Statistical Aspects of Ultracold Resonant Scattering

TL;DR

This paper develops a statistical multichannel quantum defect theory to analyze ultracold atom-molecule collisions, focusing on Fano-Feshbach resonances, hyperfine effects, and the emergence of Ericson fluctuations in the overlapping resonance regime.

Contribution

It introduces a novel combined theoretical framework to study the complex resonance phenomena in ultracold atom-molecule collisions, including the onset of Ericson fluctuations.

Findings

Assessment of resonance influence on threshold scattering

Dependence of resonances on hyperfine states

Exploration of Ericson fluctuations in ultracold collisions

Abstract

Compared to purely atomic collisions, ultracold collisions involving molecules have the potential to support a much larger number of Fano-Feshbach resonances due to the huge amount of ro-vibrational states available. In order to handle such ultracold atom-molecule collisions, we formulate a theory that incorporates the ro-vibrational Fano-Feshbach resonances in a statistical manner while treating the physics of the long-range scattering, which is sensitive to such things as hyperfine states, collision energy and any applied electromagnetic fields, exactly within multichannel quantum defect theory. Uniting these two techniques, we can assess the influence of highly resonant scattering in the threshold regime, and in particular its dependence on the hyperfine state selected for the collision. This allows us to explore the onset of Ericson fluctuations in the regime of overlapping resonances, which are well-known in nuclear physics but completely unexplored in the ultracold domain.