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arXiv:1501.06971 · Physical Review A

Two-body state with p -wave interaction in a one-dimensional waveguide under transversely anisotropic confinement

Tianyou Gao, Shi-Guo Peng, Kaijun Jiang

Published Apr 15, 2015• 13 citations
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Abstract

We theoretically study two atoms with $p$-wave interaction in a one-dimensional waveguide, investigating how the transverse anisotropy of the confinement affects the two-body state, especially the properties of the resonance. For a bound-state solution, we find there are a total of three two-body bound states due to the richness of the orbital magnetic quantum number of the $p$-wave interaction, while only one bound state is supported by the $s$-wave interaction. Two of them become nondegenerate due to the breaking of the rotation symmetry under a transversely anisotropic confinement. For a scattering solution, the effective one-dimensional scattering amplitude and scattering length are derived. We find the position of the $p$-wave confinement-induced resonance shifts apparently versus the transverse anisotropy. In addition, a two-channel mechanism for the confinement-induced resonance in a one-dimensional waveguide is generalized to the $p$-wave interaction, which was previously proposed only for the $s$-wave interaction. All our calculations are based on the parametrization of the $^{40}\mathrm{K}$-atom experiments and can thus be confirmed in future experiments.

DOI
10.1103/physreva.91.043622

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We study the confinement-induced resonance (CIR) of 173Yb^{173}\mathrm{Yb}173Yb atoms near an orbital Feshbach resonance in a quasi-one-dimensional tube with transversal anisotropy. By solving the two-body scattering problem, we obtain the location of CIR for various anisotropy ratios and magnetic fields. Our results show that the anisotropy of the trapping potential can serve as an additional knob to tune the location of CIR. In particular, one can shift the location of CIR to the region attainable in the current experiment. We also study the energy spectrum of the system and analyze the properties of CIR from the perspective of bound states. We find that as the orbital Feshbach resonance acquires two nearly degenerate scattering channels, which in general have different threshold energies, CIR takes place when the closed-channel bound-state energy becomes degenerate with one of the thresholds.
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Abstract The two-body bound and scattering properties in an one-dimensional harmonic waveguide close to free space magnetic Feshbach resonances are investigated based on the local frame transformation approach within a single partial wave approximation. An energy and magnetic field dependent free space phase shift is adopted in the current theoretical framework. For both s - and p -wave interaction, the least bound state in the waveguide dissociates into the continuum at the resonant magnetic field where the effective one-dimensional scattering length a 1D diverges. Consequently, the association of atoms into molecules in the waveguide occurs when the magnetic field is swept adiabatically across the pole of a 1D . In the vicinity of broad s -wave resonances, the resonant magnetic field is nearly independent on the transverse confining frequency ω ⊥ of the waveguide. Close to p -wave and narrow s -wave resonances, the resonant magnetic field changes as ω ⊥ varies.
We derive one-dimensional effective Hamiltonians for spin-orbit-coupled Fermi gases confined in quasi-one-dimensional trapping potentials. For an energy regime around the two-body bound-state energy, the effective Hamiltonian takes a two-channel form, where the populations in transverse excited levels are described by dressed molecules in the closed channel. For an 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.