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

Physical Review

Photoelectric Mixing of Incoherent Light

A. Theodore Forrester, R.A. Gudmundsen, Philip O. Johnson

Published Sep 15, 1955• 325 citations
Publisher

Abstract

Beats have been obtained between incoherent light sources by mixing Zeeman components of a visible spectral line at a photosurface. Periodicity in emission was observed through the excitation of a 3-cm cavity. Because of incoherence between the spectral lines and incoherence between the beats from different photocathode areas, the signal-to-shot-noise ratio at the cavity is only 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ but the beats were modulated optically, while maintaining constant total intensity and our receiver was able to yield a signal-to-noise ratio of two at the indicator. The basic idea is that, in the photoelectric process, the emission probability for electrons is proportional to the square of the resultant electric field amplitude, implying an interference between light originating in independent sources. This is a point of view which does not appear to be tested in any other experiment involving quantum effects. The experiment also demonstrates that any time delay between photon absorption and electron release must be significantly less than ${10}^{\ensuremath{-}10}$ second.

DOI
10.1103/physrev.99.1691

Related papers

Use of incoherent light to generate coherent excitation

S.R. Hartman

Time-delayed four-wave mixing signals in Na vapor using intense 7-ns pulses of 12-Å wide incoherent light centered at the Na D doublet display a 1.9-ps beat corresponding to the 6-Å splitting of the Na D lines. Collisional relaxation from an argon buffer gas is observed for relaxation times as short as the inverse bandwidth of the excitation noise. The effect of noise field induced relaxation is also examined.

International Laser Science Conference•Jan 1, 1986•0 citations

Quantum Theory of Interference Effects in the Mixing of Light from Phase-Independent Sources

U. Fano

Correlations in space and time of the light intensity from extended sources, observed by Brown and Twiss and by Forrester, were analyzed by these authors primarily in terms of field oscillations. This paper discusses an atomic process which brings out the intensity correlations, namely, the photoionization of a pair of atoms following photon emission by another pair of independently excited atoms. The calculated probability of this process depends sinusoidally on the relative positions of the four atoms and also, when the source atoms emit different frequencies, on the time interval between the photoionizations, in agreement with the macroscopic treatment. The oscillations arise from an interference of probability amplitudes which is not affected by the random phases of the source atoms. The calculation follows a standard approach but involves some novel detail.

American Journal of Physics•Aug 1, 1961•172 citations

ON THE DETERMINATION OF THE STATISTICAL PROPERTIES OF LIGHT FROM PHOTOELECTRIC MEASUREMENTS

J. PEf Ina

A relation is derived between the probability distribution of the integrated intensity of light incident on a photoelectric detector and that of the emission of n photoelectrons in a time interval (t, t + T) from the properties of a quantized electromagnetic field. Both the direct and the inverse relations are derived, thereby enabling the statistical properties of light to be determined from photoelectric measurements. An explicit expression is given for the coefficients for calculating the moments ( W k) by means of the moments (n J) (] = 1, 2 ..... k). The correctness of the operations in which generalized functions occur is confirmed by some direct calculations. The significance of photoelectric detectors has been increasing of late. Since their response is proportional to the intensity of incident light (to the square of the amplitude of light) (more exactly, to the local mean time value of the intensity), one speaks of quadratic detectors. These detectors are of basic importance in the theory of the coherence of the electromagnetic field, since if we place N such detectors into N different points in space and if we lead the outputs of these detectors to the correlator we can measure the correlation (coherence) effects of the 2N-th order in the given field [1]. Such correlation measurements provide information on the energy distribution in the radiation spectrum [2], the angular dimensions of stars [3], and the state of polarization [4] and also enable the phase of physically important functions (e.g. the scattering amplitudes) [5] to be determined. Although in such experiments the properties of photoelectrons are studied rather than of photons, they reflect the basic properties of photons. Let the probability distribution Of the emission of n photoelectrons in a time interval (t, t + T) be p(n, T, t) - p(n) and let the probability distribution of the quantity W(T, t) = W = J'tt+r I(t') dr', where I(t) is the intensity of linearly polarized light incident on the photodetector (for simplicity we assume that the sensitivity of the photocathode is a = 1), be P(W). The quantity W can be regarded as a classical characteristic of the field, the quantity n represents the quantum characteristic of the field. Then, on the basis of such a semi-classical description, in which the field is described classically, but its interaction is described quantum-wise, one can derive the following relation [6]

