Rashbon Bound States Associated with a Spherical Spin–Orbit Coupling in an Ultracold Fermi Gas with an s-Wave Interaction

Abstract

We investigate the formation of rashbon bound states and strong-coupling effects in an ultracold Fermi gas with a spherical spin–orbit interaction, $H_\mathrm{so}=\lambda {\varvec{p}}\cdot \mathbf{\sigma }$ (where $\mathbf{\sigma }=(\sigma _x,\sigma _y,\sigma _z)$ are Pauli matrices). Extending the strong-coupling theory developed by Nozières and Schmitt-Rink (NSR) to include this spin–orbit coupling, we determine the superfluid phase transition temperature $T_\mathrm{c}$, as functions of the strength of a pairing interaction $U_s$, as well as the spin–orbit coupling strength $\lambda$. Evaluating poles of the NSR particle–particle scattering matrix describing fluctuations in the Cooper channel, we clarify the region where rashbon bound states dominate the superfluid phase transition in the $U_s$–$\lambda$ phase diagram. Since the antisymmetric spin–orbit interaction $H_\mathrm{so}$ breaks the inversion symmetry of the system, rashbon bound states naturally have not only a spin-singlet and even-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 in the BCS–BEC crossover regime of a spin–orbit coupled Fermi gas.