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

Interference and Correlations in Photon and Electron Optics

C. S. Chang, P. Stehle

Published Apr 1, 1972• 11 citations
Publisher

Abstract

The quantum theory of interference effects is given. Three experiments of particular interest are treated: (i) Young-type experiments, (ii) production of beats in photocurrents, and (iii) optical modulation of electron beams. These have been of considerable interest in recent experiments using lasers. We show that they can be accounted for by the same simple quantum-mechanical principle. In the first case, we include the effect of interference in single-photon processes and correlations in multiphoton processes. Here the method of Weisskopf and Wigner is used, and useful distinction between the concept of interference and correlation is proposed. We further emphasize the dynamical aspect of the theory. In the last two cases, we use the standard method of quantum electrodynamics. Here we view the actual experimental setup as being described by a single dynamical process. The description involves the use of nonstationary states as the relevant states to describe the successive excitation. It is shown that all the three phenomena analyzed are closely related.

DOI
10.1103/physreva.5.1928

Related papers

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

Interference and tunnelling

Peter Holland

Interference by division of wavefront. The two-slit experiment Preliminary remarks In this chapter we shall be concerned with various types of interference effects exhibited by matter waves. It might be argued that all quantum mechanical phenomena are ultimately a consequence of interference, being governed as they are by a linear wave equation. Of particular interest here is the analogue for material waves of Young's double-slit experiment in optics, a classic problem in the history of quantum theory. Feynman, Leighton & Sands (1965) state that it ‘ … has in it the heart of quantum mechanics. In reality, it contains the only mystery’. We shall also treat the process of tunnelling into classically forbidden regions, a phenomenon which also involves interference in an essential way. To observe the interference of waves issuing from a common source we must split the emerging beam into two spatially separated coherent parts and subsequently recombine them (the superposition of waves from physically independent sources is a many-body problem – see §§8.8 and 12.7). As in optics there are two methods of achieving this: by division of wavefront where, for example, a wave falls on a screen containing two apertures, and by division of amplitude in which a wave is incident on a semi-transparent barrier. Interference effects achieved by the first method, discussed in this section, have been observed for electrons (Jönsson, 1961; Lichte, 1986; Tonomura et al ., 1989), neutrons (Zeilinger et al ., 1988) and (helium) atoms (Carnal & Mlynek, 1991).

Cambridge University Press eBooks•May 13, 1993•1 citation

Interference effects in spontaneous two-photon parametric scattering from two macroscopic regions

A. V. Burlakov, Maria V. Chekhova, Давид Николаевич Клышко +4 more

Two types of interference were observed using two-photon spontaneous parametric radiation from two nonlinear interaction regions. Two experimental setups analogous to the Young and Mach-Zehnder interferometers were used. An interesting feature of the two-photon Young interference is the opposite conditions for its observation by two different methods: by measuring intensity of light at a single frequency and by measuring correlation of intensities at two conjugated frequencies (method of coincidences). Two-photon Mach-Zehnder interference resembles the Ramsey method of separated fields, which is used in beam spectroscopy. A simple macroscopic quantum model agrees well with the experimental results and enables their interpretation in terms of ``biphotons'' carrying information about the pump phase.

Physical Review A•Oct 1, 1997•141 citations

Quantum optics of particles: distinctive features of a Hanbury Brown-Twiss experiment with electrons

Mark P. Silverman

Interference experiments characterized by the degree of first-order coherence (Young’s fringes, Fresnel, and Fraunhofer diffraction, etc.) have been performed with massive particles, in particular electrons and neutrons, as well as with light. Optical intensity interference or correlation experiments characterized by the degree of second-order coherence have not yet been performed with particles. The theory for such experiments shows striking differences in the behavior of electrons compared with that of light deriving from the differences in quantum statistics and charge. Photons are neutral bosons. They can be prepared in states that exhibit bunching, no bunching, or antibunching; they are unaffected by the presence of electromagnetic potentials. Electrons are charged fermions. Theory indicates that they exhibit antibunching regardless of the coherence of the source, and that their degree of second-order coherence can be influenced by electromagnetic fields through which they do not pass. A remarkable example is the Hanbury Brown-Twiss experiment with electrons that have interacted locally with the vector potential of an inaccessible magnetic field. The electron intensity correlation at two detectors is shown to be sensitive to the confined magnetic flux; experimental conditions differ considerably from those of the well-known Aharonov-Bohm effect.

