Comment on: "Nonlinear quantum effects in electromagnetic radiation of a vortex electron"

TL;DR

This paper defends the experimental findings of Remez et al. against criticisms by Karlovets and Pupasov-Maximov, clarifying the conditions under which their theoretical derivations are valid and emphasizing the significance of shaped electron wavefunctions in spontaneous emission.

Contribution

It clarifies the validity of experimental regimes and theoretical derivations related to spontaneous emission of shaped electron wavefunctions, correcting misconceptions in prior criticisms.

Findings

The criticism by Karlovets and Pupasov-Maximov is shown to be false using optical arguments and simulations.

The theoretical derivations are valid only when the electron's final state is observed with the emitted photon.

New expressions for emission rates beyond the paraxial approximation are provided.

Abstract

This comment on the Phys. Rev. A paper "Nonlinear quantum effects in electromagnetic radiation of a vortex electron" by Karlovets and Pupasov-Maximov [Phys. Rev. A 103, 12214 (2021)] addresses their criticism of the combined experimental and theoretical study "Observing the quantum wave nature of free electrons through spontaneous emission" by Remez et al, published in Phys. Rev. Lett. [Phys. Rev. Lett. 123, 060401 (2019)]. We show, by means of simple optical arguments as well as numerical simulations, that the criticism raised by Karlovets and Pupasov-Maximov regarding the experimental regime reported by Remez et al is false. Further, we discuss a necessary clarification for the theoretical derivations presented by Karlovets and Pupasov-Maximov, as they only hold for a certain experimental situation where the final state of the emitting electron is observed in coincidence with the emitted photon - which is not the common scenario in cathodoluminescence. Upon lifting the concerns regarding the experimental regime reported by Remez et al, and explicitly clarifying the electron post-selection, we believe that the paper by Karlovets and Pupasov-Maximov may constitute a valuable contribution to the problem of spontaneous emission by shaped electron wavefunctions, as it presents new expressions for the emission rates beyond the ubiquitous paraxial approximation.