An analytical approach to atomic multichannel collisions in tight harmonic waveguides

TL;DR

This paper provides an analytical framework for understanding multichannel atomic collisions in tight harmonic waveguides, highlighting confinement-induced resonances, unitarity bounds, and channel threshold effects for different particle types.

Contribution

It introduces a generalized $K$ matrix theory approach to analyze multichannel scattering and confinement-induced resonances in harmonic waveguides, including new insights into unitarity bounds and $d$-wave effects.

Findings

Derived unitarity bounds for transition coefficients.

Identified strong transmission suppression with multiple open channels.

Analyzed channel threshold singularities based on symmetry classes.

Abstract

We perform an analytical investigation in the framework of generalized $K$ matrix theory of the scattering problem in tight isotropic and harmonic waveguides allowing for several open scattering channels. The scattering behavior is explored for identical bosons and fermions, as well as for distinguishable particles, the main aspect being the confinement-induced resonances (CIR) which are attributed to different partial waves. In particular we present the unitarity bounds which emerge when considering a quasi one dimensional system. Unitarity bounds are also given for the transition coefficients, which show the limitations for efficient transversal (de-)excitations by means of CIRs. We analyze the CIR for $d$-waves and find the intriguing phenomenon of a strong transmission suppression in the presence of more than one open channel, which represents an interesting regime to be applied in the corresponding many-particle systems. The corresponding channel threshold singularities are studied and it is shown that these are solely determined by the symmetry class of the partial wave.