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

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. (paper)