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Annalen der Physik

Zur Interferenz unabhängiger Lichtstrahlen geringer Intensität

Wolfgang Radloff

Published Jan 1, 1971• 18 citations
Publisher

Abstract

Abstract We have observed the interference between two independent single mode He‐Ne laser beams. Our special equipment allowed us to record many times the interference pattern, when it was standing for a short time at the same position on the recorder. In this way we have obtained an interference picture of two independent light beams, which was (a) visible directly for the unaided eye for large intensities, (b) recorded on a photographic film for low intensities. The result of the experiments were in agreement with the statement of the quantummechanical description: We found a classical interference pattern down to very small intensities of the superposed beams. This result is discussed with regard to the quantum structure of light.

DOI
10.1002/andp.19714810210

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arXiv:physics/0503166•Chinese Physics Letters•Oct 27, 2005•4 citations
Abstract We have observed the interference between two independent single mode He‐Ne laser beams. Our special equipment allowed us to record many times the interference pattern, when it was standing for a short time at the same position on the recorder. In this way we have obtained an interference picture of two independent light beams, which was (a) visible directly for the unaided eye for large intensities, (b) recorded on a photographic film for low intensities. The result of the experiments were in agreement with the statement of the quantummechanical description: We found a classical interference pattern down to very small intensities of the superposed beams. This result is discussed with regard to the quantum structure of light.
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.
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.
Abstract The concept of nonmonochromatic modes of the radiation field introduced recently by TITULAER and GLAUBER, is employed to give a quantum mechanical description of the interference between nonmonochromatic light beams produced by different sources (e.g. lasers). The result is, in fact, that previous calculations by the author et al. in which each light beam was idealized as an excited state of one monochromatic mode, practically unchanged apply also to nonmonochromatic modes. The previous formulae describing the interference, on the other hand, are reproduced for the special case of (nonmonochromatic) modes corresponding to finitely extended beams of plane wave type, and, thus, are founded more exactly.
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.