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

Annalen der Physik

Anticorrelations in Nondegenerate Parametric Three‐Wave Interaction

Henryk Paul, W. Brunner

Published Jan 1, 1981• 10 citations
Publisher

Abstract

Abstract It is shown that the anticorrelations in the photon numbers of the signal and the idler wave, respectively, generated in parametric three‐wave interaction under suitable conditions, violate an inequality well‐known in classical communication theory. Hence, it must be concluded that these anticorrelations reflect a typical quantum mechanical feature of light. In fact, this nonclassical behaviour is responsible for the occurrence of photon antibunching in the superposition field made up of both the signal and the idler wave, as will be pointed out in some detail.

DOI
10.1002/andp.19814930202

Related papers

Double‐mode Two‐photon Absorption and Enhanced Photon Antibunching Due to Interference

A. Bandilla, H.‐H. Ritze

Abstract Inspired by results of interfering signal and idler from a nondegenerate parametric amplifier we investigate the photon statistics of the resulting field after interference of two components subjected to double‐mode two‐photon absorption. This absorption process leads to a strong correlation of the participating modes, which can be used to generate fields with photon antibunching in interference experiments. In addition the photon number can be made small, which produces enhanced antibunching.

Annalen der Physik•Jan 1, 1981•1 citation

Nondegenerate parametric interactions and nonclassical effects

A. Bandilla, G. Drobný, Igor Jex

We consider the classical and quantum-mechanical processes of three-wave interactions in different phase regimes and present numerical calculations for the quantum case, where all three modes are sizably excited from the beginning. These excitations are coherent so that various important phase regimes can be adjusted. In addition, one mode can also be prepared in a squeezed or Kerr state. The classical solutions are well known and are briefly summarized, but certain phase regimes are classically unexplored and we show here that they give interesting and surprising results. In the out-of-phase regime (where the photon numbers do not change in the first order of time) we get, with an initial Kerr state, strongly sub-Poissonian photon statistics in the signal after a short interaction time. This effect is limited by the classically described phase shifts that are present even in the parametric approximation. This nonclassical phenomenon (due to the Kerr state) helps us to understand similar nonclassical effects generated by entangled states of the pump and signal during sum-frequency generation. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Jan 1, 1996•29 citations

A Proposed Experiment to Observe Photon Antibunching in a Parametric Three-wave Interaction

Henryk Paul, W. Brunner

The difference in the group velocities for the signal and the idler wave, interacting with a sum-frequency wave in a non-linear crystal, is shown to provide a memory mechanism which determines the length of the mode volume occurring in the usual single-mode description of this process in connection with photon antibunching. The consideration also includes the degenerate case (second harmonic generation). The results suggest the use of a c.w. picosecond laser as a primary light source in an experiment designed to demonstrate the antibunching effect. The basic set-up of such an experiment is described.

Optica Acta International Journal of Optics•Mar 1, 1980•14 citations

Nonclassical Photon Interference Effects

C K Hong, Z. Y. Ou, L. Mandeļ

This chapter discusses two reported experiments in which the interference between signal and idler photons generated in the process of parametric down-conversion were investigated. Although two-photon interference effects have been treated theoretically before, it analyzes the two experiments in some detail to show how differences between the predictions of classical and quantum theories appear. The chapter compares the predictions of classical and quantum theories with the experimental results obtained. As practically all detectors of light rely on the photoelectric effect, in which a free electron is produced at the expense of a photon, the photon annihilation operator plays a key role in describing the measurement of light in the quantum theory. The time correlation between signal and idler photons produced in the parametric down-conversion process was first measured with a resolving time of about 10 nanoseconds. The interference effect can be made the basis of a measurement of the length of a photon wave packet with femtosecond time resolution.

CRC Press eBooks•Aug 12, 2020•2 citations

Photon antibunching

Henryk Paul

A review is given of recent theoretical studies devoted to the problem of generating radiation fields that exhibit the opposite of the well-known bunching of photons observed in light from thermal sources, the so-called antibunching effect. It is made clear that this phenomenon reflects the corpuscular nature of light and, hence, cannot be interpreted in terms of classical electrodynamics, needing, instead, the quantum-mechanical formalism for its description. It is shown in some detail that nonlinear interaction mechanisms like multiphoton absorption and parametric three-wave interaction are suited to change the photon statistical properties of incident (in most cases coherent) light such that the output field will be endowed with antibunching properties. Special emphasis is given to the problem of correctly specifying the dimensions of the mode volume occurring in the usual single-mode treatment of the field, which is, in fact, of great practical interest, since the magnitude of the antibunching effect is determined by the inverse average number of photons contained in that volume. In a later section it is pointed out that destructive interference with a coherent reference beam provides a means of (a) effectively enhancing photon antibunching that is already present in a high-intensity field, through reduction of the intensity, and (b) transforming phase fluctuations produced in a Kerr medium into antibunching-type intensity fluctuations. On the other hand, there exists a way of directly generating light with antibunching properties, the physical mechanism being resonance fluorescence from a single atom. The main features of this technique, both theoretical and experimental, are outlined, including a discussion of the first experimental results obtained a few years ago.

