Interference between independent photons
Abstract
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.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The tunneling parameter between sites C was measured to be 290 m−1.
“The tunneling parameter between”
From Quantum and Classical Correlations in Waveguide Lattices (2009) · cites this paper as [23]
Cites
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
Einstein, A., Podolsky, B., & Rosen, N. (1935) · Physical Review · doi:10.1103/physrev.47.777 · Cited by 16,654 · see citing works
Coherence in Spontaneous Radiation Processes
Dicke, R. H. (1954) · Physical Review · doi:10.1103/physrev.93.99 · Cited by 7,445 · see citing works
Coherent and Incoherent States of the Radiation Field
Glauber, R. J. (1963) · Physical Review · doi:10.1103/physrev.131.2766 · Cited by 6,742 · see citing works
Correlation between Photons in two Coherent Beams of Light
BROWN, R. H., & TWISS, R. Q. (1956) · Nature · doi:10.1038/177027a0 · Cited by 2,573 · see citing works
The quantum theory of the emission and absorption of radiation
Dirac, P. A. M. (1927) · Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character · doi:10.1098/rspa.1927.0039 · Cited by 2,288 · see citing works
Power Spectrum of Light Scattered by Two-Level Systems
Mollow, B. R. (1969) · Physical Review · doi:10.1103/physrev.188.1969 · Cited by 1,939 · see citing works
Berechnung der nat�rlichen Linienbreite auf Grund der Diracschen Lichttheorie
Weisskopf, V. F., & Wigner, E. P. (1930) · The European Physical Journal A · doi:10.1007/bf01336768 · Cited by 1,803 · see citing works
A Test of a New Type of Stellar Interferometer on Sirius
Brown, R. H., & Twiss, R. Q. (1956) · Nature · doi:10.1038/1781046a0 · Cited by 1,562 · see citing works
Der stetige �bergang von der Mikro- zur Makromechanik
Schr�dinger, E. (1926) · Die Naturwissenschaften · doi:10.1007/bf01507634 · Cited by 1,415 · see citing works
The Quantum Theory of Radiation
P., R. (1936) · Nature · doi:10.1038/138483a0 · Cited by 1,227 · see citing works
Quantum optics and electronics
(1965) · Nuclear Physics · doi:10.1016/0029-5582(65)90427-x · Cited by 870 · see citing works
Radiation from an N -Atom System. I. General Formalism
Lehmberg, R. H. (1970) · Physical Review A · doi:10.1103/physreva.2.883 · Cited by 795 · see citing works
An introduction to statistical communication theory
Siebert, W. M. (1961) · Journal of the Franklin Institute · doi:10.1016/0016-0032(61)90153-3 · Cited by 703 · see citing works
Theory of resonance fluorescence
Kimble, H. J., & Mandeļ, L. (1976) · Physical Review A · doi:10.1103/physreva.13.2123 · Cited by 553 · see citing works
Quantum Noise. XI. Multitime Correspondence between Quantum and Classical Stochastic Processes
Lax, M. D. (1968) · Physical Review · doi:10.1103/physrev.172.350 · Cited by 443 · see citing works
�ber die nat�rliche Linienbreite in der Strahlung des harmonischen Oszillators
Weisskopf, V. F., & Wigner, E. P. (1930) · The European Physical Journal A · doi:10.1007/bf01397406 · Cited by 435 · see citing works
Photoelectric Mixing of Incoherent Light
Forrester, A. T., Gudmundsen, R. A., & Johnson, P. O. (1955) · Physical Review · doi:10.1103/physrev.99.1691 · Cited by 326 · see citing works
Density Operators for Coherent Fields
Titulaer, U. M., & Glauber, R. J. (1966) · Physical Review · doi:10.1103/physrev.145.1041 · Cited by 288 · see citing works
Interference of Independent Photon Beams
Pfleegor, R. L., & Mandeļ, L. (1967) · Physical Review · doi:10.1103/physrev.159.1084 · Cited by 287 · see citing works
Principles of Quantum Mechanics
Young, W. H. (1974) · Physics Bulletin · doi:10.1088/0031-9112/25/8/035 · Cited by 198 · see citing works
Photon interference and correlation effects produced by independent quantum sources
Mandeļ, L. (1983) · Physical Review A · doi:10.1103/physreva.28.929 · Cited by 184 · see citing works
Emission of Radiation from a System of Many Excited Atoms
Ernst, V., & Stehle, P. (1968) · Physical Review · doi:10.1103/physrev.176.1456 · Cited by 184 · see citing works
Quantum Theory of Interference Effects in the Mixing of Light from Phase-Independent Sources
Fano, U. (1961) · American Journal of Physics · doi:10.1119/1.1937827 · Cited by 172 · see citing works
Frequency Characteristics of a Continuous-Wave He–Ne Optical Maser
Javan, A., Ballik, E. A., & Bond, W. L. (1962) · Journal of the Optical Society of America · doi:10.1364/josa.52.000096 · Cited by 166 · see citing works
Interference Fringes Produced by Superposition of Two Independent Maser Light Beams
Magyar, G., & Mandeļ, L. (1963) · Nature · doi:10.1038/198255a0 · Cited by 166 · see citing works
On the Application of Interference Methods to Astronomical Measurements
Michelson, A. A. (1920) · The Astrophysical Journal · doi:10.1086/142550 · Cited by 164 · see citing works
I. On the application of interference methods to astronomical measurements
Michelson, A. A. (1890) · The London Edinburgh and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786449008619983 · Cited by 115 · see citing works
