On Exchange of Orbital Angular Momentum Between Twisted Photons and Atomic Electrons

TL;DR

This paper derives formulas describing how twisted photons with orbital angular momentum transfer their angular momentum to atomic electrons during scattering, revealing new insights into light-matter interactions involving structured light.

Contribution

It provides the first explicit expressions for OAM transfer in elastic scattering of Laguerre-Gaussian photons from atoms, focusing on the regime where wavelength exceeds atomic size.

Findings

Derived simple formulas for OAM transfer in elastic scattering

Identified conditions where OAM transfer is maximized

Showed the dependence of OAM exchange on beam and atomic parameters

Abstract

We obtain an expression for the matrix element for a twisted (Laguerre-Gaussian profile) photon scattering from a hydrogen atom. We consider photons incoming with an orbital angular momentum (OAM) of $\ell \hbar$, carried by a factor of $e^{i \ell \phi}$ not present in a plane-wave or pure Gaussian profile beam. The nature of the transfer of $+2\ell$ units of OAM from the photon to the azimuthal atomic quantum number of the atom is investigated. We obtain simple formulae for these OAM flip transitions for elastic forward scattering of twisted photons when the photon wavelength $\lambda$ is large compared with the atomic target size $a$, and small compared the Rayleigh range $z_R$, which characterizes the collimation length of the twisted photon beam.