Optical parametric down-conversion (PDC) is a central tool in quantum optics experiments. The number of collected down-converted modes greatly affects the quality of the produced photon state. We use Silicon Photomultiplier (SiPM) number-resolving detectors in order to observe the photon-number distribution of a PDC source, and show its dependence on the number of collected modes. Additionally, we show how the stimulated emission of photons and the partition of photons into several modes determine the overall photon number. We present a novel analytical model for the optical crosstalk effect in SiPM detectors, and use it to analyze the results.

Optical parametric down-conversion is a common source for the generation of non-classical correlated photonic states. Using a parametric down-conversion source and photon-number resolving detectors, we measure the two-mode photon-number distribution of up to 10 photons. By changing the heralded collection efficiency, we control the level of correlations between the two modes. Clear evidence for photon-number correlations are presented despite detector imperfections such as low detection efficiency and other distorting effects. Two criteria, derived directly from the raw data, are shown to be good measures for the degree of correlation. Additionally, using a fitting technique, we find a connection between the measured photon-number distribution and the degree of correlation of the reconstructed original two-mode state. These observations are only possible as a result of the detection of high photon number events.PACS numbers: 42.50. Ar, 42.50.Dv, 42.65.Lm Non-classical states of light are an essential resource for novel protocols in quantum information and quantum metrology [1,2]. The most common tool for producing such states is the nonlinear process of optical parametric down-conversion (PDC). In this process, a parent pump photon is split in a nonlinear material into two daughter down-converted photons, while conserving energy and momentum. As the down-converted photons originate from a single quantum system, they possess correlations in many degrees of freedom, such as their polarization, frequency and momentum. Because for any photon emitted into one optical mode there is a sister photon emitted into the other optical mode, there are also photon-number correlations between the two modes. These correlations have been used to produce heralded Fock states [3][4][5] and enhance the precision of optical measurements [1,2,6,7].

Number-resolving single photon detectors are essential for the implementation of numerous innovative quantum information schemes. While several numberdiscriminating techniques have been previously presented, the Silicon Photo-Multiplier (SiPM) detector is a promising candidate due its rather simple integration in optical setups. On the other hand, the photon statistics obtained with the SiPM detector suffer from inaccuracies due to inherent distortions which depend on the geometrical properties of the SiPM. We have simulated the detection process in a SiPM detector and studied these distortions. We use results from the simulation in order to interpret experimental data and study the limits in which available models prevail.

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