I. P. Degiovanni, P. Traina, E. Moreva, J. Forneris, F. Piacentini, S. Ditalia Tchernij, E. Bernardi, G. Brida, I. Burenkov, E. A. Goldshmidt, S. V. Polyakov, P. Olivero, M. Genovese
In single-photon metrology the characterization of the emission statistics of the sources in order to quantifying the non-classical properties is of the utmost importance, i. e. the quality of the single photon state produced. This is particularly relevant in quantum cryptography, where uncontrolled fluctuations in the number of photons may open serious security issues. The most used parameter for this characterization is the second order Glauber’s correlation function (g(2)), which, despite having the advantage of being independent of the quantum efficiency of the detectors, has also several drawbacks, especially when one aims at the characterization of clusters of emitters or single emitters in noisy background. For these systems, new tools based on parameters that are resilient to noise and exploiting multifold coincidence events are being proven to be effective in specific contexts. In this framework we will report on the first experimental demonstration of a recently proposed criterion (Filip’s θ function)  addressed to detect nonclassical behavior in the fluorescence emission of ensembles of single-photon emitters (applied in particular to clusters of Nitrogen-Vacancy centres in diamond) . In a nutshell, the difference between the Glauber’s and the Filip’s functions is that the former relies on the multi-detection of photons in coincidence, while the latter relies on simultaneous “non-detection” of photons. We will introduce simulation results on the application of a novel technique exploiting higher order Glauber’s and Filip’s functions (θ(n) and g(n) with n > 2) simultaneously to entirely reconstruct the modes hidden in more complex optical fields such as, e.g., single photon sources in a noise-bath. This mode reconstruction method is based on optimisation algorithms requiring as input data, as said, higher order Glauber’s and Filip’s functions (that are somehow connected to high order moments of the statistics of the input photons), whose associated uncertainties increase with the order. We show that the use of both θ(n) and g(n) (rather than using only g(n) as it was done in the past) allows to reduce the functions order necessary to carry on the reconstruction, hence improving its performances.