Coupled-channel pseudopotential description of the Feshbach resonance in two dimensions

Abstract

We derive pseudopotentials that describe the scattering between two particles in two dimensions for any partial wave $m$, whose scattering strength is parametrized in terms of the phase shift ${\delta }_m$. Using our $m=0$ pseudopotential, we develop a coupled-channel model with two-dimensional (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.