Compton Upconversion of Twisted Photons: Backscattering of Particles with Non-Planar Wave Functions

TL;DR

This paper explores the generation of high-energy twisted photons via backward Compton scattering of laser photons on ultra-relativistic electrons, highlighting a new formalism to describe their scattering process and potential experimental applications.

Contribution

It introduces a novel approach to produce high-energy twisted photons and extends the scattering formalism to account for their non-plane wave quantum states.

Findings

High-energy twisted photons can be produced with increased energy via backward scattering.

The usual cross section concept is modified for twisted particles, requiring an averaged cross section.

Potential applications include atomic, nuclear, and particle physics experiments.

Abstract

Twisted photons are not plane waves, but superpositions of plane waves with a defined projection hbar m of the orbital angular momentum onto the propagation axis (m is integer and may attain values m >> 1). Here, we describe in detail the possibility to produce high-energy twisted photons by backward Compton scattering of twisted laser photons on ultra-relativistic electrons with a Lorentz-factor gamma=E/(m_e c^2) >> 1. When a twisted laser photon with the energy hbar omega ~ 1 eV performs a collision with an electron and scatters backward, the final twisted photon conserves the angular momentum m, but its energy hbar omega' is increased considerably: omega'/omega=4 gamma^2/(1+x), where x=4E hbar omega/(m_e c^2)^2. The S matrix formalism for the description of scattering processes is particularly simple for plane waves with definite 4-momenta. However, in the considered case, this formalism must be enhanced because the quantum state of twisted particles cannot be reduced to plane waves. This implies that the usual notion of a cross section is inapplicable, and we introduce and calculate an averaged cross section for a quantitative description of the process. The energetic upconversion of twisted photons may be of interest for experiments with the excitation and disintegration of atoms and nuclei, and for studying the photo-effect and pair production off nuclei in previously unexplored regimes.