Dressed molecules in an optical lattice

TL;DR

This paper develops a detailed theoretical model for atomic gases in optical lattices near Feshbach resonances, emphasizing the importance of background interactions for lithium-6 and deriving an exact two-body solution.

Contribution

It introduces a generalized Hubbard model incorporating all relevant two-body physics exactly, including background scattering for lithium-6.

Findings

Background interactions significantly affect lithium-6 near Feshbach resonance.

The model accurately captures two-body physics in optical lattices.

Background scattering can be neglected for most atoms except lithium-6.

Abstract

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 lithium-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 lithium-6 and find that the background interactions indeed have a significant effect in this case.