Self-consistent Photon Number Resolving Detector System to Optimize Photon Statistics Distribution

We establish the photon number resolution (PNR) model and calculate the conversion coefficient which can be used to optimize the voltage grouping of pulse heights corresponding to different photon number states. Then we build a self-consistent PNR detection system based on photon-counting photomultiplier, and directly obtain the photon statistics distribution of 100-MHz pulsed laser at different counting rates. We demonstrate experimentally that our model can be used to acquire more accuracy average photon number, and optimize photon statistics distribution without any calibration of the detector. Our results are valuable to precision measurements such as quantum metrology and quantum radar.