Optimization of Generalized Multichannel Quantum Defect reference functions for Feshbach resonance characterization

TL;DR

This paper demonstrates that optimizing reference functions in Generalized Multichannel Quantum Defect Theory improves the accuracy of Feshbach resonance analysis in cold atom collisions, validated through rubidium atom pair photoassociation modeling.

Contribution

It introduces a method to optimize reference functions in quantum defect theory, enhancing the modeling of Feshbach resonances in complex atomic systems.

Findings

Optimized reference functions yield weak energy dependence of quantum defects.

Agreement between quantum defect theory and Fourier Grid Hamiltonian improves with optimization.

The approach is validated on rubidium atom pair photoassociation data.

Abstract

This work stresses the importance of the choice of the set of reference functions in the Generalized Multichannel Quantum Defect Theory to analyze the location and the width of Feshbach resonance occurring in collisional cross-sections. This is illustrated on the photoassociation of cold rubidium atom pairs, which is also modeled using the Mapped Fourier Grid Hamiltonian method combined with an optical potential. The specificity of the present example lies in a high density of quasi-bound states (closed channel) interacting with a dissociation continuum (open channel). We demonstrate that the optimization of the reference functions leads to quantum defects with a weak energy dependence across the relevant energy threshold. The main result of our paper is that the agreement between the both theoretical approaches is achieved only if optimized reference functions are used.