Upper bound for the quantum coupling between free electrons and photons

TL;DR

This paper derives a simple upper bound for the quantum coupling strength between free electrons and photons, providing practical guidance for achieving strong coupling in various optical materials and structures.

Contribution

It introduces a universal, straightforward expression for the maximum quantum coupling between free electrons and photons applicable across many optical materials.

Findings

The upper bound depends on medium, electron velocity, and separation.

Numerical calculations show coupling can reach ~99% of the upper bound.

Provides practical guidance for strong electron-photon coupling.

Abstract

The quantum interaction between free electrons and photons is fundamental to free-electron based light sources and free-electron quantum optics applications. A large coupling between free electrons and photons is generally desired. In this manuscript, I obtain the upper bound for the quantum coupling between free electrons and photons. The upper bound has a straightforward expression and can be applied to a broad range of optical materials, especially widely used low-loss photonic materials. The upper bound depends on the optical medium, the free-electron velocity, and the separation between the free electron and the optical medium. With simple structures, the numerically calculated coupling coefficient can reach ~99% of the upper bound. This study provides simple and practical guidance to reach the strong coupling between free electrons and photons.