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

Journal of the Optical Society of America B

Parametric downconversion experiments in the Wigner representation

Alberto Casado, Trevor W. Marshall, Emilio Santos

Published Mar 1, 1997• 44 citations
Publisher

Abstract

The Wigner representation is developed in the Heisenberg picture for the study of experiments involving photon pairs created in the process of parametric down conversion. After the general description of a light beam and the theory of detection (restricted here to single count probabilities in the Wigner formalism) the theory of parametric downconversion is developed to the point of calculating the autocorrelations of the signal and idler beams. Two recent experiments are analyzed in detail: frustrated two-photon creation by interference, and induced coherence and indistinguishability.

DOI
10.1364/josab.14.000494

Related papers

Fourth-order interference in the Wigner representation for parametric down-conversion experiments

Alberto Casado, A. Fernández-Rueda, Trevor W. Marshall +2 more

In the Wigner formalism, after giving a general description of a light beam, the theory of parametric down-conversion is developed to second-order in the coupling constant. We then describe the detection process by calculating the auto-correlation and cross-correlations of the signal and idler beams. Four recent experiments are analyzed in detail: interference on a screen, Franson's experiments [Phys. Rev. Lett. 62, 2205 (1989)], Rarity and Tapster's experiments [Phys. Rev. Lett. 64, 2495 (1990)], and induced coherence without induced emission [X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991)].

Physical Review A•May 1, 1997•38 citations

The Weyl-Wigner formalism for the interpretation of parametric down-conversion experiments

Emilio Santos

We show that the Weyl-Wigner formalism in the Heisenberg picture may be used for the interpretation of experiments involving entangled photon pairs produced in nonlinear crystals via spontaneous parametric down-conversion. The calculations are usually no more involved than those with the Hilbert-space formalism. The WW formalism suggests a physical picture in terms of random variables and stochastic processes, but the picture is shown untenable in some instances.

•May 18, 2019•0 citations

Parametric down and up conversion in the Wigner representation of quantum optics

K. Dechoum, Trevor W. Marshall, Emilio Santos

We study spontaneous parametric processes starting from the quantized field equations in the Heisenberg picture using the common approximation of treating the laser pump as classical. After a (standard) linearization procedure we pass to the Wigner representation and the process becomes formally equivalent to the parametric interaction of two incoming zero-point modes with a pumping laser wave coupled by an optically nonlinear medium. Then the treatment of parametric down conversion and parametric up conversion are described by the Maxwell equations and look like a parametric amplification of the vacuum field. The fourth-order correlation function between the signal and idler fields is obtained in a form that makes for easy comparison with experimental results.

Journal of Modern Optics•Jun 1, 2000•25 citations

Coherence in two-photon down-conversion induced by a laser

L. J. Wang, X. Y. Zou, L. Mandeļ

Normally, the signal and idler photons produced in the process of parametric down- conversion exhibit no second-order interference. However, in the presence of an external laser beam that follows the path of the signal photon and induces stimulated down-conversions, one would expect coherence to develop between the down-converted signal and idler beams. We have demonstrated the existence of this phenomenon in an experiment with two down-converters pumped by similar pump beams, in which two mutually coherent laser beams followed the paths of the two down-converted signal photons and induced coherence between the two down- converted idler beams. The induced coherence gives rise to observable interference effects, which are presented.

Annual Meeting Optical Society of America•Jan 1, 1990•1 citation

Type II parametric downconversion in the Wigner-function formalism: entanglement and Bell's inequalities

Alberto Casado, Trevor W. Marshall, Emilio Santos

We continue the analysis of our previous papers that were devoted to type I parametric downconversion, the extension to type II being straightforward. We show that entanglement, in the Wigner representation, is merely a correlation that involves both signals and vacuum fluctuations. An analysis of the detection process opens the way to a complete description of parametric downconversion in terms of pure Maxwell electromagnetic waves.

arXiv:quant-ph/9711042•Journal of the Optical Society of America B•May 1, 1998•28 citations

Spontaneous Parametric Downconversion, Proof of Existence of Photons, and Single-Photon Interference and Quantum Eraser (Single Photon Quantum)

