Density matrix approach for quantum free-electron lasers

TL;DR

This paper introduces a density matrix approach in Lindblad form to model quantum free-electron lasers, accounting for spontaneous emission effects and providing insights into their dynamics and power evolution.

Contribution

It presents a novel density matrix formalism for quantum FELs, simplifying the description of electron and radiation dynamics and aligning with existing Wigner approach predictions.

Findings

Density matrix formalism effectively models quantum FEL dynamics.

Spontaneous emission impacts on FEL coherence are quantified.

Derived differential equation describes power evolution in the linear regime.

Abstract

The density matrix in the Lindblad form is used to describe the behavior of the Free-Electron Laser (FEL) operating in a quantum regime. The detrimental effects of the spontaneous emission on coherent FEL operation are taken into account. It is shown that the density matrix formalism provides a simple method to describe the dynamics of electrons and radiation field in the quantum FEL process. In this work, further insights on the key dynamic parameters (e.g., electron populations, bunching factor, radiation power) are presented. We also derive a simple differential equation that describes the evolution of the radiated power in the linear regime. It is confirmed that the essential results of this work agree with those predicted by a discrete Wigner approach at practical conditions for efficient operation of quantum FELs.