Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance

Abstract

In a recent article [M. Olshanii, Phys. Rev. Lett. {\bf 81}, 938 (1998)], an analytic solution of atom-atom scattering with a delta-function pseudopotential interaction in the presence of transverse harmonic confinement yielded an effective coupling constant that diverged at a `confinement induced resonance.' In the present work, we report numerical results that corroborate this resonance for more realistic model potentials. In addition, we extend the previous theoretical discussion to include two-atom bound states in the presence of transverse confinement, for which we also report numerical results hereComment: New version with major revisions. We now provide a detailed physical interpretation of the confinement-induced resonance in tight atomic waveguide