Effective Hamiltonians for quasi-one-dimensional Fermi gases with spin-orbit coupling

TL;DR

This paper derives effective one-dimensional Hamiltonians for spin-orbit coupled Fermi gases in quasi-one-dimensional traps, revealing how confinement and spin-orbit effects influence two-body bound states and resonances.

Contribution

It introduces two-channel and single-channel effective Hamiltonians for different energy regimes, incorporating spin-orbit coupling and Zeeman fields, and explains confinement-induced resonances as Feshbach resonances.

Findings

Effective Hamiltonians for different energy regimes

Spin-orbit coupling modifies resonance positions

Resonance shifts are observable with current technology

Abstract

We derive one-dimensional effective Hamiltonians for spin-orbit coupled Fermi gases confined in quasi-one-dimensional trapping potentials. For energy regime around the two-body bound state energy, the effective Hamiltonian takes a two-channel form, where the population in transverse excited levels are described by dressed molecules in the closed channel. For energy regime slightly above the continuum threshold, the effective Hamiltonian takes a single-channel form, where low-energy physics is governed by the one-dimensional interacting strength determined by three-dimensional scattering length and transverse confinement. We further discuss the effect of spin-orbit coupling and effective Zeeman field on the position of confinement-induced resonances, and show that these resonances can be understood as Feshbach resonances between the threshold of the transverse ground state and the two-body bound state associated with the transverse excited states. We expect that the shift of confinement-induced resonances can be observed under present experimental technology at attainable temperatures.