Multi-flavor bosonic Hubbard models in the first excited Bloch band of   an optical lattice
  We propose that by exciting ultra cold atoms from the zeroth to the first Bloch band in an optical lattice, novel multi-flavor bosonic Hubbard Hamiltonians can be realized in a new way. In these systems, each flavor hops in a separate direction and on-site exchange terms allow pairwise conversion between different flavors. Using band structure calculations, we determine the parameters entering these Hamiltonians and derive the mean field ground state phase diagram for two effective Hamiltonians (2D, two-flavors and 3D, three flavors). Further, we estimate the stability of atoms in the first band using second order perturbation theory and find lifetimes that can be considerable (10-100 times) longer than the relevant time scale associated with inter-site hopping dynamics, suggesting that quasi-equilibrium can be achieved in these meta-stable states. 
A. Isacsson and S. M. Girvin