Theory of inelastic confinement-induced resonances due to the coupling of center-of-mass and relative motion

TL;DR

This paper investigates anharmonicity-induced inelastic confinement-induced resonances in ultracold atoms, providing a perturbative model and analyzing their behavior across different geometries, including for attractive interactions, with implications for molecule formation.

Contribution

It introduces a perturbative model for inelastic confinement-induced resonances and compares it with exact calculations, expanding understanding to negative scattering lengths.

Findings

Resonances occur for both positive and negative scattering lengths.

The model accurately predicts resonance positions and strengths.

Confinement geometry can be tuned to control resonances.

Abstract

A detailed study of the anharmonicity-induced resonances caused by the coupling of center-of-mass and relative motion is presented for a system of two ultracold atoms in single-well potentials. As has been confirmed experimentally, these inelastic confinement-induced resonances are of interest, since they can lead to coherent molecule formation, losses, and heating in ultracold atomic gases. A perturbative model is introduced to describe the resonance positions and the coupling strengths. The validity of the model and the behavior of the resonances for different confinement geometries are analyzed in comparison with exact numerical ab initio calculations. While such resonances have so far only been detected for large positive values of the $s$-wave scattering length, it is found that they are present also for negative $s$-wave scattering lengths, i. e. for attractive interactions. The possibility to coherently tune the resonances by a variation of the external confinement geometry might pave the way for coherent molecule association where magnetic Feshbach resonances are inaccessible.