Color superfluidity of neutral ultra-cold fermions in the presence of color-flip and color-orbit fields

We describe how color superfluidity is modified in the presence of color-flip and color-orbit fields in the context of ultra-cold atoms, and discuss connections between this problem and that of color superconductivity in quantum chromodynamics. We consider s-wave interactions between different colors and we identify superfluid phases. When our system is described in a mixed color basis, the superfluid order parameter tensor is characterized by six independent components with explicit momentum dependence induced by color-orbit coupling. These results are sharp contrast to the case of zero color-flip and color-orbit fields, where the system has perfect U(3) symmetry and possess a superfluid phase that is characterized by fully gapped quasiparticle excitations with a single complex order parameter with no momentum dependence and by inert unpaired fermions representing a non-superfluid component. We analyse the order parameter tensor in a total pseudo-spin basis, investigate its momentum dependence in the singlet, triplet and quintet sectors, and compare the results with the case of spin-1/2 fermions in the presence of spin-flip and spin-orbit fields. Finally, we analyse in detail spectroscopic properties of color superfluids to help characterize all the encountered quantum phases.