Devil's staircase and supersolidity in one-dimensional dipolar Bose gases

The classical ground states of particles in a convex repulsive potential are known to have a phase portrait displaying a complete devil's staircase structure. 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. Introducing a kinetic term tunes the system away from the classical limit and results in a phase diagram with a Mott- Hubbard lobe for each rational filling fraction. Tuning the on- site interaction away from convexity 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.