K-matrix formulation of two-particle scattering in a wave guide in the presence of one-dimensional spin-orbit coupling

TL;DR

This paper develops a K-matrix scattering framework to analyze two-particle interactions in a wave guide with spin-orbit coupling, revealing how resonances can be tuned by geometry, interactions, and coupling effects.

Contribution

It introduces a novel K-matrix approach for multi-channel scattering with spin-orbit coupling in wave guides, extending low-energy effective models to higher energy regimes.

Findings

Resonance tunability via wave guide geometry and spin-orbit coupling.

Good agreement with effective low-energy Hamiltonian when energy dependence is included.

Natural description of energy regimes involving excited transverse modes.

Abstract

The creation of artificial gauge fields in neutral ultracold atom systems has opened the possibility to study the effects of spin-orbit coupling terms in clean environments. This work considers the multi-channel scattering properties of two atoms confined by a wave guide in the presence of spin-orbit coupling terms within a K-matrix scattering framework. The tunability of resonances, induced by the interplay of the external wave guide geometry, the interactions, and the spin-orbit coupling terms, is demonstrated. Our results for the K-matrix elements as well as partial and total reflection coefficients for two identical fermions interacting through a finite-range interaction potential in the singlet channel only are compared with those obtained for a strictly one-dimensional effective low- energy Hamiltonian, which uses the effective coupling constant derived in Zhang et al. [Scientific Reports 4, 1 (2014)] and Zhang et al. [Phys. Rev. A 88, 053605 (2013)] as input. In the regime where the effective Hamiltonian is applicable, good agreement is obtained, provided the energy- dependence of the coupling constant is accounted for. Our approach naturally describes the energy regime in which the bands associated with excited transverse modes lie below a subset of the bands associated with the lowest transverse modes. The threshold behavior is discussed and scattering observables are linked to bound state properties.