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Quantum Sensing and Nano Electronics and Photonics

Calibrating single-photon detectors for photon counting and quantum correlation measurements

Anthony J. Bennett, Rachel Clark

Published Mar 4, 2022• 0 citations
Publisher

Abstract

Photonic quantum technologies require single photon sources and detectors operating at high efficiency, but at high rates detector imperfections can lead to inaccurate measurements. We show that the combination of the detector deadtime and the source statistics together determine the saturation level of a single photon detector, with anti-bunched sources leading to a greater detection rate than coherent or thermal light of the same intensity. At high photon rates this behavior distorts second-, third- and fourth- order correlation measurements, in agreement with our numerical simulations. Finally, we discuss the implications for entangled light detection and photonic logic.

DOI
10.1117/12.2608260

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Photonic quantum technologies require single photon sources and detectors operating at high efficiency, but at high rates detector imperfections can lead to inaccurate measurements. We show that the combination of the detector deadtime and the source statistics together determine the saturation level of a single photon detector, with anti-bunched sources leading to a greater detection rate than coherent or thermal light of the same intensity. At high photon rates this behavior distorts second-, third- and fourth- order correlation measurements, in agreement with our numerical simulations. Finally, we discuss the implications for entangled light detection and photonic logic.
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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.
A novel high-throughput second-order correlation measurement system is developed that records and makes use of all the arrival times of photons detected at both start and stop detectors. This system is suitable, particularly for a light source having a high photon flux and a long coherence time, since it is more efficient than conventional methods by an amount equal to the product of the count rate and the correlation time of the light source. We have used this system in carefully investigating the dead time effects of detectors and photon counters on the second-order correlation function in the two-detector configuration. For a nonstationary light source, a distortion of the original signal was observed at high photon flux. A systematic way of calibrating the second-order correlation function has been devised by introducing the concept of an effective dead time of the entire measurement system.
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.
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 detectors are of great importance in spectroscopy, laser ranging, astronomy and wherever weak light detection is required, so a precise knowledge of their quantum efficiency is essential, but their calibration is by no means trivial. Traditional methods need a black body radiation source or a highly attenuated laser beam as a reference standard, or an already calibrated reference detector. It is well known that absolute measurement of the quantum efficiency, absolute in the sense that the calibration is independent of any radiometric standard or the properties of another detector, can be performed using entangled twin photons generated in optical spontaneous parametric down-conversion together with a reference detector. We have performed the first proof-of-principle experiment to determine the quantum efficiency by which no second detector or reference standard is required. This absolute self-calibration method is also based on the time correlation of photons emitted in parametric down-conversion, but with the introduction of a suitable time delay between the arrival times of the twin photons. Furthermore, we describe a scheme for absolute self-calibration of the quantum efficiency at different wavelengths by means of a pulsed source of nondegenerate down-converted photons. This method should have even greater potential for applications.