•Jan 1, 1967•1 citation

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

Light-beating spectroscopy with collisionless sources

M. S. Slutsky, Robert R. Lewis

The theory of the Forrester effect is reexamined in both classical and quantum terms. We show that temporal coherence (light beating) can arise from the interference of fields produced either by single atoms or by pairs of atoms. The singles terms, which dominate for a collisionless source with low intensity, give a light-beating signal-to-noise ratio of order unity, independent of the intensity and wavelength. This signal is also unaffected by Doppler broadening. The doubles terms, originally analyzed by Forrester, give a signal-to-noise ratio proportional to the intensity and to the square of the wavelength, and subject to Doppler broadening. Our results suggest the possibility of a new type of rf and microwave spectroscopy for excited atoms.

Physical Review A•Jan 1, 1977•2 citations

Interferometry of the intensity fluctuations in light - I. Basic theory: the correlation between photons in coherent beams of radiation

Robert Hanbury Brown, R. Q. Twiss, givenName surName

Abstract It is shown by a quantum-mechanical treatment that the emission times of photoelectrons at different points illuminated by a plane wave of light are partially correlated, and identical results are obtained by a classical theory in which the photocathode is regarded as a square-law detector of suitable conversion efficiency. It is argued that the phenomenon exemplifies the wave rather than the particle aspect of light and that it may most easily be interpreted as a correlation between the intensity fluctuations at different points on a wavefront which arise because of interference between different frequency components of the light. From the point of view of the corpuscular picture the interpretation is much less straight­forward but it is shown that the correlation is directly related to the so-called bunching of photons which arises because light quanta are mutually indistinguishable and obey Bose-Einstein statistics. However, it is stressed that the use of the photon concept before the light energy is actually detected is highly misleading since, in an interference experiment, the electromagnetic field behaves in a manner which cannot be explained in terms of classical particles. The quantitative predictions of the theory have been confirmed by laboratory experi­ments and the phenomenon has been used, in an interferometer, to measure the apparent angular diameter of Sirius: these results, together with further applications to astronomy, will be discussed in detail in later papers. It is shown that the classical and quantum treatments give identical results when applied to find the fluctuations in the photoemission current produced by a single light beam, and the connexion between these fluctuations and the correlation between photons in coherent beams is pointed out. The results given here are in full agreement with those obtained by Kahn from an analysis based on quantum statistics: however, they differ from those derived on thermodynamical grounds by Fellgett and by Clark Jones and the reasons for this discrepancy are discussed.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Nov 5, 1957•429 citations
Beats have been obtained between incoherent light sources by mixing Zeeman components of a visible spectral line at a photosurface. Periodicity in emission was observed through the excitation of a 3-cm cavity. Because of incoherence between the spectral lines and incoherence between the beats from different photocathode areas, the signal-to-shot-noise ratio at the cavity is only 3\ifmmode\times\else\texttimes\fi{}10\ensuremath−5{10}^{\ensuremath{-}5}10\ensuremath−5 but the beats were modulated optically, while maintaining constant total intensity and our receiver was able to yield a signal-to-noise ratio of two at the indicator. The basic idea is that, in the photoelectric process, the emission probability for electrons is proportional to the square of the resultant electric field amplitude, implying an interference between light originating in independent sources. This is a point of view which does not appear to be tested in any other experiment involving quantum effects. The experiment also demonstrates that any time delay between photon absorption and electron release must be significantly less than 10\ensuremath−10{10}^{\ensuremath{-}10}10\ensuremath−10 second.
Correlations in space and time of the light intensity from extended sources, observed by Brown and Twiss and by Forrester, were analyzed by these authors primarily in terms of field oscillations. This paper discusses an atomic process which brings out the intensity correlations, namely, the photoionization of a pair of atoms following photon emission by another pair of independently excited atoms. The calculated probability of this process depends sinusoidally on the relative positions of the four atoms and also, when the source atoms emit different frequencies, on the time interval between the photoionizations, in agreement with the macroscopic treatment. The oscillations arise from an interference of probability amplitudes which is not affected by the random phases of the source atoms. The calculation follows a standard approach but involves some novel detail.
