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, $H_{\rm so}=λ{\bf p}\cdot{\bf σ}$ (where ${\bf σ}=(σ_x,σ_y,σ_z)$ 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 $T_{\rm c}$, as functions of the strength of a pairing interaction $U_s$, as well as the spin-orbit coupling strength $λ$. 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 $U_{s}$-$λ$ phase diagram. Since the antisymmetric spin-orbit interaction $H_{\rm so}$ 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.