Self-calibrating photon-number-resolving detector to optimize photon statistics distribution

Abstract

We demonstrate self-calibrating of a photon-number-resolving (PNR) detector system to decrease PNR errors and optimize the photon statistics distribution. Firstly, we build a PNR detection system based on a photon-counting photomultiplier-tube single-photon detector (PMT-SPD), then use the self-calibrating method to fit photon statistics distribution of a 100 MHz pulsed laser at different counting rates. We show experimentally that our method can be used to calibrate voltage ranges of pulse height histogram corresponding to photon number states and then to optimize photon statistics distribution. It is worth mentioning that optimized photon statistics distributions agree with theoretical calculation, which shows that the optimization and reconstruction process are self-consistent and does not require any standard detectors to calibrate. Compared with preliminary reconstruction, relative errors of average photon number of optimized photon statistics distribution are reduced from 13.9%, 18%, and 21.4%, to 8%, 3.8%, and 6%, at counting rates of 1k counts per second (cps), 10k cps, and 100k cps, respectively. Our results are valuable for PNR applications such as quantum metrology, quantum radar and imaging.