Generation of High-Energy Photons with Large Orbital Angular Momentum by Compton Backscattering

Abstract: Usually, photons are described by plane waves with a definite 4-momentum. In addition to plane-wave photons, "twisted photons" have recently entered the field of modern laser optics; these are coherent superpositions of plane waves with a defined projection hbar*m of the orbital angular momentum onto the propagation axis, where m is integer. In this paper, we show that it is possible to produce high-energy twisted photons by Compton backscattering of twisted laser photons off ultra-relativistic electrons. Such photons may be of interest for experiments related to the excitation and disintegration of atoms and nuclei, and for studying the photo-effect and pair production off nuclei in previously unexplored experimental regimes.

• The paper's main contribution is demonstrating that Compton backscattering of twisted photons preserves orbital angular momentum while boosting photon energy.
• It employs integration over conical momentum components to construct twisted photon states with defined orbital angular momentum projections.
• Findings offer new experimental avenues in atomic, nuclear, and particle physics through enhanced high-energy photon manipulation.

Generation of High-Energy Photons with Large Orbital Angular Momentum by Compton Backscattering

Introduction

The production of high-energy photons possessing significant orbital angular momentum has practical applications in modern optics and particle physics. This paper explores the generation of such photons via the Compton backscattering of twisted laser photons off ultra-relativistic electrons. This mechanism potentially provides new avenues for experimental investigations into complex atomic, nuclear, and particulate interactions under previously untested conditions.

Twisted Photon Construction

Twisted photons distinguish themselves from conventional plane-wave photons through defined projections of angular momentum ($\hbar m$) along their propagation axis. This paper elaborates on the formation of twisted photon states with specified longitudinal momentum $k_z$, transverse momentum $\varkappa$, and orbital angular momentum projection $m$. The twisted states are synthesized by integrating over a spectrum of conical momentum components, which introduces rotational symmetry into the photonic wavefronts. This integration allows the quantum states to maintain a discrete set of angular momentum states, specifically $m-1$, $m$, and $m+1$, thereby supporting the creation of an "almost defined" angular momentum composite.

Compton Backscattering Mechanics

The paper extends the known Compton scattering framework to encompass twisted photons. Through the interaction, an ultra-relativistic electron collides with a twisted photon, which maintains its conical momentum distribution but experiences significant energy elevation. The analysis employs relativistic Gaussian units and detailed calculations to show how the conversion is feasible.

For traditional plane-wave photons, Compton backscattering mechanics are fastidious, leading to substantial practical use in high-energy physics. The research adapts these established formulas to the kinematic and polarization peculiarities of twisted photons. It calculates the scattering matrix $S^{\rm (TW)}_{fi}$ through integration over the momentum space, hence determining how these high-energy twisted photons might conserve their unique structural properties (orbital angular momentum) post-scattering.

High-Energy Photon Generation

The crucial result of the study is that twisted photons' orbital angular momentum is preserved through backscattering in defined geometries, most effectively when strict scattering angles are maintained. For scenarios involving perfect backscattering angles, expressions for the invariant matrix elegantly reduce, allowing substantial amplification of photon energy while retaining the original twisting attributes.

Practical Implications and Future Directions

Twisted photons with large orbital angular momentum and high-energy profiles can significantly enhance experiments related to atomic excitations, Rydberg state transitions, nuclear photo-effects, and the study of tightly bound orbital states. Prospective inquiries could investigate the influence of these photons on high-spin nuclear states or their utility in invoking nuclear fission under novel conditions.

The paper outlines critical engineering needs for detecting such photon-nucleus interactions given their small scattering angles post interaction. Future developments may include the refinement of such detection apparatuses or the exploration of new scattering configurations.

Conclusion

This analysis of generating high-energy twisted photons through Compton backscattering marks an essential contribution to advancing photon manipulation in experimental physics. These findings offer prospects for unlocking new experimental techniques and flood new light on interactions at the intersection of quantum mechanics, nuclear dynamics, and laser optics. This study paves the way for thorough experimental and theoretical exploration in manipulating high-angular-momentum photons at unprecedented energy levels.