Coupled-channel pseudo-potential description of the Feshbach resonance in two dimensions

TL;DR

This paper develops a pseudo-potential framework for describing two-particle scattering in two dimensions, enabling accurate modeling of Feshbach resonances in ultracold atomic gases.

Contribution

It introduces a coupled-channel pseudo-potential approach for 2D scattering, capturing Feshbach resonance physics with experimentally relevant predictions.

Findings

Predicts scattering length, binding energy, and molecular fraction across Feshbach resonances.

Provides a model applicable to ultracold quasi-2D atomic gases.

Enables experimental measurement of key two-body scattering properties.

Abstract

We derive pseudo-potentials that describe the scattering between two particles in two spatial dimensions for any partial wave m, whose scattering strength is parameterized in terms of the m-dependent phase shift. Using our m=0 pseudo-potential, we develop a coupled channel model with 2D zero-range interactions, which describes the two-body physics across a Feshbach resonance. Our model predicts the scattering length, the binding energy and the "closed channel molecular fraction" of two particles; these observables can be measured in experiments on ultracold quasi-2D atomic Bose and Fermi gases with present-day technology.