Quantum-classical dynamics of Rashba spin-orbit coupling

TL;DR

This paper introduces a new quantum-classical Hamiltonian model and numerical method to simulate spin-orbit coupled systems, accurately capturing dynamics beyond traditional approaches, especially in nanowire models with Rashba coupling.

Contribution

The authors develop and extend the koopmon method to treat spin-orbit coupling, improving the accuracy of quantum-classical simulations over Ehrenfest dynamics in nanowire models.

Findings

The koopmon method qualitatively reproduces fully quantum evolution across coupling regimes.

It accurately captures orbital dynamics where Ehrenfest fails.

In harmonic potentials, it matches full quantum results better than Ehrenfest.

Abstract

Mixed quantum-classical models are widely used to reduce the computational cost of fully quantum simulations. However, their general applicability across different classes of problems remains an open question. Here, we address this issue for systems featuring spin-orbit coupling. In particular, we study the interaction dynamics of quantum spin-1/2 and classical orbital momentum in one-dimensional models of Rashba nanowires. We tackle this problem by resorting to a new quantum-classical Hamiltonian model that, unlike conventional approaches, retains the Heisenberg principle and captures correlation effects beyond the common Ehrenfest approach. Based on Koopman wavefunctions in classical mechanics, the new model was recently implemented numerically via a particle scheme -- the koopmon method -- which is extended here to treat spin-orbit coupling. We apply the koopmon method to study the quantum-classical dynamics of nanowire models, with and without the presence of a harmonic potential and in both Rashba-dominated (strong coupling) and Zeeman-dominated (weak coupling) regimes. Considering realistic semiconductor parameters, the results are contrasted with both fully quantum and quantum-classical Ehrenfest dynamics. In the absence of external potential, the koopmon method qualitatively reproduces the features of the fully quantum evolution for all coupling regimes. While it exhibits a slight loss in spin accuracy compared to Ehrenfest simulations, the latter fail to capture the orbital dynamics. In the presence of a harmonic potential, the koopmon scheme reproduces the full quantum results with accuracy levels that are unachievable by the Ehrenfest model in both quantum and classical sectors. We conclude by presenting a test case that exhibits the formation of cat-like states.