Spin effects on the semiclassical trajectories of Dirac electrons

TL;DR

This paper develops a semiclassical model incorporating spin effects into electron trajectories in electromagnetic fields, revealing how structured light can control spin influence and simulate Stern-Gerlach experiments.

Contribution

It introduces a Newtonian equation derived from the Dirac equation that explicitly includes spin effects in electron trajectory analysis.

Findings

Spin effects can be manipulated using structured light polarization.

The formalism clarifies the physics behind known Dirac solutions.

A Stern-Gerlach-like setup is demonstrated with electron trajectories.

Abstract

The relativistic semiclassical evolution of the position of an electron in the presence of an external electromagnetic field is studied in terms of a Newton equation that incorporates spin effects directly. This equation emerges from the Dirac equation and allows the identification of scenarios where spin effects are necessary to understand the main characteristics of the electron trajectories. It involves the eigenvalues of the non-Hermitian operator $\Sigma_{\mu\nu}F^{\mu\nu}$ with $\Sigma_{\mu\nu}$ and $F^{\mu\nu}$ as the spin and electromagnetic tensors. The formalism allows a deeper understanding on the physics behind known analytical solutions of the Dirac equation when translational dynamics decouples from spin evolution. As an illustrative example, it is applied to an electron immersed in an electromagnetic field which exhibits chiral symmetry and optical vortices. It is shown that the polarization of intense structured light beams can be used to suppress or enhance spin effects on the electron semiclassical trajectory; the latter case yields a realization of a Stern-Gerlach apparatus for an electron