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

TL;DR

This paper combines numerical and analytical methods to study atom-atom scattering under cylindrical harmonic confinement, confirming the confinement-induced resonance and exploring bound states with realistic potentials.

Contribution

It extends previous theoretical work by providing numerical validation for the confinement-induced resonance using realistic potentials and analyzing bound states under transverse confinement.

Findings

Numerical results confirm the existence of the confinement-induced resonance.

Bound states are significantly affected by transverse harmonic confinement.

The study bridges idealized models and realistic interaction potentials.

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 here