Bound and scattering states in harmonic waveguides in the vicinity of free space Feshbach resonances

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 ${\omega }_{\perp }$ of the waveguide. Close to $p$-wave and narrow $s$-wave resonances, the resonant magnetic field changes as ${\omega }_{\perp }$ varies.

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Cited by in corpus (4)

• Probing open- and closed-channel p-wave resonances
• Width of the confinement-induced resonance in a quasi-one-dimensional trap with transverse anisotropy
• Ultracold atoms in quasi-1D traps: a step beyond the Lieb-Liniger model
• Universal energy-dependent pseudopotential for the two-body problem of confined ultracold atoms