Validity of single-channel model for a spin-orbit coupled atomic Fermi gas near Feshbach resonances

We theoretically investigate a Rashba spin-orbit coupled Fermi gas near Feshbach resonances, by using mean-field theory and a two-channel model that takes into account explicitly Feshbach molecules in the close channel. In the absence of spin-orbit coupling, when the channel coupling $g$ between the closed and open channels is strong, it is widely accepted that the two-channel model is equivalent to a single-channel model that excludes Feshbach molecules. This is the so-called broad resonance limit, which is well-satisfied by ultracold atomic Fermi gases of $^{6}$Li atoms and $^{40}$K atoms in current experiments. Here, with Rashba spin-orbit coupling we find that the condition for equivalence becomes much more stringent. As a result, the single-channel model may already be insufficient to describe properly an atomic Fermi gas of $^{40}$K atoms at a moderate spin-orbit coupling. We determine a characteristic channel coupling strength $g_{c}$ as a function of the spin-orbit coupling strength, above which the single-channel and two-channel models are approximately equivalent. We also find that for narrow resonance with small channel coupling, the pairing gap and molecular fraction is strongly suppressed by SO coupling. Our results can be readily tested in $^{40}$K atoms by using optical molecular spectroscopy.Comment: 6 pages, 6 figure

Superfluid density and Berezinskii-Kosterlitz-Thouless transition of a spin-orbit coupled Fulde-Ferrell superfluid

We theoretically investigate the superfluid density and Berezinskii-Kosterlitz-Thouless (BKT) transition of a two-dimensional Rashba spin-orbit coupled atomic Fermi gas with both in-plane and out-of-plane Zeeman fields. It was recently predicted that, by tuning the two Zeeman fields, the system may exhibit different exotic Fulde-Ferrell (FF) superfluid phases, including the gapped FF, gapless FF, gapless topological FF and gapped topological FF states. Due to the FF paring, we show that the superfluid density (tensor) of the system becomes anisotropic. When an in-plane Zeeman field is applied along the \textit{x}-direction, the tensor component along the \textit{y}-direction $n_{s,yy}$ is generally larger than $n_{s,xx}$ in most parameter space. At zero temperature, there is always a discontinuity jump in $n_{s,xx}$ as the system evolves from a gapped FF into a gapless FF state. With increasing temperature, such a jump is gradually washed out. The critical BKT temperature has been calculated as functions of the spin-orbit coupling strength, interatomic interaction strength, in-plane and out-of-plane Zeeman fields. We predict that the novel FF superfluid phases have a significant critical BKT temperature, typically at the order of $0.1T_{F}$, where $T_{F}$ is the Fermi degenerate temperature. Therefore, their observation is within the reach of current experimental techniques in cold-atom laboratories.Comment: 11 pages, 7 figure