Analytical model of overlapping Feshbach resonances

TL;DR

This paper develops an analytical multichannel quantum defect theory model to accurately describe overlapping Feshbach resonances in ultracold collisions, surpassing simple two-channel models.

Contribution

It introduces a general formula for scattering length variation near multiple overlapping resonances, validated against numerical calculations.

Findings

The model accurately predicts scattering length behavior near overlapping resonances.

Excellent agreement with coupled channels numerical calculations.

Applicable to collisions of $^7$Li and Cs atoms.

Abstract

Feshbach resonances in ultracold collisions often result from an interplay between many collision channels. Simple two-channel models can be introduced to capture the basic features, but cannot fully reproduce the situation when several resonances from different closed channels contribute to the scattering process. Using the formalism of multichannel quantum defect theory we develop an analytical model of overlapping Feshbach resonances. We find a general formula for the variation of the scattering length with magnetic field in the vicinity of an arbitrary number of resonances, characterized by simple parameters. Our formula is in excellent agreement with numerical coupled channels calculations for several cases of overlapping resonances in the collisions of two $^7$Li atoms or two Cs atoms.