Analytic description of atomic interaction at ultracold temperatures II: Scattering around a magnetic Feshbach resonance

TL;DR

This paper provides an analytic framework for describing atomic interactions near magnetic Feshbach resonances across different partial waves, enabling precise control and understanding of ultracold atomic scattering.

Contribution

It introduces a universal analytic formula for scattering near Feshbach resonances of any partial wave, expanding the theoretical tools for ultracold atomic physics.

Findings

Derived an analytic formula applicable to broad and narrow resonances of any partial wave

Provided rigorous definitions for broad and narrow resonances and their scattering characteristics

Showed how to tune effective range parameters using magnetic fields

Abstract

Starting from a multichannel quantum-defect theory, we derive analytic descriptions of a magnetic Feshbach resonance in an arbitrary partial wave $l$, and the atomic interactions around it. An analytic formula, applicable to both broad and narrow resonances of arbitrary $l$, is presented for ultracold atomic scattering around a Feshbach resonance. Other related issues addressed include (a) the parametrization of a magnetic Feshbach resonance of arbitrary $l$, (b) rigorous definitions of "broad" and "narrow" resonances of arbitrary $l$ and their different scattering characteristics, and (c) the tuning of the effective range and the generalized effective range by a magnetic field.