Electric-Type Stern-Gerlach Effect

TL;DR

This paper generalizes the Stern-Gerlach experiment from magnetic to electric fields by solving Dirac's equation, revealing spin-dependent spatial shifts in wave behavior with potential applications in spin separation and analysis.

Contribution

It introduces the electric-type Stern-Gerlach effect by deriving explicit wave solutions from Dirac's equation, expanding the understanding of spin interactions with electric fields.

Findings

Reflected and transmitted waves exhibit spin-dependent spatial shifts.

The effect depends on incident angle and spin orientation.

Potential applications in spin separation and measurement.

Abstract

The Stern-Gerlach (SG) experiment is a fundamental experiment for revealing the existence of ``spin''. In such an experiment, beams of silver atoms were sent through inhomogeneous magnetic fields to observe their deflection. Thus, the conventional SG experiment can be actually viewed as a magnetic-type spin effect. In this work, we successfully generalize the SG effect from magnetic-type to electric-type by solving Dirac's equation with a potential barrier, thus revealing an extraordinary spin effect. Beams of Dirac's particles can be regarded as matter waves. Based on Dirac's equation, we obtain the explicit forms of the incident, reflected, and transmitted waves. The electric-type SG effect shows that the reflected and transmitted waves can have notable spatial shifts, which depend on the spin direction and the incident angle of incident wave. The electric-type SG effect has potential applications to separating Dirac's particles with different spin directions and to estimating the spin direction of Dirac's particles. Some discussions related to the interaction between spin and electric field are also made.