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-dimensional $\ell$-periodic optical superlattices is investigated. The system of interacting bosons is modeled in terms of a Bose-Hubbard Hamiltonian whose site-dependent local potentials and hopping amplitudes reflect the periodicity of the lattice partition in $\ell$-site cells. Relying on the exact mapping between the hard-core limit of the boson Hamiltonian and the model of spinless noninteracting fermions, incompressible insulator domains are shown to exist for rational fillings that are predicted to be compressible in the atomic limit. The corresponding boundaries, qualitatively described in a {\it multiple-site} mean-field approach, are shown to exhibit an unusual loophole shape. A more quantitative description of the loophole domain boundaries at half filling for the special case $\ell$ = 2 is supplied in terms of analytic strong-coupling expansions and quantum Monte Carlo simulations.