Wave-particle duality as a fundamental tenet of quantum mechanics is crucial for advancing comprehension of quantum theories and developing quantum technologies with practical applications. However, taking into account experimental impact factors to develop a feasible measurement for wave-like and particle-like properties of light fields is an ongoing challenge, and the non-classicality extraction and determination remains to be explored. In this work, feasibly measurable second-order photon correlations based on Hanbury Brown−Twiss and Hong−Ou−Mandel interferences are employed to analyze the evolution of wave−particle duality for various input states. The wave-particle dualities of chaotic, coherent and mixed classical states as functions of time delay and coherence time are investigated. The realistic impacts of background noise, detection efficiency, intensity ratio and phase differences on the wave−particle duality of non-classical (Fock and squeezed coherent) states are unveiled. In noisy backgrounds with low detection efficiencies, efficient enhancement and extraction of non-classicality and a continuous transition from classical to non-classical region are achieved in single photon state mixed with coherent state by adjusting the phase difference from 0 to π/2 . The non-classicality of squeezed coherent state can be induced by the classical wave-like and particle-like properties. The research provides a practical precision measurement of wave−particle duality that is helpful for the improvement of high-resolution quantum imaging and sensing.
Wave-particle duality as a fundamental tenet of quantum mechanics is crucial for advancing comprehension of quantum theories and developing quantum technologies with practical applications. However, taking into account experimental impact factors to develop a feasible measurement for wave-like and particle-like properties of light fields is an ongoing challenge, and the non-classicality extraction and determination remains to be explored. In this work, feasibly measurable second-order photon correlations based on Hanbury Brown−Twiss and Hong−Ou−Mandel interferences are employed to analyze the evolution of wave−particle duality for various input states. The wave-particle dualities of chaotic, coherent and mixed classical states as functions of time delay and coherence time are investigated. The realistic impacts of background noise, detection efficiency, intensity ratio and phase differences on the wave−particle duality of non-classical (Fock and squeezed coherent) states are unveiled. In noisy backgrounds with low detection efficiencies, efficient enhancement and extraction of non-classicality and a continuous transition from classical to non-classical region are achieved in single photon state mixed with coherent state by adjusting the phase difference from 0 to π/2 . The non-classicality of squeezed coherent state can be induced by the classical wave-like and particle-like properties. The research provides a practical precision measurement of wave−particle duality that is helpful for the improvement of high-resolution quantum imaging and sensing.
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.
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.
A single photon exhibits wave-particle duality in the Young's double-slit interferometer. The duality characterized by an interference visibility and a which-path information has trade-off relation known as complementarity. These quantities are related to the first-order coherence, and the interference is based on the phase correlation between lights coming from two arms. However according to quantum optics theory, such a simple wave-particle picture is not enough to understand the nature because the theory showed an importance of higher-order coherence in the sense of both interference and statistical distribution of photons. Second-order intensity correlation is especially crucial to reveal distinctive quantum features of photons with no classical analogue. Here, in an intensity interferometric scenario as represented by the Hong-Ou-Mandel interferometer, we discuss a wave-particle duality of light based on a which-path information and a quantity characterizing a magnitude of the intensity interferometric effect. We show, for classical light, the two quantities obey the complementary principle similar to the case of the double-slit experiment, but do not for nonclassical light. The nonclassical light such as photons at two arms is allowed to show larger which-path information and intensity interference simultaneously beyond the complementary relation. Moreover, the violation reveals a new nonclassical nature of light although both of the above two quantities seem to be understandable classically, which is never found from a consideration of only one side of wave-particle duality.
We study continuous variable coherence of phase-dependent squeezed state based on an extended Hanbury Brown-Twiss scheme. High-order coherence is continuously varied by adjusting squeezing parameter r, displacement α, and squeezing phase θ. We also analyze effects of background noise γ and detection efficiency η on the measurements. As the squeezing phase shifts from 0 to π, the photon statistics of the squeezed state continuously change from the anti-bunching (g(n) < 1) to super-bunching (g(n) > n!) which shows a transition from particle nature to wave nature. The experiment feasibility is also examined. It provides a practical method to generate phase-dependent squeezed states with high-order continuous-variable coherence by tuning squeezing phase θ. The controllable coherence source can be applied to sensitivity improvement in gravitational wave detection and quantum imaging.
The second-order intensity correlation of entangled photons has been intensively studied for decades, particularly for the Hong-Ou-Mandel (HOM) effect and nonlocal correlation -- key quantum phenomena that have no classical counterparts. Recently, a path-entangled two-photon state has been experimentally demonstrated for both bosonic (symmetric) and fermionic (anti-symmetric) HOM effects by manipulating the photon phase at one input port. Entanglement represents a quantum superposition of path- or energy-correlated two-photon states with a relative phase. According to the conventional quantum mechanics, this phase is not an individual property but collective attribute of interacting photons. Here, the wave nature of photons is employed to coherently analyze the phase-controlled HOM effects recently observed in npj Quantum Info. 5, 43 (2019). A pure coherence approach is applied to derive a general solution for these phase-controlled HOM effects. Consequently, the quantum mystery of HOM effects, traditionally interpreted through the particle nature of quantum mechanics, is revealed as a coherent phenomenon between entangled photons via a selective choice of correlated photons.
I briefly review second order or two-photon correlations starting from the Hanbury Brown-Twiss correlations to its modern versions in quantum optics studies. With this background, I address some foundational issues in the physics of quantum correlations and quantum entanglement and argue in favour of the validity of Einstein locality, to settle a long-standing debate. Understanding entanglement from this perspective has applications in quantum information theory, especially in gaining intuition about the relation between different measures of entanglement and its time evolution. Some examples are highlighted. I discuss how ideas on photon correlations applied to squeezing fluctuations in coherent light have become important in metrology, and perhaps crucial, in the successful operation of high sensitivity gravitational wave detectors.