Pairing superfluidity in spin-orbit coupled ultracold Fermi gases

We review some recent progresses on the study of ultracold Fermi gases with synthetic spin-orbit coupling. In particular, we focus on the pairing superfluidity in these systems at zero temperature. Recent studies have shown that different forms of spin-orbit coupling in various spatial dimensions can lead to a wealth of novel pairing superfluidity. A common theme of these variations is the emergence of new pairing mechanisms which are direct results of spin-orbit-coupling-modified single-particle dispersion spectra. As different configurations can give rise to single-particle dispersion spectra with drastic differences in symmetry, spin dependence and low-energy density of states, spin-orbit coupling is potentially a powerful tool of quantum control, which, when combined with other available control schemes in ultracold atomic gases, will enable us to engineer novel states of matter.