An efficient scheme for photon statistics measurement is presented based on the Hanbury-Brown-Twiss configuration. We set the sampling time Ts to satisfy the relationship of TslTdlTm, where Td is the dead time of each detector and Tm is the laser pulse repetition period. And each single photon detector cannot detect more than one photon in each pulse. The approach can sufficiently eliminate the influences of the detector's dead time on photon statistics. At last, the photon statistics of coherent field is experimentally determined.
An efficient scheme for photon statistics measurement is presented based on the Hanbury-Brown-Twiss configuration. We set the sampling time Ts to satisfy the relationship of TslTdlTm, where Td is the dead time of each detector and Tm is the laser pulse repetition period. And each single photon detector cannot detect more than one photon in each pulse. The approach can sufficiently eliminate the influences of the detector's dead time on photon statistics. At last, the photon statistics of coherent field is experimentally determined.
The direct measurement of the Mandel parameter of weak laser pulses, with 10 ns pulse duration time and the mean number of photon per pulse nˉ being approximately 0.1, is investigated by recording every photocount event. With the Hanbury Brown and Twiss detection scheme, and not more than one photon per pulse being detected during the sample time by single-photon counters, we have found that the single mode diode laser with driving current lower than the threshold yields a sub-Poissonian statistics. In addition, when the diode laser driving current is much higher than the threshold, it is validated that the Mandel parameterQ C of the Poissonian coherent state is nearly −nˉ/2 . The experimental results are in good agreement with theoretical prediction considering the measurement error.
The direct measurement of the Mandel para-meter of weak laser pulses, with 10 ns pulse duration timeand the mean number of photon per pulse h-being approxi-mately 0.1, is investigated by recording every photocountevent. With the Hanbury Brown and Twiss detection scheme,and not more than one photon per pulse being detected dur-ing the sample time by single-photon counters, we havefound that the single mode diode laser with driving currentlower than the threshold yields a sub-Poissonian statistics. Inaddition, when the diode laser driving current is muchhigher than the threshold, it is validated that the Mandelparameter Qc of the Poissonian coherent state is nearly-n/2. The experimental results are in good agreement withtheoretical prediction considering the measurement error.
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.
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-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 Q 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.
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.