Resonance-facilitated three-channel p-wave scattering

TL;DR

This paper introduces a resonance-facilitated three-channel model for p-wave Feshbach resonances, explaining complex threshold effects with a simplified approach that captures the influence of a closed-channel shape resonance.

Contribution

The study develops a novel three-channel model that simplifies the analysis of Feshbach resonances by mediating all coupling through the Feshbach state, improving upon traditional two-channel models.

Findings

The three-channel model accurately explains the nonlinear binding energy variation.

The resonance-facilitated structure reduces model complexity.

The model captures the effects of a closed-channel shape resonance.

Abstract

Feshbach resonances of arbitrary width are typically described in terms of two-channel models. Within these models, one usually considers a single dressed resonance, with the option to extend the analysis by including resonant open-channel features that can drastically change the observed threshold effects. For the strong $^{40}\mathrm{K}$ p-wave resonance studied in Ref. \cite{ahmed2021}, the interplay between an open-channel shape resonance and the Feshbach resonance could explain the unexpected nonlinear variation of the binding energy with magnetic field. However, the presented two-channel treatment relies on the introduction of two independent fitting parameters, whereas the typical Breit-Wigner expression would only account for one. This results in an effective magnetic moment that acquires a nonphysical value, which is an indication of a major shortcoming of the two-channel model treatment. In this study, we observe how the presence of a closed-channel shape resonance explains the physical mechanism behind the observations and demonstrates the need of a three-channel treatment. We introduce our novel model as \textit{resonance facilitated}, where all coupling is mediated by the Feshbach state, while there is no direct coupling between the additional channel and the open channel. Notably, the resonance-facilitated structure greatly reduces the complexity of the full three-channel model. The typical Breit-Wigner form of the two-channel Feshbach formalism is retained and the full effect of the added channel can be captured by a single resonance dressing factor, which describes how the free propagation in the Feshbach state is dressed by the added channel.