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Annalen der Physik

Enhanced Nonclassical Third‐Order Spatial Intensity Correlations in Three‐Beam Interferences<

Th. Richter

Published Jan 1, 1991• 0 citations
Publisher

Abstract

Abstract The joint probability of detecting simultaneously three photons at two and three points in the superposition field of three independent plane waves with the same frequency but random phases is calculated and compared with the results of a classical wave theory. Significant differences occur for sufficiently weak fields. We find that the differences between the quantum mechanical and classical predictions concerning the third order intensity correlation functions are more pronounced in a three‐beam than in a two‐beam interference experiment.

DOI
10.1002/andp.19915030809

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Abstract The joint probability of detecting simultaneously three photons at two and three points in the superposition field of three independent plane waves with the same frequency but random phases is calculated and compared with the results of a classical wave theory. Significant differences occur for sufficiently weak fields. We find that the differences between the quantum mechanical and classical predictions concerning the third order intensity correlation functions are more pronounced in a three‐beam than in a two‐beam interference experiment.
The joint probability of detecting simultaneously three photons at three different points in the superposition field of two independent plane waves with random phases is calculated and compared with the results of a classical wave theory. There are important differences when the number of photons is small. In particular, if there is one photon in one beam and two photons in the other one, three photodetectors can be placed at positions such that all three never respond at once, even though one beam intensity is two times stronger than the other.
The joint probability of simultaneously detecting four photons at at least two different points in the superposition field of two independent plane waves with random phases is calculated and compared with the results of a classical wave theory. There are important differences when the number of photons is small. In particular, if there is one photon in one beam and three photons in the other one, two two-photon detectors can be placed at positions such that they never both respond at the same time, even though the intensity of one beam is three times stronger than that of the other. This conclusion has no classical analogue.
Interference effects produced by independent quantum sources are investigated, when the state of the field is not describable as a simple mixture of coherent states. The results of classical and quantum-mechanical calculations are compared. Whereas correlation effects are predicted both classically and quantum mechanically when the sources have random phases, there are important differences when the number of atoms is small. In particular, when each source consists of just one atom, the joint probability of detecting two photons at two different points in the receiving plane is found to vanish when the distance between them is an odd number of half fringes. Finally it is shown that when the number of atoms of each source is subject to Poisson fluctuations, one recovers the solution given by classical optics for thermal light, no matter how weak the sources may be on the average.
We develop a nonclassicality criterion for the interference of three delayed, but otherwise identical, light fields in a three-mode Bell interferometer. We do so by comparing the prediction of quantum mechanics with those of a classical framework in which independent sources emit electric fields with random phases. In particular, we evaluate third-order correlations among output intensities as a function of the delays, and show how the presence of a correlation revival for small delays cannot be explained by the classical model of light. The observation of a revival is thus a nonclassicality signature, which can be achieved only by sources with a photon-number statistics that is highly sub-Poissonian. Our analysis provides strong evidence for the nonclassicality of the experiment discussed by Menssen et al. [Phys. Rev. Lett. 118, 153603 (2017)], and shows how a collective ``triad'' phase affects the interference of any three or more light fields, irrespective of their quantum or classical character.
The conditions are examined under which interference effects should be observable in the superposition of two light beams derived from independent sources. The quantum-mechanical description of these effects differs from the classical description principally in that it is necessarily based on expectation values of the light intensity at one or more space-time points. It is shown that pure states of the radiation field which are not energy states give rise to interference effects, but in that case the two beams cannot meaningfully be described as statistically independent. For a realistic description mixed states have to be introduced, when the expectation value of the intensity gives no indication of interference effects. On the other hand, the intensity correlation at two space-time points is a periodic function of the separation of the points and indicates the presence of transient interference effects. The effects become readily observable only when the average photon occupation number of each cell of phase space is appreciably greater than 1, and this explains why laser beams were needed for the experimental observations. It is pointed out that, even in these experiments, each photon may be regarded as interfering only with itself.
Although we tend to think of optical interference as a classical wave phenomenon, recent experiments have revealed a number of effects that are not describable in classical terms. This is particularly true of interference effects involving the detection of a photon pair. We shall refer to them as fourth order interference, on the grounds that the joint probability density for the detection of one photon at r sub 1 at time t and another r sub 2 at time t is proportional to the fourth order correlation function of the field. This probability is readily measured when two photodetectors are positioned at r sub 1 and r sub 2 and the signals from the two detectors are fed to a coincidence counter that registers 'simultaneous' detections by the two detectors in coincidence. The topics covered include: fourth order interference measurements; the Franson experiment; and experimental test of the de Broglie guided wave theory.