Rashbon bound states associated with a spherical spin-orbit coupling in an ultracold Fermi gas with an $s$-wave interaction

摘要

We investigate the formation of rashbon bound states and strong-couplingeffects in an ultracold Fermi gas with a spherical spin-orbit interaction,$H_{\rm so}=\lambda{\bf p}\cdot{\bf \sigma}$ (where ${\bf\sigma}=(\sigma_x,\sigma_y,\sigma_z)$ are Pauli matrices). Extending thestrong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR) toinclude this spin-orbit coupling, we determine the superfluid phase transitiontemperature $T_{\rm c}$, as functions of the strength of a pairing interaction$U_s$, as well as the spin-orbit coupling strength $\lambda$. Evaluating polesof the NSR particle-particle scattering matrix describing fluctuations in theCooper channel, we clarify the region where rashbon bound states dominate thesuperfluid phase transition in the $U_{s}$-$\lambda$ phase diagram. Since theantisymmetric spin-orbit interaction $H_{\rm so}$ breaks the inversion symmetryof the system, rashbon bound states naturally have, not only a spin-singlet andeven-parity symmetry, but also a spin-triplet and odd-parity symmetry. Thus,our results would be also useful for the study of this parity mixing effect inthe BCS-BEC crossover regime of a spin-orbit coupled Fermi gas.