Understanding photon-count dynamics is crucial for applications such as quantum random number generators and quantum key distributions, where random and memoryless photon-count arrival processes are essential for performance and security. We investigated the fluctuation dynamics of aggregated photon-count time series for two distinct light sources: a 780-nm laser diode and a spontaneous parametric down-conversion source, using detrended fluctuation analysis (DFA) and the index of dispersion for intervals (IDI). Despite the degradation of photon statistics to Poissonian due to optical losses and detector inefficiencies, our analysis reveals significant long-range dependence at large timescales. The DFA scaling exponents α[over ¯]>0.75 and IDI values c_{k}^{2}>1 at high mean photon count and large aggregation timescales indicate photon-count fluctuations deviated from Poisson model. Our findings underscore the necessity of models beyond Poisson statistics to accurately describe the photon-count dynamics over extended timescales.
Understanding photon-count dynamics is crucial for applications such as quantum random number generators and quantum key distributions, where random and memoryless photon-count arrival processes are essential for performance and security. We investigated the fluctuation dynamics of aggregated photon-count time series for two distinct light sources: a 780-nm laser diode and a spontaneous parametric down-conversion source, using detrended fluctuation analysis (DFA) and the index of dispersion for intervals (IDI). Despite the degradation of photon statistics to Poissonian due to optical losses and detector inefficiencies, our analysis reveals significant long-range dependence at large timescales. The DFA scaling exponents α[over ¯]>0.75 and IDI values c_{k}^{2}>1 at high mean photon count and large aggregation timescales indicate photon-count fluctuations deviated from Poisson model. Our findings underscore the necessity of models beyond Poisson statistics to accurately describe the photon-count dynamics over extended timescales.
Abstract This study investigates photon-count fluctuation dynamics of two light sources, namely a spontaneous parametric down-conversion (SPDC) light source and a 780 nm attenuated laser diode (LD). White noise integral with customizable memory function is used to model the mean square displacements (MSDs) and the probability density functions (PDFs) for both light sources. This approach overcomes the limitation of monofractal scaling of fractional Brownian motion (fBm) model characterized by a single Hurst exponent. The memory function used has an exponential-tempered power-law relation, parametrized by μ and β, where β modulates the extent of memory parameter μ. Although optical losses and detector inefficiencies degrade photon statistics to Poissonian at post-detection, our findings reveal notable memory effects at higher mean photon counts, especially in the SPDC source with memory parameter μ ⪆ 1.00, compared to the classical LD, which remained relatively constant at μ ⪅ 1.00. Both light sources shared similar correction parameters β, which indicates they have identical photon-count fluctuations at short time but diverge significantly at longer time. This work highlights the need for models beyond fBm, capable of capturing complex MSD behaviors of photon-count fluctuations.
We investigate the fluctuation dynamics of photons generated by spontaneous parametric down conversion (SPDC) using detrended fluctuation analysis (DFA). SPDC photon pairs were generated via a periodically poled potassium titanyl phosphate waveguide, pumped by a 405 nm continuous-wave laser. The scaling exponents obtained from DFA reveal that SPDC photons exhibit long-range correlations at high pump power regimes. The average scaling exponent of DFA increases from 0.67 to 0.97 as the laser diode drive current increases, indicating the existence of long-range correlations. Our analysis concluded that the scaling exponent of aggregated time series is correlated to the number of SPDC photon pairs.
Constraints on the Origin of Universal 1/f2 Photon-Count Spectra at Baseband
A series of 11.6-d-duration photon-counting experiments, employing a broad variety of light sources with different statistical properties and optical spectra, were carried out over a 1.5-yr period. All of the photon-count spectra at baseband followed a common 1/f2 form over the frequency range 1×10−6⩽f⩽5×10−4 Hz, corresponding to a timescale range 33 min $ \leqslant T_f \leqslant 11.6$ d, where Tf≡1/f. The lower and upper timescale limits were established by the photodetector noise floor and the duration of the individual experiments, respectively. Unlike ordinary Brownian motion, all of the measured photon-count sample paths exhibited irregular long-timescale fluctuations, with durations ranging from hours to days. It has been established that the photon-count spectra cannot plausibly be ascribed to fluctuations of the current, voltage, or temperature of the source or the detector, nor to technical sources of noise associated with the optical system or local environment. Although the physical origin of the photon-count fluctuations remains unresolved, several heterodox hypotheses are set forth. From a statistical point-of-view, the photon counts appear to follow a doubly stochastic Poisson process with a slowly varying random intensity. Analogous experiments that rely on ionizing radiation and direct-conversion solid-state radiation detectors are proposed.
Abstract Photon counting provides a valuable tool for measuring quantum properties of light. Unavoidable imperfections of photon detectors lead to discrepancies between the statistics of photons and statistics of photon counts. Here we consider dead-time corrections and influence of intensity fluctuations for simulated Poissonian statistics of photo counts for the pulsed or continuous wave coherent light sources. We analyse dependence between the statistical moments of corrected distribution and the mean photon number, dead-time, and level of intensity fluctuations.
If a beam of light is coherent, then the photons constituting the beam arrive at random moments in time. Consequently, the photon counting statistics in a given time interval below the coherence time, should in theory follow a Poissonian distribution. When the measurement interval exceeds the coherence time, the distribution should broaden and become a super-Poissonian distribution. The aim of this study is to experimentally demonstrate the Poissonian nature of light, as well as quantifying the transition to a super-Poissonian distribution. In the experiment, a low-intensity laser beam was measured with single-photon detectors, able to capture individual photons. The arrival time of the photons was detected with an oscilloscope, and the data further analysed with our own Python code. The probability distribution of the arrival time of photons was constructed and fitted with a Poissonian distribution for different time intervals. The results showed a clear Poissonian distribution for all intervals from 0.2 μs up to 2000 μs. We did however, observe tendencies of randomness for the longest measured intervals. A Poissonian distribution is defined by the variance being equal to the mean, whilst for a super-Poissonian distribution the variance is higher. The biggest measured ratio between the variance and the mean in our experiment was 1.06 for interval time 2000 μs, which is too small to infer super-Poissonian. Due to limited data memory, our dataset was restricted in length and resolution. Therefore, longer intervals could not be studied without statistical uncertainty. To cross-check the result we also calculated the probability distribution for the arrival time itself. The result perfectly fitted an exponential distribution which was in accordance with the theory of coherent light. Hence, within the given measurement accuracy and statistical uncertainty, it is safe to conclude that the laser beam is coherent for all tested time intervals. However, this does not allow us to conclude that it is a single-mode laser.
Abstract Measurement of photon statistics is an important tool for the verification of quantum properties of light. Due to the various imperfections of real single photon detectors, the observed statistics of photon counts deviates from the underlying statistics of photons. Here we analyze statistical properties of coherent states, and investigate a connection between Poissonian distribution of photons and sub-Poissonian distribution of photon counts due to the detector dead-time corrections. We derive a functional dependence between the mean number of photons and the mean number of photon counts, as well as connection between higher-order statistical moments, for the pulsed or continuous wave coherent light sources, and confirm the results by numerical simulations.