Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings of the Royal Society of Edinburgh Section A Mathematics

26.—Recent Light on Optical Interference

Richard M. Sillitto

Published Jan 1, 1972• 5 citations
Publisher

Abstract

Synopsis The interpretation of optical interference experiments at low light intensities and with independent light sources is discussed. A new experiment on interference between modulated light beams is described briefly, and its significance is indicated. There are two appendices, one a fuller discussion of the conditions under which interference and intensity correlation may be produced, the other a comment on one aspect of Jánossy and Nagy's discussion (1956) of the feasibility of the alternating slit interference experiment.

DOI
10.1017/s0080454100009109

Related papers

Interference of Independent Photon Beams

R. L. Pfleegor, L. Mandeļ

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.

Physical Review•Jul 25, 1967•285 citations

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

R. L. Pfleegor, L. Mandeļ

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.

Journal of the Optical Society of America•Jul 1, 1968•67 citations

Interference between independent photons

Henryk Paul

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.

Reviews of Modern Physics•Jan 1, 1986•147 citations

Quantum Theory of Interference Effects Produced by Independent Light Beams

L. Mandeļ

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.

Physical Review•Apr 6, 1964•54 citations

LII.On interference phenomena

Arthur Schuster

1. ~"~.OUY ?and RA'ZLEIG~r :~ have recently] discussed ~9t the question of interference phenomena observed with a source of white light, and have arrived at important results.When the two interfering beams pass through the slit of a spectroscope, the spectrum is seen to be crossed alternately by bright and dark bands, and if high resolving powers are used, these interference effects may be observed, although the difference of path of the two original beams is considerable.This well-known fact has always been taken to prove that the vibrations of the white light are to a certain extent " regular," and efforts have been made to find by experiment the limits of that regularity.The futility of these efforts has been completely demonstrated by Gouy and Rayleigh, who have proved that the bright and dark bands alluded to would appear with sufficient resolving power, even if light consisted of perfectly irregularly distributed instantaneous impulses.These investigations would seem, therefore, to lead to the conclusion that a source of light is completely defined by the distribution of energy in the * Oommun~cated by the Author.

The London Edinburgh and Dublin Philosophical Magazine and Journal of Science•Jun 1, 1894•19 citations

Progress in correlated optics

Kai Wang

We discuss in brief some interesting optical experiments based on intensity correlation measurement,such as ghost imaging,ghost interference,sub-wavelength interference and nonlocal double-slit interference,performed with both entangled two-photon states generated by spontaneous parametric down-conversion,and with thermal light.Some debates in this topic are also mentioned.

•Jan 1, 2008•0 citations
Synopsis The interpretation of optical interference experiments at low light intensities and with independent light sources is discussed. A new experiment on interference between modulated light beams is described briefly, and its significance is indicated. There are two appendices, one a fuller discussion of the conditions under which interference and intensity correlation may be produced, the other a comment on one aspect of Jánossy and Nagy's discussion (1956) of the feasibility of the alternating slit interference experiment.
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.
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.
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.
1. ~"~.OUY ?and RA'ZLEIG~r :~ have recently] discussed ~9t the question of interference phenomena observed with a source of white light, and have arrived at important results.When the two interfering beams pass through the slit of a spectroscope, the spectrum is seen to be crossed alternately by bright and dark bands, and if high resolving powers are used, these interference effects may be observed, although the difference of path of the two original beams is considerable.This well-known fact has always been taken to prove that the vibrations of the white light are to a certain extent " regular," and efforts have been made to find by experiment the limits of that regularity.The futility of these efforts has been completely demonstrated by Gouy and Rayleigh, who have proved that the bright and dark bands alluded to would appear with sufficient resolving power, even if light consisted of perfectly irregularly distributed instantaneous impulses.These investigations would seem, therefore, to lead to the conclusion that a source of light is completely defined by the distribution of energy in the * Oommun~cated by the Author.