Devil's staircases and supersolids in a one-dimensional dipolar Bose gas

We consider a single-component gas of dipolar bosons confined in a one-dimensional optical lattice, where the dipoles are aligned such that the long-ranged dipolar interactions are maximally repulsive. In the limit of zero intersite hopping and sufficiently large on-site interaction, the phase diagram is a complete devil's staircase for filling fractions between 0 and 1, wherein every commensurate state at a rational filling is stable over a finite interval in chemical potential. We perturb away from this limit in two experimentally motivated directions involving the addition of hopping and a reduction in the on-site interaction. The addition of hopping alone yields a phase diagram, which we compute in perturbation theory in the hopping, where the commensurate Mott phases now compete with the superfluid. Further softening of the on-site interaction yields alternative commensurate states with double occupancies which can form a staircase of their own, as well as one-dimensional "supersolids" which simultaneously exhibit discrete broken symmetries and superfluidity.