Modified Bethe-Peierls boundary condition for ultracold atoms with Spin-Orbit coupling

TL;DR

This paper derives a modified Bethe-Peierls boundary condition for ultracold atoms with spin-orbit coupling, accounting for anisotropy and the dependence of scattering length on SO coupling, aiding future few- and many-body studies.

Contribution

The authors present a general form of the modified BP boundary condition applicable to arbitrary spin-orbit coupling in ultracold atoms, revealing conditions where the scattering length remains unaffected.

Findings

Modified BP boundary condition includes anisotropic terms.

Scattering length can be SO-coupling independent in specific systems.

Result aids in understanding few- and many-body physics with SO coupling.

Abstract

We show that the Bethe-Peierls (BP) boundary condition should be modified for ultracold atoms with spin-orbit (SO) coupling. Moreover, we derive a general form of the modified BP boundary condition, which is applicable to a system with arbitrary kind of SO coupling. In the modified BP condition, an anisotropic term appears and the inter-atomic scattering length is normally SO-coupling dependent. For the special system in the current experiments, however, it can be proved that the scattering length is SO-coupling independent, and takes the same value as in the case without SO coupling. Our result is helpful for the study of both few-body and many-body physics in SO-coupled ultracold gases.