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Acta Physica Sinica

Analysis and measurement of high-order photon correlations of light fields

Yanqiang Guo, Lijing Wang, Yu Wang, Xin Fang, Tong Zhao, Xiaomin Guo

Published Jan 1, 2020• 3 citations
Publisher

Abstract

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.

DOI
10.7498/aps.69.20200325

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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.
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.
The researches on higher-order coherence and quantum statistics of light field are the important researching issues in quantum optics. In 1956, Hanbury-Brown and Twiss (HBT) (Hanbury-Brown R, Twiss R Q 1956 Nature 177 27) revolutionized optical coherence and demonstrated a new form of photon correlation. The landmark experiment has far-reaching influenced and even inspired the quantum theory of optical coherence that Glauber developed to account for the conclusive observation by HBT. Ever since then, the HBT effect has motivated extensive studies of higher-order coherence and quantum statistics in quantum optics, as well as in quantum information science and cryptography. Based on the HBT scheme, the degree of coherence and photon number distribution of light field can be derived from correlation measurement and photon counting technique. With the rapid development of the photoelectric detection technology, single-photon detection, which is the most sensitive and very widespread method of optical measurement, is used to characterize the natures of light sources and indicate their differences. More recently, HBT scheme combined with single-photon detection was used to study spatial interference, ghost imaging, azimuthal interference effect, deterministic manipulation and detection of single-photon source, etc. Due to broadband RF spectrum, noiselike feature, hypersensitivity to the initial conditions and long-term unpredictability, chaotic laser meets the essential requirements for information security and cryptography, and has been developed in many applications such as chaos-based secure communications and physical random number generation, as well as public-channel secure key distribution. But the research mainly focused on macroscopic dynamics of the chaotic laser. Moreover, the precision of measurement has reached a quantum level at present. Quantum statistcs of light field can also uncover profoundly the physical nature of the light. Thus, it is important to exploit the higher-order degree of coherence and photon statistics of chaotic field, which contribute to characterizing the field and distinguishing it from others. In this paper, photon number distribution and second-order degree of coherence of a chaotic laser are analyzed and measured based on HBT scheme. The chaotic laser is composed of a distributed feedback laser diode with optical feedback in fiber external cavity configuration. The bandwidth of the chaotic laser that we obtain experimentally is 6.7 GHz. The photon number distribution of chaotic laser is fitted by Gaussian random distribution, Possionian distribution and Bose-Einstein distribution. With the increase of the mean photon number, the photon number distribution changes from Bose-Einstein distribution into Poissonian distribution and always accords with Gaussian random distribution well. The second-order coherence g(2)(0) drops gradually from 2 to 1. By changing the bias current (I = 1.0Ith-2.0Ith) and feedback strength (010%), we compare and illustrate different chaotic dynamics and g(2)(0). From low frequency fluctuation to coherence collapse, the chaotic laser shows bunching effect and fully chaotic field can be obtained at the broadest bandwidth. Furthermore, the physical explanation for sub-chaotic or weakening of bunching effect is provided. It is concluded that this method can well reveal photon statistics of chaotic laser and will open up an avenue to the research of chaos with quantum optics, which merges two important fields of modern physics and is extremely helpful for the high-speed remote chaotic communication.
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.
The Hanbury Brown–Twiss (HBT) interferometer, which is used to measure the correlation of two photons or two light beams, has played a crucial role in quantum optics and quantum information. We propose a generalized HBT interferometer, which is able to measure the correlation of photons or light beams up to eight in a single experimental run. With an improved time correlated single-photon counting (TCSPC) algorithm, two-, three-, and four-photon coincidence counts, and the degree of fifth-order coherence of pseudothermal light are measured with a data collection time of 60 s. The generalized HBT interferometer can be used to measure the correlation of two multi-photon detection events by simulating photon number resolving detectors with multiple single-photon detectors. The generalized HBT interferometer and improved TCSPC algorithm provide a versatile framework for studying multi-photon correlations and interference, which is helpful to understand the physics of multi-photon interference and may find applications in fluorescence lifetime imaging and other techniques using TCSPC.
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.