Exact two-body solutions and Quantum defect theory of two dimensional dipolar quantum gas

TL;DR

This paper derives exact two-body solutions for a 2D dipolar quantum gas, develops an analytic quantum defect theory, and reveals unique scattering resonances across all partial waves in ultracold polar molecules.

Contribution

It provides the first exact solutions and quantum defect framework for 2D dipolar interactions, revealing novel scattering resonance phenomena.

Findings

Resonance occurs simultaneously in all partial waves for attractive interactions

Analytic quantum defect theory is constructed for 2D dipolar systems

Scattering phase shifts are significantly affected by these resonances

Abstract

In this paper, we provide the two-body exact solutions of two dimensional (2D) Schr\"{o}dinger equation with isotropic $\pm 1/r^3$ interactions. Analytic quantum defect theory are constructed base on these solutions and are applied to investigate the scattering properties as well as two-body bound states of ultracold polar molecules confined in a quasi-2D geometry. Interestingly, we find that for the attractive case, the scattering resonance happens simultaneously in all partial waves which has not been observed in other systems. The effect of this feature on the scattering phase shift across such resonances is also illustrated.