Exotic phases of interacting p-band bosons

We study a model of interacting bosons that occupy the first excited p-band states of a two-dimensional optical lattice. In contrast to the much studied single band Bose-Hubbard Hamiltonian, this more complex model allows for non-trivial superfluid phases associated with condensation at non-zero momentum and staggered order of the orbital angular momentum in addition to the superfluid-Mott insulator transition. More specifically, we observe staggered orbital angular momentum order in the Mott phase at commensurate filling and superfluidity at all densities. We also observe a transition between the staggered angular momentum superfluid phase and a striped superfluid, with an alternation of the phase of the superfluid along one direction. The transition between these two phases was observed in a recent experiment, which is then qualitatively well described by our model.