Rebka, G. A., & Pound, R. V. (1957) · Nature · doi:10.1038/1801035a0 · Cited by 79 · see citing works
The damped driven two-level atom
Mollow, B. R., & Miller, M. M. (1969) · Annals of Physics · doi:10.1016/0003-4916(69)90289-9 · Cited by 72 · see citing works
Further Experiments on Interference of Independent Photon Beams at Low Light Levels*†
Pfleegor, R. L., & Mandeļ, L. (1968) · Journal of the Optical Society of America · doi:10.1364/josa.58.000946 · Cited by 67 · see citing works
Induced and Spontaneous Emission in a Coherent Field
Senitzky, I. R. (1958) · Physical Review · doi:10.1103/physrev.111.3 · Cited by 67 · see citing works
The interference phenomena of light at very low intensities
Jánossy, L., & Náray, Z. (1957) · Acta Physica Academiae Scientiarum Hungaricae · doi:10.1007/bf03157612 · Cited by 39 · see citing works
Quantum Effects in the Interaction between Electrons and High-Frequency Fields. I
Senitzky, I. R. (1954) · Physical Review · doi:10.1103/physrev.95.904 · Cited by 37 · see citing works
Photonen‐Korrelationen in der spontanen Emission eines Zwei‐Atom‐Systems
Richter, T. (1979) · Annalen der Physik · doi:10.1002/andp.19794910404 · Cited by 37 · see citing works
Interferenz zwischen unabhängigen Photonen
Paul, H., Brunner, W., & Richter, G. (1963) · Annalen der Physik · doi:10.1002/andp.19634670509 · Cited by 36 · see citing works
Self-citationJánossy, L., & Náray, Z. (1958) · Il Nuovo Cimento · doi:10.1007/bf02747689 · Cited by 31 · see citing works
Absorption und Streuung quantenmechanisch kohärenter Strahlen. II. Wechselwirkung mit N Atomen
Brunner, W., Paul, H., & Richter, G. (1965) · Annalen der Physik · doi:10.1002/andp.19654700105 · Cited by 29 · see citing works
Self-citationRadiation Properties of a Continuously Pumped Two‐Atom System
Steudel, H., & Richter, T. (1978) · Annalen der Physik · doi:10.1002/andp.19784900205 · Cited by 27 · see citing works
Ein Beitrag zur Quantentheorie der optischen Kohärenz
Paul, H. (1966) · Fortschritte der Physik · doi:10.1002/prop.19660140104 · Cited by 19 · see citing works
Self-citationZur Interferenz unabhängiger Lichtstrahlen geringer Intensität
Radloff, W. (1971) · Annalen der Physik · doi:10.1002/andp.19714810210 · Cited by 18 · see citing works
Absorption und Streuung quantenmechanisch kohärenter Strahlen. I Wechselwirkung mit einem Atom
Brunner, W., Paul, H., & Richter, G. (1964) · Annalen der Physik · doi:10.1002/andp.19644690704 · Cited by 16 · see citing works
Self-citationLichtreflexion im Formalismus der Quantenelektrodynamik
Paul, H., Brunner, W., & Richter, G. (1966) · Annalen der Physik · doi:10.1002/andp.19664720505 · Cited by 13 · see citing works
Self-citationMicrowave Experiments and Their Optical Analogs
Hull, G. F. (1949) · American Journal of Physics · doi:10.1119/1.1989694 · Cited by 13 · see citing works
Zur Quantentheorie der Kohärenz der Laserstrahlung
Paul, H., Brunner, W., & Richter, G. (1965) · Annalen der Physik · doi:10.1002/andp.19654710110 · Cited by 10 · see citing works
Self-citationSpontane Strahlung eines Zwei‐Atom‐Systems
Steudel, H. (1971) · Annalen der Physik · doi:10.1002/andp.19714820107 · Cited by 10 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Multiphoton entanglement and interferometry
Pan, J.-W., Chen, Z.-B., Lu, C.-Y., Weinfurter, H., Zeilinger, A., & Żukowski, M. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.777 · Cited by 1,410 · see citing works
“Interference of photons emerging from independent sources (Mandel, 1983; Paul, 1986) has no classical analogue and can be understood only by the interference of probability amplitudes of multi-particle detection events.”
BackgroundQuantum and Classical Correlations in Waveguide Lattices
Bromberg, Y., Lahini, Y., Morandotti, R., & Silberberg, Y. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.253904 · Cited by 318 · see citing works
Photon correlations in two-dimensional waveguide arrays and their classical estimate
Keil, R., Szameit, A., Dreisow, F., Heinrich, M., Nolte, S., & Tünnermann, A. (2010) · Physical Review A · doi:10.1103/physreva.81.023834 · Cited by 44 · see citing works
II Quantum Phenomena in Optical Interferometry
Hariharan, P., & Sanders, B. C. (1996) · Progress in Optics · doi:10.1016/s0079-6638(08)70313-5 · Cited by 36 · see citing works
- Authors
- Paul, H.
- Corresponding author
- Paul, H.
- ORCID
- Paul, H.
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 1986-01-01
- Volume
- 58
- Issue
- 1
- Pages
- 209-231
- ISSN
- 0034-6861 (ISSN-L)
- OpenAlex
- W1974304030
- Cited by
- 147
- References
- 45
- Citations by year
- 2026: 1 · 2025: 6 · 2024: 5 · 2023: 3 · 2022: 3 · 2021: 7 · 2020: 4 · 2019: 8 · 2018: 5 · 2017: 4 · 2016: 5 · 2015: 6 · 2014: 4 · 2013: 5 · 2012: 5
- FWCI
- 2.82
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Reviews of Modern Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Strong Light-Matter Interactions
- Keywords
- photon interference, intensity correlations, spontaneous emission, laser attenuation, quantum-classical correspondence
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
