Scattering and bound states in two-dimensional anisotropic potentials

TL;DR

This paper introduces a new computational framework for analyzing scattering and bound states in anisotropic two-dimensional potentials, with applications to polar molecules in layered ultracold systems.

Contribution

It provides a systematic approximation method for phase shifts and binding energies in anisotropic 2D potentials, suitable for efficient numerical calculations.

Findings

Scattering varies significantly with polarization direction.

Interlayer binding energies exceed thermal energies at ultracold temperatures.

The method accurately predicts phase shifts and binding energies for polar molecules.

Abstract

We propose a framework for calculating scattering and bound state properties in anisotropic two-dimensional potentials. Using our method, we derive systematic approximations of partial wave phase shifts and binding energies. Moreover, the method is suitable for efficient numerical computations. We calculate the s-wave phase shift and binding energy of polar molecules in two layers polarized by an external field along an arbitrary direction. We find that scattering depends strongly on their polarization direction and that absolute interlayer binding energies are larger than thermal energies at typical ultracold temperatures.