Anderson lattice description of photoassociation in an optical lattice

We consider atomic mixtures of bosons and two-component fermions in an optical lattice potential. We show that if the bosons are in a Mott-insulator state with precisely one atom per lattice, the photoassociation of bosonic and fermionic atoms into heteronuclear fermionic molecules is described by the Anderson lattice model. We determine the ground-state properties of an inhomogeneous version of that model in the strong atom-molecule coupling regime, including an additional harmonic trap potential. Various spatial structures arise from the interplay between the atom-molecule correlations and the confining potential. Perturbation theory with respect to the tunneling coupling between fermionic atoms shows that antiferromagnetic correlations develop around a spin-singlet core of fermionic atoms and molecules.