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 A

Light-beating spectroscopy with collisionless sources

M. S. Slutsky, Robert R. Lewis

Published Jan 1, 1977• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.15.272

Related papers

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

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

Photoelectric Mixing of Incoherent Light

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

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.

Physical Review•Sep 15, 1955•325 citations

Single-photon superradiant beating from a Doppler-broadened ladder-type atomic ensemble

Yoon‐Seok Lee, Sang Min Lee, Heonoh Kim +1 more

We report on heralded-single-photon superradiant beating in the spontaneous four-wave mixing process of Doppler-broadened ladder-type $^{87}\mathrm{Rb}$ atoms. When Doppler-broadened atoms contribute to two-photon coherence, the detection probability amplitudes of the heralded single photons are coherently superposed despite inhomogeneous broadened atomic media. Single-photon superradiant beating is observed, which constitutes evidence for the coherent superposition of two-photon amplitudes from different velocity classes in the Doppler-broadened atomic ensemble. We present a theoretical model in which the single-photon superradiant beating originates from the interference between wavelength-separated two-photon amplitudes via the reabsorption filtering effect.

Physical Review A•Dec 22, 2017•16 citations

Quantum interference effects in two-photon spectroscopy

M. M. Salour

Interaction of atoms with two intense coherent time-delayed short pulsed standing waves produces quantum interference effects in the atomic fluorescence. This type of quantum interference effect applied to Doppler-free two-photon spectroscopy (an extension of the Ramsey method of separated r.f. or microwave fields in atomic beam experiments) offers a number of important improvements in the presently available techniques of ultra-high-resolution spectroscopy of atoms, molecules, and crystals.

Reviews of Modern Physics•Jul 1, 1978•90 citations

Observation of temporal beating in first- and second-order intensity measurement between independent Raman Stokes fields in atomic vapor

L. Q. Chen, Cheng-ling Bian, Guo-Wan Zhang +2 more

By using spontaneous Raman processes in the high-gain regime, we produce two independent Raman Stokes fields from an atomic ensemble. Temporal beating is observed between the two directly generated Stokes fields in a single realization. The beat frequency is found to be a result of an ac Stark frequency shift effect. However, due to the spontaneous nature of the process, the phases of the two Stokes fields change from one realization to another so that the beat signal disappears after averaging over many realizations. On the other hand, the beat signal is recovered in an intensity correlation measurement, showing a two-photon interference effect. The beat signal in intensity correlation enables us to obtain dephasing information in the Raman process. The dephasing effect is found to depend on the temperature of the atomic medium.

Physical Review A•Sep 27, 2010•13 citations
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.
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 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.
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.
We report on heralded-single-photon superradiant beating in the spontaneous four-wave mixing process of Doppler-broadened ladder-type 87Rb^{87}\mathrm{Rb}87Rb atoms. When Doppler-broadened atoms contribute to two-photon coherence, the detection probability amplitudes of the heralded single photons are coherently superposed despite inhomogeneous broadened atomic media. Single-photon superradiant beating is observed, which constitutes evidence for the coherent superposition of two-photon amplitudes from different velocity classes in the Doppler-broadened atomic ensemble. We present a theoretical model in which the single-photon superradiant beating originates from the interference between wavelength-separated two-photon amplitudes via the reabsorption filtering effect.
By using spontaneous Raman processes in the high-gain regime, we produce two independent Raman Stokes fields from an atomic ensemble. Temporal beating is observed between the two directly generated Stokes fields in a single realization. The beat frequency is found to be a result of an ac Stark frequency shift effect. However, due to the spontaneous nature of the process, the phases of the two Stokes fields change from one realization to another so that the beat signal disappears after averaging over many realizations. On the other hand, the beat signal is recovered in an intensity correlation measurement, showing a two-photon interference effect. The beat signal in intensity correlation enables us to obtain dephasing information in the Raman process. The dephasing effect is found to depend on the temperature of the atomic medium.