Modeling of single-photon avalanche diode photon counts from spontaneous parametric down-conversion using fractional Poisson processes

This work introduces a novel, to our knowledge, approach using a dead-time-modified generalized fractional Poisson process (GFPP) to model the interarrival time statistics of photon counts from a spontaneous parametric down-conversion (SPDC) light source. The model accurately describes the experimental interarrival time histograms across a range of photon count rates, with power-law behavior at short timescales and exponential decay at long timescales. The analysis of the fitted parameters ( ξ , α and β ) reveals that the detection process can be characterized as a dead-time-modified Erlang-type process ( β ≈1), where the fractional order 0< α <1 quantifies the temporal clustering of photon detection events attributed to afterpulsing and twilight pulses. Cross-validation through Monte Carlo simulations confirms that the photon count distributions are consistent with the interarrival time analysis.