Time-correlated single photon counting is a technique to record low level light signals with very high time resolution. We first describe the experimental apparatus and briefly outline the statistical interpretation of the measurement series. After, we propose a stochastic model for the formulation of interference patterns based on doubly stochastic autoregressive model class. We suggest the application of optimal filtering technique conceived in [R. J. Elliott et al., (1997)] in order to estimate the underlying intensity process of the Poisson type measurement series. Finally, we present some results of the identification of realistic data that is although in coincidence with the general view of interference experiments, goes beyond the physical interpretation and may deepen our understanding of the quantum world.
Time-correlated single photon counting is a technique to record low level light signals with very high time resolution. We first describe the experimental apparatus and briefly outline the statistical interpretation of the measurement series. After, we propose a stochastic model for the formulation of interference patterns based on doubly stochastic autoregressive model class. We suggest the application of optimal filtering technique conceived in [R. J. Elliott et al., (1997)] in order to estimate the underlying intensity process of the Poisson type measurement series. Finally, we present some results of the identification of realistic data that is although in coincidence with the general view of interference experiments, goes beyond the physical interpretation and may deepen our understanding of the quantum world.
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 process is the key element for the interpretation of the results in quantum mechanics experiments. Here weinvestigate the influence of the detector technical characteristics (e.g. detector’s dead time) upon the photon distribution a inparametric down-conversion experiment. We show that the information on photon counting for signal, idle and coincidencescan be optimized by using a correlation pattern between time-window used of the measurements, detector’s dead time andthe speed of electronic circuits. Fine tuning of these parameters allows for the maximization of information transfer betweenthe quantum system and the experimental device. We prove this by comparing known physical properties of down convertedphotons with those measured with different experimental setups.
High-order photon correlations of light fields are important for characterizing the quantum nature. Since Hanbury Brown and Twiss conducted the pioneering experiments in the 1950s, the HBT effect has inspired extensive research on high-order photon correlation in quantum optics, quantum information, and quantum imaging. The Single-photon counting module is one of the most widely used single-photon detectors. Due to its high detection efficiency and low dark counts in the visible and near-infrared region, it is reasonably chosen for basic research on quantum mechanics. Many researches have demonstrated that the maximum value of second-order photon correlation g(2)(τ) at zero delay (τ = 0) can be used to distinguish different light fields. Therefore, the HBT scheme containing two single photon detectors have been widely used in many advanced studies, such as space interference, ghost imaging, single photon detection with high efficiency, etc. However, higher-order photon correlations g(n) (n > 2) can reveal more measurable characteristics of light fields, such as information about the non-Gaussian scattering process, the skewness and kurtosis of photon number distribution, etc. When the extended HBT scheme is used to measure higher-order photon correlations, the experimental conditions including quantum efficiency and background noise greatly affect the photon correlation measurement. The influences of the counting rate and resolution time of the detection system on the measurements are also very important and cannot be ignored. Therefore, the comprehensive considering of various influence factors is necessary for accurately measuring the high-order photon correlations and also a challenge. In this paper, we present a method based on double Hanbury Brown-Twiss scheme for the accurate measuring of high-order photon correlations g(n) (n > 2). The system consists of four single photon counting modules and is used to detect and analyze the joint distribution probability of temporal photon correlation. Considering the effects of the background noise and overall efficiency, theoretically, we analyze the correlations of the third- and fourth-order photon with the incident light intensity, squeezing parameter and photon number respectively for thermal state, coherent state, squeezed vacuum state, and Fock state. Meanwhile, experimentally we study the influences of resolution time and counting rate on correlations of the coherent state and thermal state with third- and fourth-order photon. On condition that the resolution time is 210 ns and the counting rate is 80 kc/s, the correlations of third and fourth-order photon with the thermal state at zero time delay are accurately measured, and the relative statistical deviations of the measured vales from the theoretical values are 0.3% and 0.8%, respectively. In addition, the third- and fourth-order photon correlations of the thermal state at different delay times are also observed. It is demonstrated that the high-order photon correlations of light fields are measured accurately by comprehensively analyzing various influencing factors. This technique provides a promising and useful tool to investigate quantum correlated imaging and quantum coherence of light fields.
Single photon count distributions at the outputs of a Mach-Zehnder interferometer are highly dependent on the phase difference between the two arms of the apparatus, so photocount records can be used to estimate an unknown optical phase. Experimental results have shown that phase information can be inferred from the data even at low mean input intensities of ⪅10 photons. Here we consider the optimal Bayesian parameter estimate for the model used by a previous frequentist analysis. In the limit of high input intensity the observation is well-modelled as an intensity measurement of a classical wave in Gaussian measurement noise, however in the low intensity regime this simple model does not apply. It seems that no generally valid closed-form estimator for this problem exists without making the Gaussian approximation. Moreover the 2π radian ambiguity in phase estimates presents a problem in defining cost functions to compare estimator performance, and we consider two reasonable alternatives. We present a numerical study of the experiment along with a novel numerical approach to this problem which out-performs the existing estimators and with a squared error that approaches the Cramer-Rao lower bound previously derived in the literature, in the limit where that bound is valid.
Single-photon interference experiments are attempted in the time domain using true single-photon streams. Self-heterodyning beats are clearly observed by letting the field associated with a single photon interfere with itself on a field-quadratic detector, which is a time analogue of Young's two-slit interference experiment. The temporal first-order coherence of single-photon fields, i.e., transient interference fringes, develops as cumulative detection events are mapped point-by-point onto a virtual capture frame by properly correlating the time-series data. The ability to single out photon counts at a designated timing paves the way for digital heterodyning with faint light for such use as phase measurement and quantum information processing.
Subtracting accidental coincidences is a common practice in quantum optics experiments. For zero mean Gaussian states, such as a squeezed vacuum, we show that if one removes accidental coincidences, the measurement results are quantitatively the same for both photon coincidences at very low flux and intensity covariances. Consequently, pure quantum effects at the photon level, like interference of photon wave functions or photon bunching, are reproduced in the correlation of fluctuations of macroscopic beams issued from spontaneous down-conversion. This is true both in experiment if the detection resolution is smaller than the coherence cell (size of the mode) and in stochastic simulations based on sampling the Wigner function. We also discuss the limitations of this correspondence, such as Bell inequalities (for which one cannot subtract accidental coincidences), highly multimode situations such as quantum imaging, and higher-order correlations.