Superfluid-Insulator Transition of Strongly Interacting Fermi Gases in Optical Lattices

We study a quantum phase transition between fermion superfluid (SF) and band insulator (BI) of fermions in optical lattices. The destruction of the band insulator is driven by the energy gain in promoting fermions from valance band to various conducting bands to form Cooper pairs. We show that the transition must take place in rather shallow lattice height, $V_{o}/E_{R}$ between 2.23 and 4.14. The latter is the prediction of mean field theory while the former is the value for opening a band gap. As one moves across resonance to the molecule side, the SF-BI transition evolves into the SF-Mott insulator transition of bosonic molecules. We shall also present the global phase diagram for SF-Insulator transition for the BCS-BEC family.