Universal scattering phase shift in the presence of spin-orbit coupling

TL;DR

This paper develops a theoretical framework for understanding the universal low-energy scattering phase shifts of ultracold atoms with spin-orbit coupling, revealing how new parameters modify scattering behavior independently of potential details.

Contribution

It introduces a perturbative approach to include spin-orbit coupling effects and derives explicit forms of new scattering parameters for universal low-energy behavior.

Findings

Universal scattering phase shift behavior is established.

New scattering parameters depend on spin-orbit coupling.

Explicit formulas derived for spherical-square-well potential.

Abstract

Scattering phase shift, as a key parameter in scattering theory, plays an important role in characterizing low-energy collisions between ultracold atoms. In this work, we theoretically investigate the universal low-energy behavior of the scattering phase shifts for cold atoms in the presence of spin-orbit coupling. We first construct the asymptotic form of the two-body wave function when two fermions get as close as the interaction range, and consider perturbatively the correction of the spin-orbit coupling up to the second order, in which new scattering parameters are introduced. Then for elastic collisions, the scattering phase shifts are defined according to the unitary scattering $S$ matrix. We show how the low-energy behavior of the scattering phase shifts is modified by these new scattering parameters introduced by spin-orbit coupling. The universality of the scattering phase shifts is manifested as the independence of the specific form of the interatomic potential. The explicit forms of the new scattering parameters are analytically derived within a model of the spherical-square-well potential. Our method provides a unified description of the low-energy properties of scattering phase shifts in the presence of spin-orbit coupling.