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

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}{sub 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.

我们推导出了赝势，它描述了二维中任意分波m下两个粒子之间的散射，其散射强度根据相移\(\delta_m\)进行参数化。利用我们的m = 0赝势，我们建立了一个具有二维（2D）零程相互作用的耦合通道模型，该模型描述了费什巴赫共振中的两体物理。我们的模型预测了两个粒子的散射长度、结合能以及“闭通道分子分数”；利用现有的技术，在超冷准二维原子玻色气体和费米气体的实验中可以测量这些可观测量。