Dressed molecules in an optical lattice

We present the theory of an atomic gas in an optical lattice near a Feshbach resonance. We derive from first principles a generalized Hubbard model that incorporates all the relevant two-body physics exactly, except for the background atom - atom scattering. For most atoms, the background interactions are negligible, but this is not true for Li-6, which has an exceptionally large background scattering length near the experimentally relevant Feshbach resonance at 834 G. Therefore, we show how to include background atom - atom scattering by solving the on-site two-body Feshbach problem exactly. We apply the obtained solution to Li-6 and find that the background interactions indeed have a significant effect in this case.