Multi-channel scattering and Feshbach resonances: Effective theory, phenomenology, and many-body effects

TL;DR

This paper develops a microscopic effective theory for multi-channel atom scattering and Feshbach resonances, linking detailed microscopic parameters to observable phenomena and analyzing medium effects and energy dependence in ultracold alkali gases.

Contribution

It introduces a comprehensive microscopic framework for Feshbach resonances that incorporates medium effects, energy dependence, and corrections to simplified models, with applications to $^{40}$K atoms.

Findings

Medium effects significantly influence Feshbach resonance properties.

Measurement of rethermalization rates can determine the Feshbach molecule's magnetic moment.

Energy dependence introduces a negative effective range proportional to the resonance width.

Abstract

A low energy effective theory based on a microscopic multi-channel description of the atom-atom interaction is derived for the scattering of alkali atoms in different hyperfine states. This theory describes all scattering properties, including medium effects, in terms of the singlet and triplet scattering lengths and the range of the atom-atom potential and provides a link between a microscopic description of Feshbach scattering and more phenomenological approaches. It permits the calculation of medium effects on the resonance coming from the occupation of closed channel states. The examination of such effects are demonstrated to be of particular relevance to an experimentally important Feshbach resonance for $^{40}$K atoms. We analyze a recent rethermalization rate experiment on $^{40}$K and demonstrate that a measurement of the temperature dependence of this rate can determine the magnetic moment of the Feshbach molecule. Finally, the energy dependence of the Feshbach interaction is shown to introduce a negative effective range inversely proportional to the width of the resonance. Since our theory is based on a microscopic multi-channel picture, it allows the explicit calculation of corrections to commonly used approximations such as the neglect of the effective range and the treatment of the Feshbach molecule as a point boson.