Mean-field theory of Bose–Fermi mixtures in optical lattices

We extend the results of Lewenstein et al. [Phys. Rev. Lett. 92 (2004) 050401] and determine the phase diagram of a mixture of ultracold bosons and polarized fermions placed in an optical lattice using mean field theory. We obtain the analytic form of the phase boundaries separating the composite fermion phases that involve pairing of fermions with one or more bosons, or bosonic holes, from the bosonic superfluid coexisting with Fermi liquid. We compare the results with numerical simulations and discuss their validity and relevance for current experiments. We present a careful discussion of experimental requirements necessary to observe the composite fermions and investigate their properties.