In a near-field four-photon correlation measurement, ghost imaging with classical incoherent light is investigated. By applying the Klyshko advanced-wave picture, we consider the properties of four-photon spatial correlation and find that the fourth-order spatial correlation function can be decomposed into multiple lower-order correlation functions. On the basis of the spatial correlation properties, a proof-of-principle four-photon ghost imaging is proposed, and the effect of each part in a fourth-order correlation function on imaging is also analyzed. In addition, the similarities and differences among ghost imaging by fourth-, second-, and third-order correlations are also discussed. It is shown that the contrast and visibility of fourth-order correlated imaging are improved significantly, while the resolution is unchanged. Such studies can be very useful in better understanding multi photon interference and multi-channel correlation imaging.
In a near-field four-photon correlation measurement, ghost imaging with classical incoherent light is investigated. By applying the Klyshko advanced-wave picture, we consider the properties of four-photon spatial correlation and find that the fourth-order spatial correlation function can be decomposed into multiple lower-order correlation functions. On the basis of the spatial correlation properties, a proof-of-principle four-photon ghost imaging is proposed, and the effect of each part in a fourth-order correlation function on imaging is also analyzed. In addition, the similarities and differences among ghost imaging by fourth-, second-, and third-order correlations are also discussed. It is shown that the contrast and visibility of fourth-order correlated imaging are improved significantly, while the resolution is unchanged. Such studies can be very useful in better understanding multi photon interference and multi-channel correlation imaging.
We investigate the fourth-order spatial correlation properties of pseudo-thermal light in the photon counting regime, and apply the Klyshko advanced-wave picture to describe the process of four-photon coincidence counting measurement. We deduce the theory of a proof-of-principle four-photon coincidence counting configuration, and find that if the four randomly radiated photons come from the same radiation area and are indistinguishable in principle, the fourth-order correlation of them is 24 times larger than that when four photons come from different radiation areas. In addition, we also show that the higher-order spatial correlation function can be decomposed into multiple lower-order correlation functions, and the contrast and visibility of low-order correlation peaks are less than those of higher orders, while the resolutions all are identical. This study may be useful for better understanding the four-photon interference and multi-channel correlation imaging.
We theoretically discuss the four-photon spatial correlation property under different detection schemes. Compared with the two- and three-photon spatial correlation of thermal light source, we found that the enhancement in the visibility and the contrast when the fourth-order spatial correlation function is measured with quadruple coincidence measurement in the single photon counting regime. The resolution, however, is not changed when we scan three of four detectors with identical speed and direction. But if we scan two of three detectors in opposite directions and same speed, simultaneously, other two in identical direction and speed of one detector is twice of that of the other, we can see that both the contrast and resolution are improved significantly. We also show that the conclusion can be applied to the Nth-order ghost imaging.
Abstract We theoretically discuss the fourth-order spatial correlation and four-photon bunching properties of pseudo-thermal light in the photon counting regime. It is found that four-photon bunching has the maximum correlation. If they all come from the same spatial cell in phase space, then fourth-order spatial correlation can be decomposed into not only auto-correlation and cross-correlation of second- and third- order, but the pure correlations among four photons as well, which is just the four-photon bunching. In addition, we also show that the contribution from four-photon bunching leads to the enhancement of the resolution and visibility in fourth-order ghost imaging. More precisely, the contribution from four-photon bunching to fourth-order spatial correlation is equal to the sum of all contributions from two-photon bunching and three-photon bunching when three reference detectors are scanned along the identical orientation and speed. On the other hand, the sum of all contributions from two-photon bunching and three-photon bunching to fourth-order spatial correlation will exceed the contribution from four-photon bunching, when two of three reference detectors are scanned in the same orientation and the speed of one reference detector is twice that of the other; meanwhile, the other two reference detectors are moved with opposite orientation but identical speed.
In a near-field three-photon correlation measurement, we observed the third-order temporal and spatial correlation functions of chaotic thermal light in the single-photon counting regime. In the study, we found that the probability of jointly detecting three randomly radiated photons from a chaotic thermal source by three individual detectors is 6 times greater if the photodetection events fall in the coherence time and coherence area of the radiation field than if they do not. From the viewpoint of quantum mechanics, the observed phenomenon is the result of three-photon interference. By making use of this property, we measured the three-photon thermal light lensless ghost image of a double spot and achieved higher visibility compared with the two-photon thermal light ghost image.
Multiparticle interference is one of the most surprising consequences of quantum mechanics. In quantum theory, a interference happens between different, yet indistinguishable probability amplitudes. Probability amplitudes can be nonlocal when they are connected with systems including several particles. The interference between these nonlcoal probability amplitudes sometimes can only be understood by quantum theory. In this dissertation, the multiphoton coherence of thermal light is studied, theoretically and experimentally, as the consequences of interference between nonlcoal probability amplitudes. The study showed that the higher order correlation functions of thermal light had higher contrast compared with the lower order correlation functions. For example, the contrast of the Nth order correlation function of thermal light can reach N!:1. This is because in higher order correlation functions there are more cross terms from interference contribute to the correlation peak. In this dissertation, the high contrast property is employed to increase the contrast of thermal light ghost imaging. An experiment showed that the contrast of the third order ghost image is significantly improved compared with that of the second order ghost image.
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.