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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.
A new three dimensional model of the FEL is presented. A system of scaled, coupled Maxwell Lorentz equations are derived in the paraxial limit. A minimal number of limiting assumptions are made and the equations are not averaged in the longitudinal d
A commonly held tenet is that lasers well above threshold emit photons in a coherent state, which follow a Poissonian statistics when measured in photon number. This feature is often exploited to build quantum-based random number generators or to der
In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the average error
We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap to partitions of given integers into distinct parts, studied in number theory. Using methods of quantum statistical physics we derive analytic expressions for cumulants of
When ground state atoms are accelerated through a high Q microwave cavity, radiation is produced with an intensity which can exceed the intensity of Unruh acceleration radiation in free space by many orders of magnitude. The cavity field at steady st