Orbital order of spinless fermions near an optical Feshbach resonance
  We study the quantum phases of a three-color Hubbard model that arises in the dynamics of the p-band orbitals of spinless fermions in an optical lattice. Strong, color-dependent interactions are induced by an optical Feshbach resonance. Starting from the microscopic scattering properties of ultracold atoms, we derive the orbital exchange constants at 1/3 filling on the cubic optical lattice. Using this, we compute the phase diagram in a Gutzwiller ansatz. We find novel phases with 'axial orbital order' in which pz and px + ipy (or px - ipy) orbitals alternate. 
Philipp Hauke, Erhai Zhao, Krittika Goyal, Ivan H. Deutsch, W. Vincent   Liu, Maciej Lewenstein
cond-mat.quant-gas cond-mat.str-el