Reviews of Modern Physics•Oct 1, 1982•328 citations

Antibunching of photons in a coherent radiation field coupled to a non-degenerate parametric oscillator beyond rotating wave approximation

Swapan Mandal, Mohosin Alam, Monojit Kora +1 more

Under the classical (strong) pump condition, the Hamiltonian involving the signal and the idler modes of a non-degenerate parametric oscillator is exhibited. Without using the usual rotating wave approximation (RWA), the analytical solutions of the field operators are used to investigate the antibunching of photons of the input radiation field coupled to the non-degenerate parametric oscillator. By using the symbolic calculation, the antibunching of photons for both the signal and idler modes are investigated. In particular, the effects of the inclusion of rotating wave approximated terms on the antibunching of photons are clearly indicated. To substantiate the analytical results, the temporal evolution of signal photon and idler photons, and the antibunching effects of the signal and idler modes are investigated numerically by using the QuTip 3.1.0. The exact numerical results obtained by QuTip 3.1.0 matches extremely well with those of the analytical results. The present article and hence the analytical method might be of use for investigating the situations of having ultra-strongly and deep-strongly coupled systems where the possibilities of using RWA is completely ruled out.

Pramana•May 15, 2021•4 citations
Abstract It is shown that the anticorrelations in the photon numbers of the signal and the idler wave, respectively, generated in parametric three‐wave interaction under suitable conditions, violate an inequality well‐known in classical communication theory. Hence, it must be concluded that these anticorrelations reflect a typical quantum mechanical feature of light. In fact, this nonclassical behaviour is responsible for the occurrence of photon antibunching in the superposition field made up of both the signal and the idler wave, as will be pointed out in some detail.
Abstract Inspired by results of interfering signal and idler from a nondegenerate parametric amplifier we investigate the photon statistics of the resulting field after interference of two components subjected to double‐mode two‐photon absorption. This absorption process leads to a strong correlation of the participating modes, which can be used to generate fields with photon antibunching in interference experiments. In addition the photon number can be made small, which produces enhanced antibunching.
We consider the classical and quantum-mechanical processes of three-wave interactions in different phase regimes and present numerical calculations for the quantum case, where all three modes are sizably excited from the beginning. These excitations are coherent so that various important phase regimes can be adjusted. In addition, one mode can also be prepared in a squeezed or Kerr state. The classical solutions are well known and are briefly summarized, but certain phase regimes are classically unexplored and we show here that they give interesting and surprising results. In the out-of-phase regime (where the photon numbers do not change in the first order of time) we get, with an initial Kerr state, strongly sub-Poissonian photon statistics in the signal after a short interaction time. This effect is limited by the classically described phase shifts that are present even in the parametric approximation. This nonclassical phenomenon (due to the Kerr state) helps us to understand similar nonclassical effects generated by entangled states of the pump and signal during sum-frequency generation. \textcopyright{} 1996 The American Physical Society.
The difference in the group velocities for the signal and the idler wave, interacting with a sum-frequency wave in a non-linear crystal, is shown to provide a memory mechanism which determines the length of the mode volume occurring in the usual single-mode description of this process in connection with photon antibunching. The consideration also includes the degenerate case (second harmonic generation). The results suggest the use of a c.w. picosecond laser as a primary light source in an experiment designed to demonstrate the antibunching effect. The basic set-up of such an experiment is described.
This chapter discusses two reported experiments in which the interference between signal and idler photons generated in the process of parametric down-conversion were investigated. Although two-photon interference effects have been treated theoretically before, it analyzes the two experiments in some detail to show how differences between the predictions of classical and quantum theories appear. The chapter compares the predictions of classical and quantum theories with the experimental results obtained. As practically all detectors of light rely on the photoelectric effect, in which a free electron is produced at the expense of a photon, the photon annihilation operator plays a key role in describing the measurement of light in the quantum theory. The time correlation between signal and idler photons produced in the parametric down-conversion process was first measured with a resolving time of about 10 nanoseconds. The interference effect can be made the basis of a measurement of the length of a photon wave packet with femtosecond time resolution.
A review is given of recent theoretical studies devoted to the problem of generating radiation fields that exhibit the opposite of the well-known bunching of photons observed in light from thermal sources, the so-called antibunching effect. It is made clear that this phenomenon reflects the corpuscular nature of light and, hence, cannot be interpreted in terms of classical electrodynamics, needing, instead, the quantum-mechanical formalism for its description. It is shown in some detail that nonlinear interaction mechanisms like multiphoton absorption and parametric three-wave interaction are suited to change the photon statistical properties of incident (in most cases coherent) light such that the output field will be endowed with antibunching properties. Special emphasis is given to the problem of correctly specifying the dimensions of the mode volume occurring in the usual single-mode treatment of the field, which is, in fact, of great practical interest, since the magnitude of the antibunching effect is determined by the inverse average number of photons contained in that volume. In a later section it is pointed out that destructive interference with a coherent reference beam provides a means of (a) effectively enhancing photon antibunching that is already present in a high-intensity field, through reduction of the intensity, and (b) transforming phase fluctuations produced in a Kerr medium into antibunching-type intensity fluctuations. On the other hand, there exists a way of directly generating light with antibunching properties, the physical mechanism being resonance fluorescence from a single atom. The main features of this technique, both theoretical and experimental, are outlined, including a discussion of the first experimental results obtained a few years ago.
Under the classical (strong) pump condition, the Hamiltonian involving the signal and the idler modes of a non-degenerate parametric oscillator is exhibited. Without using the usual rotating wave approximation (RWA), the analytical solutions of the field operators are used to investigate the antibunching of photons of the input radiation field coupled to the non-degenerate parametric oscillator. By using the symbolic calculation, the antibunching of photons for both the signal and idler modes are investigated. In particular, the effects of the inclusion of rotating wave approximated terms on the antibunching of photons are clearly indicated. To substantiate the analytical results, the temporal evolution of signal photon and idler photons, and the antibunching effects of the signal and idler modes are investigated numerically by using the QuTip 3.1.0. The exact numerical results obtained by QuTip 3.1.0 matches extremely well with those of the analytical results. The present article and hence the analytical method might be of use for investigating the situations of having ultra-strongly and deep-strongly coupled systems where the possibilities of using RWA is completely ruled out.