Quantum states of p-band bosons in optical lattices

We study a gas of repulsively interacting bosons in the first excited band of an optical lattice. We explore this p-band physics both within the framework of a standard mean-field theory as well as with the more accurate generalized Gutzwiller ansatz. We find the phase diagrams for two- and three-dimensional systems and characterize the first Mott-states which typically possess an integer or half-integer vortex structure. Furthermore, we find that even though the p-band model has strongly anisotropic kinetic energies and interflavor interaction terms are missing in the lowest band theory, the mean-field theory becomes useful quite rapidly once the transition from the Mott insulator to the superfluid is crossed.