Superfuid-insulator transitions at noninteger filling in optical lattices of fermionic atoms

We determine the superfluid transition temperatures T-c and the ground states of the attractive Hubbard model and find unusual insulating phases associated with noninteger filling at sufficiently strong pairing attraction vertical bar U vertical bar. These states, distinct from the band-and Mott-insulating phases, derive from pair localization; pair hopping at large vertical bar U vertical bar and high densities is impeded by intersite, interpair repulsive interactions. The best way to detect the breakdown of superfluidity is by using fermionic optical lattices, which should reveal these unusual forms of "bosonic" order, reflecting ground-state pairing without condensation.