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Physical Review A

Effects of counting rate and resolution time on a measurement of the intensity correlation function

Y. Li, Geng-Yuan Li, Y. C. Zhang, X. Y. Wang, Ji-Guo Zhang, Junmin Wang, T. C. Zhang

Published Jul 25, 2007• 18 citations
Publisher

Abstract

Non-photon-number-resolving single-photon-counting modules (SPCM's), also called on-off photon detectors, have been used in quantum optics for investigating the properties of various light fields based on the Hanbury-Brown-Twiss (HBT) experiment. However, for different incident light fields the experimental conditions can affect the measured photon statistics. In this paper, the second-order degree of coherence ${g}^{(2)}$, known as the important factor for quantitying a single-photon source, is experimentally investigated by means of the HBT scheme consisting of two SPCM's. By comparing the results of coherent field with that of the thermal field, we show that the measured ${g}^{(2)}$ is affected by the photon-counting rate and the resolution time from pulsed to continuous wave fields. The proper counting rate and resolution time for characterizing the exact photon statistical properties of input fields are determined.

DOI
10.1103/physreva.76.013829

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Non-photon-number-resolving single-photon-counting modules (SPCM's), also called on-off photon detectors, have been used in quantum optics for investigating the properties of various light fields based on the Hanbury-Brown-Twiss (HBT) experiment. However, for different incident light fields the experimental conditions can affect the measured photon statistics. In this paper, the second-order degree of coherence g(2){g}^{(2)}g(2), known as the important factor for quantitying a single-photon source, is experimentally investigated by means of the HBT scheme consisting of two SPCM's. By comparing the results of coherent field with that of the thermal field, we show that the measured g(2){g}^{(2)}g(2) is affected by the photon-counting rate and the resolution time from pulsed to continuous wave fields. The proper counting rate and resolution time for characterizing the exact photon statistical properties of input fields are determined.
Photon statistical properties of coherent field and thermal field are experimentally studied by means of direct photon counting using only one single-photon-counting module (SPCM) operating in Geiger mode. The second-order degree of coherence as affected by photon counting rate and selected resolution time is investigated systematically. By taking into account all the experimental factors which can influence the g(2), the second-order degree of coherence of an unknown optical field can be determined quickly and simply via single SPCM when choosing proper detecting conditions. In our experiment, when the counting rate is about 109 kc/s and the resolution time varies from 28 ns to 212 ns, the measured results can reliably reflect the different second-order degree of coherence of coherent and thermal fields.
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.
We investigated the properties of various light fields based on the Hanbury-Brown-Twiss(HBT)experiment consisted by two single-photon-counting modules(SPCMs),one 50/50beam splitter and the Fast-Com P7888card.Having experimentally investigated the second-order degree of coherence g2(τ)for the continuous-wave and the pulse lasers and the single-photon source generated by single atom,we confirmed the experiment results by theoretical analysis.Specially,we have achieved a high quality of single-photon source based on single atom trapped in the magnetic-optical trap and the far-off-resonance trap with g(2)(τ=0)=0.09and g(2)(τ=0)=0.08,respectively.Using the pulse laser and the single atom,we can perform the triggered single photon experiment.
The second-order degree of coherence of pseudo-thermal light and coherence time are experimentally studied via the Hanbruy-Brown-Twiss (HBT) scheme. The system consists of two non-photon-number-resolving single- photon-counting modules (SPCMs) operating in the Geiger mode. We investigate the coherence time of the incident beam for different spot sizes on a ground glass and speeds of a rotating ground glass. The corresponding coherence time can be obtained from Gaussian fitting for the measured second-order degree of coherence. The results show that the coherence time of measured pseudo-thermal light depends on the spot sizes and the rotating speeds of the ground glass. The maximum value of the second-order degree of coherence is reduced as the rotating speed decreases. This result can be well explained by the model of mixed thermal and coherent fields with different ratios.
Abstract We present an experimental technique that can accurately measure the high-order photon correlations of various light fields based on double Hanbury Brown–Twiss scheme. The system consists of four conventional binary response single-photon counting modules which are non-photon-number-resolving detectors. We theoretically analyze the effects of the experimental conditions on the high-order photon correlations of coherent, chaotic thermal, Fock and squeezed vacuum states with considering the overall efficiency and background noise. In experiment, we determine the proper resolution time from 2 9 = 512 ns to 2 11 = 2048 ns and counting rate from 10 kc s −1 to 100 kc s −1 for characterizing the exact second-, third- and fourth-order photon correlations of chaotic thermal state. At complete time delays, we also observe the third- and fourth-order photon correlations of chaotic thermal state, with the maximum high-order correlation values of 5.99 ± 0.02 and 23.9 ± 0.2 respectively, which are in good agreement with the theoretical values of 6 and 24. The demonstrated experimental technique with high accuracy is a promising tool for investigating quantum optical coherence and ghost imaging.
Single-photon-counting modules (SPCM's), with their high quantum efficiency, have been widely used to investigate effectively the photon statistics of various light sources, such as the single-photon state and emission light from controlled molecules, atoms, and quantum dots. However, such SPCM's cannot distinguish the arrivals of one photon and two (or more than two) photons at a moment, which makes measurement correction in real experiments. We analyze the effect of SPCM's on photon statistics based on the Hanbury-Brown-Twiss configuration when the total efficiency and background are considered, and it shows that the measured second-order degree of coherence and Mandel QQQ factor for different quantum states, including single-photon states and squeezed vacuum states, are corrected in different forms. A way of determining the squeezing of a squeezed vacuum state based on single-photon detection is presented.