Quantum Phases of the Extended Bose-Hubbard Hamiltonian: Possibility of   a Supersolid State of Cold Atoms in Optical Lattices
  Cold atom optical lattices typically simulate zero-range Hubbard models. We discuss the theoretical possibility of using excited states of optical lattices to generate extended range Hubbard models. We find that bosons confined to higher bands of optical lattices allow for a rich phase diagram, including the supersolid phase. Using Gutzwiller, mean field theory we establish the parameter regime necessary to maintain metastable states generated by an extended Bose-Hubbard model. 
V.W. Scarola and S. Das Sarma