Observation of the Larmor and Gouy Rotations with Electron Vortex Beams

TL;DR

This paper reports the observation of Larmor and Gouy rotations in electron vortex beams, revealing unique rotational phenomena due to orbital angular momentum interactions with magnetic lenses, confirmed by experiments aligning with theoretical predictions.

Contribution

It demonstrates the first experimental observation of Larmor and Gouy rotations in electron vortex beams, highlighting phenomena absent in optical systems.

Findings

Larmor rotation is independent of OAM magnitude.

Gouy phase causes OAM-dependent Gouy rotation.

Combined effects lead to additive or subtractive rotations.

Abstract

Electron vortex beams carrying intrinsic orbital angular momentum (OAM) are produced in electron microscopes where they are controlled and focused using magnetic lenses. We observe various rotational phenomena arising from the interaction between the OAM and magnetic lenses. First, the Zeeman coupling, proportional to the OAM and magnetic field strength, produces an OAM-independent Larmor rotation of a mode superposition inside the lens. Second, hen passing through the focal plane, the electron beam acquires an additional Gouy phase dependent on the absolute value of the OAM. This brings about the Gouy rotation of the superposition image proportional to the sign of the OAM. A combination of the Larmor and Gouy effects can result in the addition (or subtraction) of rotations, depending on the OAM sign. This behaviour is unique to electron vortex beams and has no optical counterpart, as Larmor rotation occurs only for charged particles. Our experimental results are in agreement with recent theoretical predictions.