Interaction of electron vortices and optical vortices with matter and processes of orbital angular momentum exchange

The quantum processes involved in the interaction of matter with, separately, an electron vortex (EV) and an optical vortex (OV) are described, with matter modeled in terms of a neutral two-particle atomic system, allowing for both the internal (electronic-type) motion and the gross (center-of-mass-type) motion of matter to be taken into account. The coupling of the atomic system to the EV is dominated by Coulomb forces, while that of the OV is taken in the $\mathbf{p}·\mathbf{A}$ canonical form which couples $\mathbf{A}$, the transverse vector potential of the optical vortex, to the linear momenta of the two-particle system. An analysis of the dipole active transition matrix element is carried out in each case. The electron vortex is found to be capable of exchanging its orbital angular momentum (OAM) with both the electronic and the center-of-mass motions of the atomic system in an electric dipole transition. In contrast, for electric dipole transitions the optical vortex is found to be capable of exchanging OAM only with the center of mass. The predictions are discussed with reference to recent experiments on electron-energy-loss spectroscopy using EVs traversing magnetized iron thin-film samples and those involving OVs interacting with chiral molecules.

Figure 1

The relevant coordinate frames in the description of the interaction between a two-particle neutral system and a Bessel-type optical or electron vortex beam (schematic). The vortex position variable ${\mathbf{r}}_v$ relative to the laboratory frame is given in cylindrical coordinates; $\mathbf{R}$ is the position variable of the atomic center of mass, and $\mathbf{q}$ stands for the position variable of the internal (electron-type) motion. The projections of the three position vector variables on the $xy$ plane are seen to have azimuthal angular positions ${\phi }_v$, ${\phi }_R$, and ${\phi }_q$ respectively.