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Journal of the Optical Society of America

Further Experiments on Interference of Independent Photon Beams at Low Light Levels*†

R. L. Pfleegor, L. Mandeļ

Published Jul 1, 1968• 67 citations
Publisher

Abstract

Interference fringes produced by the superposition of light beams from two independent lasers have been investigated under conditions where the light flux was so low that one photon was usually received at the detector before the next one was emitted by one or the other source. Because the average number of photons detected in each observation was only about 10, a photon correlation technique was used to demonstrate the presence of interference fringes. The measurement procedure was automated, and this led to much greater statistical accuracy than was previously reported. The effect of varying the observation time and the number of interference fringes sampled was investigated, and found to be in good agreement with theory.

DOI
10.1364/josa.58.000946

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Interference fringes produced by the superposition of light beams from two independent lasers have been investigated under conditions where the light flux was so low that one photon was usually received at the detector before the next one was emitted by one or the other source. Because the average number of photons detected in each observation was only about 10, a photon correlation technique was used to demonstrate the presence of interference fringes. The measurement procedure was automated, and this led to much greater statistical accuracy than was previously reported. The effect of varying the observation time and the number of interference fringes sampled was investigated, and found to be in good agreement with theory.
Interference effects produced by the superposition of the light beams from two independent single-mode lasers have been investigated experimentally. It is found that interference takes place even under conditions in which the light intensities are so low that, with high probability, one photon is absorbed before the next one is emitted by one or the other source. Since the average number of registered photons per trial was only about 10, photon correlation techniques were required to demonstrate the interference. The interpretation of the experiment, and the question whether it demonstrates interference between two photons, are discussed.
It has been shown that light beams from two independent lasers can produce interference effects at light levels corresponding to the presence, with a high degree of probability, of only one photon in the system. However, the statistical accuracy of earlier experiments performed in the spatial domain has been limited by the fact that individual observations were restricted to very short time intervals, during which only a few photons were registered. This paper describes an experiment performed in the time domain that overcomes these problems and demonstrates interference between two independent laser beams, at the single-photon level, over much longer observation times.
Abstract The reconciliation of wave-like optical interference phenomena with the particle-like properties of the quantized radiation field has intrigued physicists since the early years of the present century. Two main topics of discussion have been the effect of very low light levels-of the order of one photon at a time in the interferometer-on the interference fringes, and the possibility of determining which of the two optical paths through the interferometer were taken by the photons that produce the fringes. The first experiment with very low light levels was performed by Taylor (1909) at the instigation of J. J. Thomson. He found that Young’s interference fringes persisted when the low light levels were compensated by long photographic exposure times.
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.
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.
A comprehensive review is given of investigations, both theoretical and experimental, that demonstrate interference to take place even when the fields involved are produced by independent sources. The physical situation is rather different for coherent and incoherent fields. In the first case, where the sources are lasers, a conventional interference pattern can be observed which is adequately described by the classical theory. In the present paper, special attention is paid to the question of whether this interference persists when the two laser beams become strongly attenuated. In the second case, the sources are individual atoms excited by a pumping mechanism, that emit spontaneously and, hence, independently from each other. In those circumstances, no interference pattern can show up. However, it becomes evident from both the classical and the quantum-mechanical theory that interference effects can still be established by observing intensity correlations rather than the intensity itself. This point is discussed in greater detail. The pioneering experiments of Forrester, Gudmundson and Johnson, and Brown and Twiss are reviewed in this context. Especially interesting from the theoretical point of view is the case of two emitting atoms, since then the classical and the quantum-mechanical description differ significantly, the quantum theory predicting the intensity correlations to be distinctly stronger than those following from classical considerations. This specific quantum-mechanical feature is shown to be intimately connected with the corpuscular aspect of light.