Homonuclear ultracold elastic $s$-wave collisions of alkali atoms via multichannel quantum defect theory

TL;DR

This paper compares different multichannel quantum defect theory methods for modeling ultracold homonuclear alkali atom collisions, benchmarking their accuracy against numerical calculations and experimental data to understand their limitations.

Contribution

It introduces and compares three approaches for calculating the short-range K-matrix in MQDT for alkali atom collisions, highlighting their effectiveness and limitations.

Findings

MQDT approximations can accurately predict Feshbach resonance positions

Different methods vary in their agreement with experimental data

Benchmarking against coupled-channels calculations reveals approximation limitations

Abstract

Multichannel quantum defect theory (MQDT) provides a powerful toolkit for describing and understanding collisions of cold alkali atoms. Various MQDT approximations differ primarily in how they characterize the so-called short-ranged $K$-matrix, ${\mathbf K}_{\text{sr}}$, which encapsulates the short-ranged, high-energy physics into a handful of low-energy parameters that exhibit simple and smooth dependence on energy and field. Here, we compare three different methods for computing ${\mathbf K}_{\text{sr}}$ for homonuclear collisions of alkali atoms, from lithium to cesium. The MQDT calculations are benchmarked against numerically converged coupled-channels calculations that use a log-derivative propagator out to the asymptotic region. We study how well these approximations reproduce positions of $s$-wave magnetic Feshbach resonances, comparing to experiment where possible, and identify the limitations of various approximations.