Quantum theory of superfluorescence based on two-point correlation functions

TL;DR

This paper develops a quantum theoretical framework based on two-point correlation functions to describe superfluorescence phenomena in the x-ray and XUV domains, accounting for fast decay and incoherent processes.

Contribution

It introduces a generalized, correlation-based formalism for superfluorescence in high-energy regimes, including incoherent effects via Lindblad operators, extending previous optical models.

Findings

The formalism can model collective emission in various regimes.

Inclusion of incoherent processes relevant to x-ray/XUV domains.

Numerical examples align with recent experimental observations.

Abstract

Irradiation of a medium by short intense pulses from x-ray / XUV free electron lasers can result in saturated photoionization of inner electronic shells. As a result an inversion of populations between core levels appears. The resulting fluorescent radiation can be amplified during its propagation through the inverted medium and results in intense, quasi transform-limited radiation bursts. While the optical counterpart of this phenomena, known as superfluorescence, was intensively investigated, a generalized treatment is needed in the x-ray / XUV domain, where the dynamics of pumping and evolution due to fast decay processes play a crucial role. To provide a general theoretical approach, we start from the fundamental, quantized minimal coupling Hamiltonian of light-matter interaction and after a series of approximations arrive at a closed system of equations for the two-point correlation function of atomic coherences and the two-time correlation function of the emitted field. The obtained formalism enables us to investigate collective spontaneous emission in various regimes. It is extended consistently to include incoherent processes that are relevant in the x-ray / XUV domain. These processes are introduced into the formalism by corresponding Lindblad superoperators. The connection to other approaches is discussed and numerical examples related to recent experiments are presented.