Ultracold-atom collisions in atomic waveguides : A two-channel analysis

TL;DR

This paper analyzes low-dimensional ultracold atom collisions near Feshbach resonances using a two-channel model, revealing how confinement affects scattering and bound states, with comparisons to zero-range models.

Contribution

It introduces a detailed two-channel analysis of ultracold atom collisions in waveguides, highlighting the effects of resonance parameters and confinement on scattering and bound states.

Findings

Resonance parameters significantly influence low-dimensional scattering.

Confinement induces bound states not present in free space.

Effective range approximation's validity varies with dimensionality.

Abstract

Low dimensional behavior of two ultra-cold atoms trapped in two-and one-dimensional waveguides is investigated in the vicinity of a magnetic Feshbach resonance. A quantitative two-channel model for the Feshbach mechanism is used allowing an exhaustive analysis of low-dimensional resonant scattering behavior and of the confinement induced bound states. The role of the different parameters of the resonance is depicted in this context. Results are compared with the ones of the zero-range approach. The relevance of the effective range approximation in low dimensions is studied. Examples of known resonances are used to illustrate the bound state properties.