Fractional-filling loophole insulator domains for ultracold bosons in optical superlattices

The zero-temperature phase diagram of a Bose-Einstein condensate confined in realistic one-dimensionall-periodic optical superlattices is investigated. The system of interacting bosons is modeled in terms of aBose-Hubbard Hamiltonian whose site-dependent local potentials and hopping amplitudes reflect the periodicityof the lattice partition in l-site cells. Relying on the exact mapping between the hardcore limit of theboson Hamiltonian and the model of spinless noninteracting fermions, incompressible insulator domains areshown to exist for rational fillings that are predicted to be compressible in the atomic limit. The correspondingboundaries, qualitatively described in a multiple-site mean-field approach, are shown to exhibit an unusualloophole shape. A more quantitative description of the loophole domain boundaries at half filling for the specialcase l=2 is supplied in terms of analytic strong-coupling expansions and quantum Monte Carlo simulations.