Coupled $\ell$-wave confinement-induced resonances in cylindrically symmetric waveguides

TL;DR

This paper develops a semi-analytical method for understanding atomic scattering in harmonic waveguides, revealing coupled $ ext{l}$-wave confinement-induced resonances and providing analytical resonance conditions validated by numerical data.

Contribution

It introduces a comprehensive semi-analytical approach that accounts for all partial waves and their coupling in harmonic waveguides, advancing the understanding of confinement-induced resonances.

Findings

Analytical resonance conditions derived using $K$-matrix formalism.

Good agreement between analytical results and numerical data.

Identification of coupled $ ext{l}$-wave confinement-induced resonances.

Abstract

A semi-analytical approach to atomic waveguide scattering for harmonic confinement is developed taking into account all partial waves. As a consequence $\ell$-wave confinement-induced resonances are formed being coupled to each other due to the confinement. The corresponding resonance condition is obtained analytically using the $K$-matrix formalism. Atomic scattering is described by transition diagrams which depict all relevant processes the atoms undergo during the collision. Our analytical results are compared to corresponding numerical data and show very good agreement.