Mimicking multi-channel scattering with single-channel approaches

TL;DR

This paper numerically solves the full multi-channel problem of ultracold atom collisions with Feshbach resonances and evaluates how well single-channel approximations replicate key features, aiding simpler modeling of complex quantum systems.

Contribution

It provides a comprehensive numerical analysis of the multi-channel problem and assesses the validity of single-channel approaches in ultracold atomic collisions with Feshbach resonances.

Findings

Single-channel approximations qualitatively reflect multi-channel results at short distances.

SC approaches can be used to study molecular processes in external traps or many-body systems.

The conformance of SC methods is explained by the two-channel approximation for MFRs.

Abstract

The collision of two atoms is an intrinsic multi-channel (MC) problem as becomes especially obvious in the presence of Feshbach resonances. Due to its complexity, however, single-channel (SC) approximations, which reproduce the long-range behavior of the open channel, are often applied in calculations. In this work the complete MC problem is solved numerically for the magnetic Feshbach resonances (MFRs) in collisions between generic ultracold 6Li and 87Rb atoms in the ground state and in the presence of a static magnetic field B. The obtained MC solutions are used to test various existing as well as presently developed SC approaches. It was found that many aspects even at short internuclear distances are qualitatively well reflected. This can be used to investigate molecular processes in the presence of an external trap or in many-body systems that can be feasibly treated only within the framework of the SC approximation. The applicability of various SC approximations is tested for a transition to the absolute vibrational ground state around an MFR. The conformance of the SC approaches is explained by the two-channel approximation for the MFR.