Short-range correlations in dilute atomic Fermi gases with spin-orbit coupling

We study the short-range correlation strength of three-dimensional spin-half dilute atomic Fermi gases with spin-orbit coupling. The interatomic interaction is modeled by the contact pseudopotential. In the high-temperature limit, we derive the expression for the second-order virial expansion of the thermodynamic potential via the ladder diagrams. We further evaluate the second-order virial expansion in the limit that the spin-orbit coupling constants are small and find that the correlation strength between the fermions increases as the fourth power of the spin-orbit coupling constants. At zero temperature, we consider the cases in which there are symmetric spin-orbit couplings in two or three directions. In such cases, there is always a two-body bound state of zero net momentum. In the limit that the average interparticle distance is much larger than the dimension of the two-body bound state, the system primarily consists of condensed bosonic molecules that fermions pair to form; we find that the correlation strength also becomes bigger compared to that in the absence of spin-orbit coupling. Our results indicate that generic spin-orbit coupling enhances the short-range correlations of the Fermi gases. Measurement of such enhancement by photoassociation experiment is also discussed.