Measuring quantum states of light is at the basis of both the investigations of fundamental Quantum Optics and of the applications of Quantum Information. Several different detection strategies can be exploited to measure the different aspects of light. For instance, optical homodyne detection addresses the wave-like properties of optical states while direct detection explores the particle-like features. Moreover, new hybrid schemes addressing both wave-like and particle-like aspects of light have recently been introduced. As to direct detection, different intensity regimes can be investigated by either single-photon detectors, photon-number resolving (PNR) detectors or macroscopic detectors.
In particular, PNR detectors can give access to the number of photons in pulsed states, thus allowing the reconstruction of the photon-number statistics, of auto- and cross-correlations, both in the classical and in the quantum domain. Among the many kinds of PNR detectors available nowadays (also including fiber-loop detectors, visible-light photon counters, transition-edge sensors and superconductive nanowires), we used hybrid photodetectors (HPDs) and Si-photomultipliers (SiPM) that have the advantage of a rather easy operation at room temperature. Of course also such detectors are affected by imperfections, such as a limited dynamic range and rather low repetitions rate (HPDs) or dark count and cross talk (SiPM). Moreover, both classes of detectors have rather low quantum efficiencies (about 50%), which nevertheless do not prevent measuring quantum features of light.
We elaborated a model of the detectors and the detection chain and devised self-consistent calibration strategies to be performed on the very light under investigation. The calibration value is then used to evaluate shot-by-shot detected-photon numbers that, of course, also include all the effects (dark count and cross talk) characterizing the detectors. By using the numbers measured at each shot, statistics and correlations can be evaluated.
In spite of their limitations, by using HPDs and SiPMs we demonstrated the reconstruction of photon-number statistics of classical and nonclassical states, we measured classical and quantum correlations and we generated non-Gaussian and sub-Poissonian conditional states.