Muhammad Umair

Spontaneous parametric downconversion At the heart of all quantum optics experiments is called as Spontaneous parametric downconversion. This is a downconversion process when the output frequency is smaller than the input frequency. The whole process is Spontaneous. Experimentally we have to downconvert the photons and convert them into pairs of a photon. We use the Beta-barium borate(BBO) crystals to downconvert the coming violet-blue laser. We find the maximum number of counts on detectors and their coincidence. When the BBO crystals is well aligned, we find no difference in detecting vertically or horizontally polarized photons because they are orthogonal to each other. Proof of existence of photons We want to investigate the properties and verification of quantization of light. Experimently we want to establish the existence of single photon which shows the grainy-ness of individual photon quantum mechanically and shows wave like behaviour classically. We get the coincidences counts on detectors with addition of detector B’ by using PBS in the path of signal beam. Experimentally we prove the Quantum as well as classical nature of light by the measurement of second-order degree coherence in light g2(0). For classically the g2(0)≥1 and quantum mechanically g2(0)=0.When we add the delay time interval of 1ns after reflected and transmitted photons from PBS signal beam. The delay generator did not create a significant difference in the coincidence counts detection in the value of g2(τ ). Single photon interference and quantum eraser we want to observe the interference by making the single photons pass through the interferometer, and we will see the interference of the single photons. If the light passes through the interferometer, the visibility of the interference pattern to which extent these fringes are observed is dependent on the extent to which the ’which-way’ or ’which-path’ information is available to the experimenter. If the observer knows the information about the ’which-way’ of the light path, then we cannot observe the inference pattern. Because we only can make an interference pattern if we erase the which-way information of the light path. If you erase the information about the’ which-way,’ we can observe a very high interference pattern. We can erase the information about the light path’s ’which-way’ or ’which-path’ by using a polarizer and orienting at 45o. In this way, we can observe a very high pattern. If we introduce the angle of the polarizer at 0o or 90o, we see very low interference.

•Nov 1, 2023•0 citations
The Wigner representation is developed in the Heisenberg picture for the study of experiments involving photon pairs created in the process of parametric down conversion. After the general description of a light beam and the theory of detection (restricted here to single count probabilities in the Wigner formalism) the theory of parametric downconversion is developed to the point of calculating the autocorrelations of the signal and idler beams. Two recent experiments are analyzed in detail: frustrated two-photon creation by interference, and induced coherence and indistinguishability.
In the Wigner formalism, after giving a general description of a light beam, the theory of parametric down-conversion is developed to second-order in the coupling constant. We then describe the detection process by calculating the auto-correlation and cross-correlations of the signal and idler beams. Four recent experiments are analyzed in detail: interference on a screen, Franson's experiments [Phys. Rev. Lett. 62, 2205 (1989)], Rarity and Tapster's experiments [Phys. Rev. Lett. 64, 2495 (1990)], and induced coherence without induced emission [X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991)].
We study spontaneous parametric processes starting from the quantized field equations in the Heisenberg picture using the common approximation of treating the laser pump as classical. After a (standard) linearization procedure we pass to the Wigner representation and the process becomes formally equivalent to the parametric interaction of two incoming zero-point modes with a pumping laser wave coupled by an optically nonlinear medium. Then the treatment of parametric down conversion and parametric up conversion are described by the Maxwell equations and look like a parametric amplification of the vacuum field. The fourth-order correlation function between the signal and idler fields is obtained in a form that makes for easy comparison with experimental results.
Normally, the signal and idler photons produced in the process of parametric down- conversion exhibit no second-order interference. However, in the presence of an external laser beam that follows the path of the signal photon and induces stimulated down-conversions, one would expect coherence to develop between the down-converted signal and idler beams. We have demonstrated the existence of this phenomenon in an experiment with two down-converters pumped by similar pump beams, in which two mutually coherent laser beams followed the paths of the two down-converted signal photons and induced coherence between the two down- converted idler beams. The induced coherence gives rise to observable interference effects, which are presented.
Spontaneous parametric downconversion At the heart of all quantum optics experiments is called as Spontaneous parametric downconversion. This is a downconversion process when the output frequency is smaller than the input frequency. The whole process is Spontaneous. Experimentally we have to downconvert the photons and convert them into pairs of a photon. We use the Beta-barium borate(BBO) crystals to downconvert the coming violet-blue laser. We find the maximum number of counts on detectors and their coincidence. When the BBO crystals is well aligned, we find no difference in detecting vertically or horizontally polarized photons because they are orthogonal to each other. Proof of existence of photons We want to investigate the properties and verification of quantization of light. Experimently we want to establish the existence of single photon which shows the grainy-ness of individual photon quantum mechanically and shows wave like behaviour classically. We get the coincidences counts on detectors with addition of detector B’ by using PBS in the path of signal beam. Experimentally we prove the Quantum as well as classical nature of light by the measurement of second-order degree coherence in light g2(0). For classically the g2(0)≥1 and quantum mechanically g2(0)=0.When we add the delay time interval of 1ns after reflected and transmitted photons from PBS signal beam. The delay generator did not create a significant difference in the coincidence counts detection in the value of g2(τ ). Single photon interference and quantum eraser we want to observe the interference by making the single photons pass through the interferometer, and we will see the interference of the single photons. If the light passes through the interferometer, the visibility of the interference pattern to which extent these fringes are observed is dependent on the extent to which the ’which-way’ or ’which-path’ information is available to the experimenter. If the observer knows the information about the ’which-way’ of the light path, then we cannot observe the inference pattern. Because we only can make an interference pattern if we erase the which-way information of the light path. If you erase the information about the’ which-way,’ we can observe a very high interference pattern. We can erase the information about the light path’s ’which-way’ or ’which-path’ by using a polarizer and orienting at 45o. In this way, we can observe a very high pattern. If we introduce the angle of the polarizer at 0o or 90o, we see very low interference.