Annual Meeting Optical Society of America•Jan 1, 1986•0 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

A simple field theoretic description of photon interference

Daniel F. Walls

A description of photon-interference experiments of the Young’s type using the techniques of quantum-field theory is presented. In particular, an explicit illustration of Dirac’s statement that a photon interferes only with itself is given. The interference patterns produced by a one photon, an n photon and a coherent photon field are calculated. A discussion of the degree of optical coherence possessed by the above fields is also incorporated. by the above fields is also incorporated.

American Journal of Physics•Oct 1, 1977•63 citations
The quantum theory of interference effects is given. Three experiments of particular interest are treated: (i) Young-type experiments, (ii) production of beats in photocurrents, and (iii) optical modulation of electron beams. These have been of considerable interest in recent experiments using lasers. We show that they can be accounted for by the same simple quantum-mechanical principle. In the first case, we include the effect of interference in single-photon processes and correlations in multiphoton processes. Here the method of Weisskopf and Wigner is used, and useful distinction between the concept of interference and correlation is proposed. We further emphasize the dynamical aspect of the theory. In the last two cases, we use the standard method of quantum electrodynamics. Here we view the actual experimental setup as being described by a single dynamical process. The description involves the use of nonstationary states as the relevant states to describe the successive excitation. It is shown that all the three phenomena analyzed are closely related.
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.
Interference by division of wavefront. The two-slit experiment Preliminary remarks In this chapter we shall be concerned with various types of interference effects exhibited by matter waves. It might be argued that all quantum mechanical phenomena are ultimately a consequence of interference, being governed as they are by a linear wave equation. Of particular interest here is the analogue for material waves of Young's double-slit experiment in optics, a classic problem in the history of quantum theory. Feynman, Leighton & Sands (1965) state that it ‘ … has in it the heart of quantum mechanics. In reality, it contains the only mystery’. We shall also treat the process of tunnelling into classically forbidden regions, a phenomenon which also involves interference in an essential way. To observe the interference of waves issuing from a common source we must split the emerging beam into two spatially separated coherent parts and subsequently recombine them (the superposition of waves from physically independent sources is a many-body problem – see §§8.8 and 12.7). As in optics there are two methods of achieving this: by division of wavefront where, for example, a wave falls on a screen containing two apertures, and by division of amplitude in which a wave is incident on a semi-transparent barrier. Interference effects achieved by the first method, discussed in this section, have been observed for electrons (Jönsson, 1961; Lichte, 1986; Tonomura et al ., 1989), neutrons (Zeilinger et al ., 1988) and (helium) atoms (Carnal & Mlynek, 1991).
Two types of interference were observed using two-photon spontaneous parametric radiation from two nonlinear interaction regions. Two experimental setups analogous to the Young and Mach-Zehnder interferometers were used. An interesting feature of the two-photon Young interference is the opposite conditions for its observation by two different methods: by measuring intensity of light at a single frequency and by measuring correlation of intensities at two conjugated frequencies (method of coincidences). Two-photon Mach-Zehnder interference resembles the Ramsey method of separated fields, which is used in beam spectroscopy. A simple macroscopic quantum model agrees well with the experimental results and enables their interpretation in terms of ``biphotons'' carrying information about the pump phase.
Interference experiments characterized by the degree of first-order coherence (Young’s fringes, Fresnel, and Fraunhofer diffraction, etc.) have been performed with massive particles, in particular electrons and neutrons, as well as with light. Optical intensity interference or correlation experiments characterized by the degree of second-order coherence have not yet been performed with particles. The theory for such experiments shows striking differences in the behavior of electrons compared with that of light deriving from the differences in quantum statistics and charge. Photons are neutral bosons. They can be prepared in states that exhibit bunching, no bunching, or antibunching; they are unaffected by the presence of electromagnetic potentials. Electrons are charged fermions. Theory indicates that they exhibit antibunching regardless of the coherence of the source, and that their degree of second-order coherence can be influenced by electromagnetic fields through which they do not pass. A remarkable example is the Hanbury Brown-Twiss experiment with electrons that have interacted locally with the vector potential of an inaccessible magnetic field. The electron intensity correlation at two detectors is shown to be sensitive to the confined magnetic flux; experimental conditions differ considerably from those of the well-known Aharonov-Bohm effect.
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.