Scattering and effective interactions of ultracold atoms with spin-orbit coupling

TL;DR

This paper derives an analytical scattering amplitude for ultracold atoms with arbitrary spin and spin-orbit coupling, revealing how SO coupling can induce scattering resonances and aiding the calculation of bound states.

Contribution

It provides a new analytical framework for understanding scattering and bound states of SO-coupled ultracold atoms, including resonance conditions and effective interaction renormalization.

Findings

SO coupling can induce scattering resonance in ultracold atoms.

Analytical expression for two-body scattering amplitude with arbitrary spin.

Renormalization relation for effective contact interaction in SO-coupled systems.

Abstract

We derive an analytical expression for the scattering amplitude of two ultracold atoms of arbitrary spin and with general spin-orbit (SO) coupling, on the basis of our recent work (Phys. Rev. A \textbf{86}, 053608 (2012)). As an application, we demonstrate that SO coupling can induce scattering resonance in the case with finite scattering length. The same approach can be applied to calculate the two-body bound state of SO-coupled ultracold atoms. For the ultracold spin-1/2 fermi gases in three- or two- dimensional systems with SO coupling, we also obtain the renormalization relation of effective contact interaction with momentum cutoff, as well as the applicability of Huang-Yang pseudo-potential.