Vacuum Faraday effect for electrons

Abstract

The optical Faraday effect describes the rotation of linear polarization upon propagation through a medium in the presence of a longitudinal magnetic field. The effect arises from a different phase delay between the right and left handed polarization components of the light. In this paper we predict a Faraday effect for a completely different system: electron vortices. Free electron vortex states were recently observed in transmission electron microscopy experiments, and they introduce new degrees of freedom into the probing of matter with electron beams. We associate a rotation of a vortex superposition with the fact that different phases are acquired by oppositely handed vortices propagating in a magnetic field. We show that, in contrast to the optical Faraday effect, the rotation of the electron beam occurs in vacuum and arises from the intrinsic chirality of the constituent vortex states.