Number-state reconstruction with a single SPAD

Single-photon avalanche detectors (SPADs) are used ubiquitously in optical and quantum science, but they are not photon-number-resolving detectors. Despite this, in this work we present results that show that a single SPAD can still be used to perform number-state reconstruction. Through detector characterization and use of maximum-likelihood analysis, we perform number-state reconstruction with a single SPAD and obtain good agreement with independently measured distributions for both Poissonian and anti-bunched light. Our method works well for input photon much smaller than the detector inverse recovery time, and we explore the limitations of the algorithm at input rates up to roughly one input photon per dead time. Our algorithm is applicable when the light pulse has duration and correlation timescale of at least a few dead times, fitting many of today's atomic physics and quantum optics experiments.