Prediction of Feshbach resonances from three input parameters

TL;DR

This paper presents a simple yet accurate model for predicting Feshbach resonances in ultracold alkali gases using only three key parameters, enabling efficient analysis and parameter extraction from experimental data.

Contribution

The authors introduce a minimal parameter model based on multichannel quantum defect theory that accurately predicts Feshbach resonance locations with limited input data.

Findings

Accurately predicts resonance locations for $^{6}$Li--$^{40}$K and $^{40}$K--$^{87}$Rb.

Matches results from more complex coupled channels calculations.

Can determine scattering lengths from experimental resonance data.

Abstract

We have developed a model of Feshbach resonances in gases of ultracold alkali metal atoms using the ideas of multichannel quantum defect theory. Our model requires just three parameters describing the interactions - the singlet and triplet scattering lengths, and the long range van der Waals coefficient - in addition to known atomic properties. Without using any further details of the interactions, our approach can accurately predict the locations of resonances. It can also be used to find the singlet and triplet scattering lengths from measured resonance data. We apply our technique to $^{6}$Li--$^{40}$K and $^{40}$K--$^{87}$Rb scattering, obtaining good agreement with experimental results, and with the more computationally intensive coupled channels technique.