The ground state and its topological properties of 3D spin-orbit Coupled Degenerate Fermi Gases

3D degenerate Fermi gases in the presence of spin-orbit coupling, inducing various kinds of physical findings and phenomena, have attracted tremendous attention in these years. Here, we investigate the 3D spin-orbit Coupled degenerate Fermi gases in theory and first present the analytic expression of its ground state. Besides, our study have provided an innovative perspective into understanding the topological properties of a 3D unconventional superconductors, and described the topological phase transitions in trivial and topological phase areas, respectively. Further, such system is provided with a richer set of Cooper pairings than traditional superconductors; the dual Cooper pairs with same spin directions emerge and exhibit peculiar behaviors, leading to topological phase transitions. Our study and discussion can be generalized to some other types of unconventional superconductors and the areas of optical lattices.