Atom-atom scattering under cylindrical harmonic confinement: Numerical and analytic studies of the confinement induced resonance

It was recently predicted [Phys. Rev. Lett. 81, 938 (1998)10.1103/PhysRevLett.81.938] that atom-atom scattering under transverse harmonic confinement is subject to a “confinement-induced resonance” where the effective one-dimensional coupling strength diverges at a particular ratio of the confinement and scattering lengths. As the initial prediction made use of the zero-range pseudopotential approximation, we now report numerical results for finite-range interaction potentials that corroborate this resonance. In addition, we now present a physical interpretation of this effect as a novel type of Feshbach resonance in which the transverse modes of the confining potential assume the roles of “open” and “closed” scattering channels.