  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.
