BEC–BCS crossover in an optical lattice

Abstract

We present the microscopic theory for the BEC–BCS crossover of an atomic Fermi gas in an optical lattice, showing that the Feshbach resonance underlying the crossover in principle induces strong multiband effects. Nevertheless, the BEC–BCS crossover itself can be described by a single–band model since it occurs at magnetic fields that are relatively far away from the Feshbach resonance. A criterion is proposed for the latter, which is obeyed by most known Feshbach resonances in ultracold atomic gases.