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arXiv:1608.07941 · Chinese Physics B

Second-order temporal interference of two independent light beams at an asymmetrical beam splitter

Jianbin Liu, Jingjing Wang, Zhuo Xu

Published Jan 1, 2017• 4 citations
arXivHTMLPDF

Abstract

The second-order temporal interference of classical and nonclassical light at an asymmetrical beam splitter is discussed based on two-photon interference in Feynman's path integral theory. The visibility of the second-order interference pattern is determined by the properties of the superposed light beams, the ratio between the intensities of these two light beams, and the reflectivity of the asymmetrical beam splitter. Some requirements about the asymmetrical beam splitter have to be satisfied in order to ensure that the visibility of the second-order interference pattern of nonclassical light beams exceeds the classical limit. The visibility of the second-order interference pattern of photons emitted by two independent single-photon sources is independent of the ratio between the intensities. These conclusions are important for the researches and applications in quantum optics and quantum information when an asymmetrical beam splitter is employed.

DOI
10.1088/1674-1056/26/1/014201

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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.
By analyzing the first-order interference of two independent thermal light beams in Feynman's path integral theory, we conclude that it is impossible to observe the transient first-order interference pattern by superposing two independent thermal light beams if the initial phases of the photons in thermal light are random. The result suggests that the classical model of thermal light field within the coherence time may not be the same as the one of laser light field within the coherence time.
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 formation process of the second-order interference pattern is studied experimentally in the photon counting regime by superposing two independent single-mode continuous-wave lasers. Two-photon interference based on the superposition principle in Feynman's path integral theory is employed to interpret the experimental results. The second-order interference pattern of classical light can be formulated when, with high probability, there are only two photons in the interferometer at one time. The studies are helpful in understanding the second-order interference of classical light in the language of photons. The method and conclusions can be generalized to the third- and higher-order interference of light and interference of massive particles.
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The quantum theory of fourth-order interference of light is presented in a general format and compared with classical wave theory. The conditions under which nonclassical phenomena occur are discussed. In particular, the interference between the quantum field and classical field may give rise to a nonclassical effect. For some special states of light, the interference pattern does not disappear even though one field is much stronger than the other, for which no classical analog exists. Fourth-order effects in the interference between two independent fields are analyzed in detail. It is pointed out that the fourth-order interference between independent fields will not disappear when the integration time of detection is of the order of the reciprocal bandwidth of the two light fields as long as the spectra of the two fields are symmetric around the same center frequency, and for some correlated fields, the interference does not vanish even if the detection time is much larger than the reciprocal bandwidth of the fields. A new type of fourth-order interference experiment involving a beam splitter is proposed in which local realism of the Einstein-Podolsky-Rosen form is violated for quantum mechanics. This general argument is then applied to the interference between two photons generated in the parametric down-conversion process. The possibility of violations of Bell's inequalities in interference experiments is investigated.