Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices

We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices by studying the Bose-Fermi Hubbard model including parabolic confining potentials. We present the exact solution in the limit of vanishing hopping (ultradeep lattices) and study the resulting domain structure of composite particles. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimensionality within perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose-Fermi mixtures in optical lattices.