Wave function of a photon produced in the resonant scattering of twisted light by relativistic ions

TL;DR

This paper theoretically investigates how twisted light interacts with relativistic ions, revealing that the scattered photons can also carry angular momentum, which has implications for generating twisted x- and gamma-rays at CERN's Gamma Factory.

Contribution

The authors develop a quantum state approach to analyze angular momentum transfer in resonant scattering of twisted light by ions, applicable to various ion structures.

Findings

Scattered radiation can be a superposition of twisted modes with specific angular momentum projections.

Higher angular momentum states can be generated through higher multiplicity transitions.

Resonant scattering exhibits a large cross section, making it effective for twisted photon production.

Abstract

We present a theoretical investigation of the resonant elastic scattering of twisted light, carrying angular momentum, by partially stripped ions. Special emphasis is placed on a question of whether the scattered radiation is also twisted. In order to investigate such an "angular momentum transfer", we develop an approach that allows us to find a quantum state of the final photon without projecting it onto a detector state. A general expression for this so--called \textit{evolved} state of outgoing radiation is derived and it can be used to analyze the resonant scattering by any ion, independently of its shell structure. Here, we illustrate our approach with the strong electric dipole $n S_{0} \to n' P_{1} \to n S_{0}$ transitions, which play an important role for the Gamma Factory project at CERN. For the incident Bessel light, the scattered radiation is shown to be in a superposition of twisted modes with the projections of the total angular momentum $m_f = 0, \pm 1$. The larger values of $m_f$ can be efficiently generated by inducing transitions of higher multiplicity. This angular momentum transfer, together with a remarkable cross section that is many orders of magnitude larger than that of the backward Compton scattering, makes the resonant photon scattering an effective tool for the production of twisted x-- and even gamma--rays at the Gamma Factory facility.