Topological quantum phase transitions of ultracold fermions in optical lattices

We consider the possibility of topological quantum phase transitions of ultracold fermions in optical lattices, which can be studied as a function of interaction strength or atomic filling factor (density). The phase transitions are connected to the topology of the elementary excitation spectrum, and occur only for non-zero angular momentum pairing (p-wave, d-wave and f-wave), while they are absent for s-wave. We construct phase diagrams for the specific example of highly anisotropic optical lattices, where the proposed topological phase transitions are most pronounced. To characterize the existence of these topological transitions, we calculate several measurable quantities including momentum distribution, quasi-particle excitation spectrum, atomic compressibility, superfluid density, and sound velocities.