Signatures of pairing and spin-orbit coupling in correlation functions of Fermi gases

We derive expressions for density-density and spin-spin correlation functions in the (greatly enhanced) pseudogap phase of spin-orbit-coupled Fermi gases. Density-density correlation functions are found to be relatively insensitive to the presence of these Rashba spin-orbit effects. To arrive at spin-spin correlation functions we derive new f-sum rules, valid even in the absence of a spin conservation law. Our spin-spin correlation functions are shown to be fully consistent with these f-sum rules. Importantly, they provide a clear signature of the Rashba band structure and separately help to establish the presence of a pseudogap.