Quantum state features of the FEL radiation from the occupation number statistics

TL;DR

This paper introduces a maximum likelihood method to reconstruct the photon occupation number distribution of FEL radiation, aiming to confirm thermal or Poissonian statistics in SASE and seeded FELs, respectively, and extends to harmonic generation analysis.

Contribution

It proposes a novel maximum likelihood approach for reconstructing FEL radiation photon statistics from no-click events, enabling quantum state characterization without photon counting.

Findings

SASE-FEL radiation exhibits thermal photon number statistics.

Seeded-FEL light shows Poissonian photon statistics.

Method can be extended to study quantum features in harmonic generation.

Abstract

The statistical features of the radiation emitted by Free-Electron Lasers (FELs), either by Self-Amplified Spontaneous Emission (SASE-FELs) or by seeded emission (seeded-FELs), are attracting increasing attention because of the use of such light in probing high energy states of matter and their dynamics. While the experimental studies conducted so far have mainly concentrated on correlation functions, here we shift the focus towards reconstructing the distribution of the occupation numbers of the radiation energy states. In order to avoid the various drawbacks related to photon counting techniques when large numbers of photons are involved, we propose a Maximum Likelihood reconstruction of the diagonal elements of the FEL radiation states in the energy eigenbasis based on the statistics of no-click events. The ultimate purpose of such a novel approach to FEL radiation statistics is the experimental confirmation that SASE-FEL radiation exhibits thermal occupation number statistics, while seeded-FEL light Poissonian statistics typical of coherent states and thus of laser light. In this framework, it is interesting to note that the outcome of this work can be extended to any process of harmonic generation from a coherent light pulse, unlocking the gate to the study of the degree to which the original distinctive quantum features deduced from the statistical photon number fluctuations are preserved in non-linear optical processes.