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

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.

8 pages, 3 figures

References in corpus (12)

• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• BCS-BEC crossover induced by a synthetic non-Abelian gauge field
• Topological Fulde-Ferrel-Larkin-Ovchinnikov states in Spin-orbit Coupled Fermi Gases
• Unconventional superfluid in a two-dimensional Fermi gas with anisotropic spin-orbit coupling and Zeeman fields
• Majorana fermions in one-dimensional spin-orbit coupled Fermi gases
• Topological Fulde-Ferrell superfluid in spin-orbit coupled atomic Fermi gases
• Molecule and polaron in a highly polarized two-dimensional Fermi gas with spin-orbit coupling
• Conditions of Low Dimensionality for Strongly Interacting Atoms Under a Transverse Trap
• Effective low-dimensional Hamiltonian for strongly interacting atoms in a transverse trap
• Significance of dressed molecules in a quasi-two-dimensional polarized Fermi gas

Cited by in corpus (6)

• Universal few-body physics and cluster formation
• Universal relations for hybridized $s$- and $p$-wave interactions from spin-orbital coupling
• K-matrix formulation of two-particle scattering in a wave guide in the presence of one-dimensional spin-orbit coupling
• Confinement-induced Resonance of Alkaline-earth-metal-like Atoms in Anisotropic Quasi-one-dimensional Traps
• First and second sound of a unitary Fermi gas in highly elongated harmonic traps
• Confinement-Induced Resonances in Rabi-Coupled Bosonic Mixtures