straightforward mean-field theory. Using this theory, we discuss the equilibrium properties of fermionic molecules created from atom pairs in the gas. We also address the formation of molecules when the magnetic field is ramped across the resonance, and we present a simple Landau-Zener result for this process.