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Journal of Physics Communications

Photon interference of second- and third-order correlation generated by two fluorescence sources

Siqiang Zhang, Faizan Raza, Irfan Ahmed, Wei Li, Kaichao Jin, Yanpeng Zhang

Published Aug 28, 2019• 2 citations
Publisher

Abstract

Abstract We demonstrate the second- and third-order temporal correlation of two independent pseudo-thermal fluorescence (FL) sources. The two distinguishable sources become indistinguishable following the delay in Feynman’s path. The second- and third-order correlation demonstrates the strong bunching amplitude surrounded by variable oscillations and interfering side bands (beats). Specifically, three-photon bunching is overlapped by two-photon bunching, and further decomposed into multiple lower order correlation functions. Here, the strong interference arises from source and path indistinguishable terms (varying time offset, laser frequency and the bandwidth of FL sources); The support for this idea comes from Feynman’s path integral theory and sub wavelength interference for such kind of sources with appropriate detection schemes. Such phenomena may serve as modulation and carrier for quantum communication channels.

DOI
10.1088/2399-6528/ab3e7b

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Abstract We demonstrate the second- and third-order temporal correlation of two independent pseudo-thermal fluorescence (FL) sources. The two distinguishable sources become indistinguishable following the delay in Feynman’s path. The second- and third-order correlation demonstrates the strong bunching amplitude surrounded by variable oscillations and interfering side bands (beats). Specifically, three-photon bunching is overlapped by two-photon bunching, and further decomposed into multiple lower order correlation functions. Here, the strong interference arises from source and path indistinguishable terms (varying time offset, laser frequency and the bandwidth of FL sources); The support for this idea comes from Feynman’s path integral theory and sub wavelength interference for such kind of sources with appropriate detection schemes. Such phenomena may serve as modulation and carrier for quantum communication channels.
The multi-order quantum beating effect of three-photon temporal interference generated by three nondegenerate fluorescence sources is studied. The third-order temporal correlation function of three nondegenerate photons results from the superposition of two-photon and three-photon bunching, multi-order quantum beating and temporal interference of three-photon. The simulate results show strong quantum beating and photon bunching behavior. The visibility of interference pattern, and the switching between photon bunching and beating effect can be modulated by the frequency difference, bandwidth of photons and the relative time delay of detectors. Such controllable coherent signal has potential applications as router and logic gate in quantum communication and information processing.
The second-order interference of two independent photons with different spectra in a Shih–Alley/Hong–Ou–Mandel interferometer is studied in Feynman’s path integral theory. There is a second-order interference pattern for photons with different spectra if the photons are indistinguishable for the employed detection system. The conditions to observe the second-order temporal beating with photons of different spectra are analyzed. The influence of the response time of the detection system on the observed second-order interference pattern is also discussed. It is a direct result of that measurement in quantum mechanics is dependent on the employed measuring apparatus. The results are helpful to understand the physics of two-photon interference in different schemes.
The first- and second-order temporal interference between two independent thermal and laser light beams is discussed by employing the superposition principle in Feynman's path integral theory. It is concluded that the first-order temporal interference pattern can not be observed by superposing two independent thermal and laser light beams, while the second-order temporal interference pattern can be observed in the same condition. These predictions are experimentally verified by employing pseudothermal light to simulate thermal light. The relationship between the indistinguishability of alternatives and photons is analyzed. The conclusions are helpful to understand the interference of different kinds of light and the difference between the coherence properties of thermal and laser light.
In this thesis we discuss an extension of the historical Hanbury Brown and Twiss experiment and investigate spatial intensity correlations of higher-orders in the radiation field of statistically independent light sources. The light sources can be non-classical like single-photon emitters or classical, obeying thermal or coherent statistics. Although the light sources are assumed to emit the photons in an incoherent manner, we find spatial photon correlations in the far field which can be explained by the quantum mechanical concept of multi-photon interferences. We demonstrate that spatial correlation measurements between indistinguishable photons based on linear optical detection techniques can be used to overcome the resolution limit of classical optics (Abbe/Rayleigh limit) and also to manipulate the spatial radiation characteristic of the light sources. Both remarkable properties of higher-order intensity correlations have been experimentally verified using statistically independent pseudothermal light sources. Due to the fact that the reported correlation measurements require neither special quantum tailoring of light nor N-photon absorbing media, they are of particular interest for the field of quantum imaging and quantum information processing. The thesis is divided into three main parts: In the first part (Chapter 2 and 3) we introduce a quantum path formalism which allows to describe multi-photon interferences arising in both classical and nonclassical light fields. This quantum path approach explains the origin of the underlying interference mechanism of the higher-order spatial intensity correlation functions in a transparent and simple manner. Moreover, it enables us to compare the multi-photon interferences obtained by nonclassical single-photon emitters with those generated by classical light sources. In the course of this discussion it appears that Dirac's famous statement “Each photon interferes only with itself. Interference between two different photons never occurs.” should better read “A multi-photon state of independent photons only interferes with itself. Interference between different multi-photon states never occurs.” This general statement summarizes the physics behind all multi-photon interference phenomena investigated in this thesis. In the second part of the thesis (Chapter 4) we investigate particular multi-photon interference measurements of independent light sources in the context of quantum imaging. We demonstrate that the Nth-order spatial intensity correlation functions display at specific ‘magic’ detector positions the ability to filter sub-wavelength information out of the light fields arising from N incoherently radiating light sources. These multi-photon interference patterns achieve a higher resolution for N>2 than the classical Abbe/Rayleigh limit for imaging the light source. In case of N single-photon emitters we theoretically show that the super-resolving interference patterns obtained for the ‘magic’ detector positions are identical to the ones generated by NOON states with N-1 photons. Quite unexpected, the same is true for N thermal light sources, except for a reduced visibility. Experimental results with up to eight independent thermal light sources confirm this approach to improve the spatial resolution in imaging. In the last part of this thesis (Chapter 5) we finally demonstrate that multi-photon detections can lead to a strong angular focussing of incoherent photons emitted again by either uncorrelated single-photon sources or statistically independent classical light sources. For this effect the sources can be far away from each other and do not interact. The mth-order intensity correlation measurement causes source correlations which produce a heralded peaked emission pattern for the initially uncorrelated light sources. In particular, we show that if m-1 photons have been detected in a particular direction, the conditional probability to detect the mth photon in the same direction can be as high as 100 %. Owing to the great flexibility of detector positions for the correlation measurement, a wide variety of additional detection schemes exists which produces similar directional photon emission patterns. This theoretically predicted measurement-induced focussing was experimentally confirmed with up to eight pseudothermal light sources for three particular detection schemes.
Two-photon interference (TPI) is a fundamental phenomenon in quantum optics and plays a crucial role in optical quantum technologies. TPI is commonly considered as quantum interference with an upper bound of 100% for both the TPI and the beat visibility in contrast to its classical counterpart with a maximum visibility of 50%. However, this is not always the case. Here, we report a simultaneous observation of quantum and classical TPI of single photons with ultralong coherence time, which is five orders of magnitude longer than the photon correlation time. We observe a TPI visibility of 94.3% ± 0.2% well above the 50% classical limit indicating the quantum feature, and a beat visibility of 50% reflecting the classical feature. In addition an anti-bunching central dip due to single-photon anti-correlation, we also observe two bunching side peaks in cross correlation curves for indistinguishable photons. Using the general wave superposition theory and the quantum field approach, we derive the same cross correlation functions, which fully reproduce and explain the experiments. Our results reveal that the quantum and classical features of TPI result from the same interference, as the fourth-order temporal interference arises from the second-order temporal interference between two photons on the timescale of the photon coherence time.