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We study a model of an equal mixture of two species of fermions in a deepoptical lattice at a filling of two fermions per site. At weak inter-speciesinteraction, the system is a band insulator. When the inter-species interactionis tuned via a Feshbach resonance to be larger than an energy related to theenergy separation of the first and second Bloch band, atoms populate equallythe two Bloch bands. With weak tunneling between sites of the optical lattice,the system becomes a Mott insulator with the low energy effective Hamiltonianof a spin-1 Heisenberg antiferromagnet, because of a Hund's rule like couplingbetween the two bands. We discuss experimental signatures of these two types ofinsulators.Comment: 4 pages, 2 .eps files. Version essentially as publishe

Fermions in optical lattices near a Feshbach resonance: From band insulator to Mott insulator