A relation is derived between the probability distribution of the integrated intensity of light incident on a photoelectric detector and that of the emission of n photoelectrons in a time interval (t, t + T) from the properties of a quantized electromagnetic field. Both the direct and the inverse relations are derived, thereby enabling the statistical properties of light to be determined from photoelectric measurements. An explicit expression is given for the coefficients for calculating the moments ( W k) by means of the moments (n J) (] = 1, 2 ..... k). The correctness of the operations in which generalized functions occur is confirmed by some direct calculations. The significance of photoelectric detectors has been increasing of late. Since their response is proportional to the intensity of incident light (to the square of the amplitude of light) (more exactly, to the local mean time value of the intensity), one speaks of quadratic detectors. These detectors are of basic importance in the theory of the coherence of the electromagnetic field, since if we place N such detectors into N different points in space and if we lead the outputs of these detectors to the correlator we can measure the correlation (coherence) effects of the 2N-th order in the given field [1]. Such correlation measurements provide information on the energy distribution in the radiation spectrum [2], the angular dimensions of stars [3], and the state of polarization [4] and also enable the phase of physically important functions (e.g. the scattering amplitudes) [5] to be determined. Although in such experiments the properties of photoelectrons are studied rather than of photons, they reflect the basic properties of photons. Let the probability distribution Of the emission of n photoelectrons in a time interval (t, t + T) be p(n, T, t) - p(n) and let the probability distribution of the quantity W(T, t) = W = J'tt+r I(t') dr', where I(t) is the intensity of linearly polarized light incident on the photodetector (for simplicity we assume that the sensitivity of the photocathode is a = 1), be P(W). The quantity W can be regarded as a classical characteristic of the field, the quantity n represents the quantum characteristic of the field. Then, on the basis of such a semi-classical description, in which the field is described classically, but its interaction is described quantum-wise, one can derive the following relation [6]
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 theory of the Forrester effect is reexamined in both classical and quantum terms. We show that temporal coherence (light beating) can arise from the interference of fields produced either by single atoms or by pairs of atoms. The singles terms, which dominate for a collisionless source with low intensity, give a light-beating signal-to-noise ratio of order unity, independent of the intensity and wavelength. This signal is also unaffected by Doppler broadening. The doubles terms, originally analyzed by Forrester, give a signal-to-noise ratio proportional to the intensity and to the square of the wavelength, and subject to Doppler broadening. Our results suggest the possibility of a new type of rf and microwave spectroscopy for excited atoms.
Abstract It is shown by a quantum-mechanical treatment that the emission times of photoelectrons at different points illuminated by a plane wave of light are partially correlated, and identical results are obtained by a classical theory in which the photocathode is regarded as a square-law detector of suitable conversion efficiency. It is argued that the phenomenon exemplifies the wave rather than the particle aspect of light and that it may most easily be interpreted as a correlation between the intensity fluctuations at different points on a wavefront which arise because of interference between different frequency components of the light. From the point of view of the corpuscular picture the interpretation is much less straight­forward but it is shown that the correlation is directly related to the so-called bunching of photons which arises because light quanta are mutually indistinguishable and obey Bose-Einstein statistics. However, it is stressed that the use of the photon concept before the light energy is actually detected is highly misleading since, in an interference experiment, the electromagnetic field behaves in a manner which cannot be explained in terms of classical particles. The quantitative predictions of the theory have been confirmed by laboratory experi­ments and the phenomenon has been used, in an interferometer, to measure the apparent angular diameter of Sirius: these results, together with further applications to astronomy, will be discussed in detail in later papers. It is shown that the classical and quantum treatments give identical results when applied to find the fluctuations in the photoemission current produced by a single light beam, and the connexion between these fluctuations and the correlation between photons in coherent beams is pointed out. The results given here are in full agreement with those obtained by Kahn from an analysis based on quantum statistics: however, they differ from those derived on thermodynamical grounds by Fellgett and by Clark Jones and the reasons for this discrepancy are discussed.