Modulated superfluid phases of lattice bosons in a non-abelian gauge field

We consider the two-component Bose-Hubbard model subject to non-abelian gauge fields that give rise to spin-orbit coupling. We obtain the phase diagram based on an extended mean field theory and find many exotic superfluid phases (polarized, striped, checkerboard). We characterize the superfluid phases by finding their collective excitations within random phase approximation (RPA) and discuss the possibility of novel topological defects.