Anderson Lattice Description of Photoassociation in an Optical Lattice

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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 anti-ferromagnetic correlations develop around a spin-singlet core of fermionic atoms and molecules.