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

Theory of two-photon correlations and Bell’s inequality

H. Fearn

Published Dec 1, 1989• 1 citation
Publisher

Abstract

An interference experiment in which signal and idler photons from a parametric oscillator (paramp) were mixed by a beam splitter and the coincidence count rate was measured has been outlined by Ou Mandel , [ Phys. Rev. Lett.61, 50 ( 1988)]. The theory of the joint two-photon detection probability has been generalized to include nondegenerate photons and time delays between the photons at the beam splitter. Previously, two-photon Fock states were employed in this analysis. We consider the squeezed vacuum output of a paramp in a cavity. The results derived here reduce to the special case derived by Ou and Mandel. Furthermore, a cascade emission process is treated by using a rate equation approach.

DOI
10.1364/josab.6.002420

Related papers

Theory of two-photon interference

H. Fearn, R. Loudon

The interference effects that can be observed in the two output arms of a lossless beam splitter are calculated for incident light in the form of a photon-pair excitation in the two input arms. The output state that occurs when the photon pair is excited in a single input arm resembles that expected for independent classical particles, whereas quantum interference effects occur when the photon pair is divided between the two input arms. Detailed output photocount correlation functions are calculated for two-photon input states produced by a two-atom light source, a degenerate or nondegenerate parametric oscillator in a high-Q cavity, and an atomic cascade emission light source.

Journal of the Optical Society of America B•May 1, 1989•124 citations

Signatures of Hong–Ou–Mandel interference at microwave frequencies

M J Woolley, Claus Lang, Christopher Eichler +2 more

Two-photon quantum interference at a beam splitter, commonly known as Hong–Ou–Mandel interference, is a fundamental demonstration of the quantum mechanical nature of electromagnetic fields and a key component of various quantum information processing protocols. The phenomenon was recently demonstrated with microwave-frequency photons by Lang et al (2013 Nature Phys. 9 345–8). This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the microwave fields at the outputs of the beam splitter using linear detectors. Here we present the calculation of these correlation functions for the cases of inputs corresponding to: (i) trains of pulsed Gaussian or Lorentzian single microwave photons and (ii) resonant fluorescent microwave fields from continuously driven circuit QED systems. In both cases, the signature of two-photon quantum interference is a suppression of the second-order cross-correlation function for small delays. The experiment described in Lang et al (2013) was performed with trains of Lorentzian single photons, and very good agreement with experimental data is obtained. The results are relevant not only to interference experiments using circuit QED systems, but any such setup with highly controllable sources and time-resolved detection.

arXiv:1304.6068•New Journal of Physics•Oct 23, 2013•21 citations

Signatures of Hong-Ou-Mandel interference at microwave frequencies

Woolley, Matthew J., Claus Lang, Christopher Eichler +2 more

Two-photon quantum interference at a beam splitter, commonly known as Hong–Ou–Mandel interference, is a fundamental demonstration of the quantum mechanical nature of electromagnetic fields and a key component of various quantum information processing protocols. The phenomenon was recently demonstrated with microwave-frequency photons by Lang et al (2013 Nature Phys. 9 345–8). This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the microwave fields at the outputs of the beam splitter using linear detectors. Here we present the calculation of these correlation functions for the cases of inputs corresponding to: (i) trains of pulsed Gaussian or Lorentzian single microwave photons and (ii) resonant fluorescent microwave fields from continuously driven circuit QED systems. In both cases, the signature of two-photon quantum interference is a suppression of the second-order cross-correlation function for small delays. The experiment described in Lang et al (2013) was performed with trains of Lorentzian single photons, and very good agreement with experimental data is obtained. The results are relevant not only to interference experiments using circuit QED systems, but any such setup with highly controllable sources and time-resolved detection.

•Oct 1, 2013•23 citations

Photon localization In parametric downconversion

John G. Rarity, P. R. Tapster

Quantum mechanical models of beam splitters1 predict interesting fourth-order interference effects when nonclassical light is used. If indistinguishable one-photon states are simultaneously input into each port of a 50/50 beam splitter, the theory predicts that each output will contain either two photons or none. A naive (particle) theory would predict a mixture of two’s and one’s. The required |1,1〉 photon state can be selected in nondegenerate parametric downconversion experiments by photon-counting coincidence detection. The disappearance of this coincidence after a beam splitter has recently been studied,1-2 and the range of path length differences over which the effect can be seen is related by Fourier transform to the photon bandwidth. In our work the bandwidth is not limited by external filters, and we have developed a theory which relates the measured photon length to the geometry of the apparatus and the detailed phase matching conditions at the parametric crystal. This theory of phase matching viewed through a beam splitter produces some unexpected results when the beam splitter is tilted and when large aperture detectors are considered.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations

Violation of Bell’s Inequality with Photons from Independent Sources

T. B. Pittman, J. D. Franson

We report a violation of Bell's inequality using one photon from a parametric down-conversion source and a second photon from an attenuated laser beam. The two photons were entangled at a beam splitter using the postselection technique of Shih and Alley [Phys. Rev. Lett. 61, 2921 (1988)]]. A quantum interference pattern with a visibility of 91% was obtained using the photons from these independent sources, as compared with a visibility of 99.4% using two photons from a central parametric down-conversion source.

arXiv:quant-ph/0301169•Physical Review Letters•Jun 19, 2003•73 citations

Fourth-order interference in parametric downconversion

John G. Rarity, P. R. Tapster

A two-photon state can be selected by coincidence detection of photon pairs created in parametric downconversion. We demonstrate a reduction in the coincidence-count rate when pairs of photons are combined in a beam splitter. This reduction occurs only when photon wave functions overlap and can permit accurate (subpicosecond) relative timing measurements. We relate the width of the coincidence reduction to the bandwidth of the downconverted light and thence to the detailed phase-matching conditions in the parametric downconversion crystal. We also demonstrate that the loss of coincidences is associated with an increased probability of detection of photon pairs in each output of the beam splitter.

Journal of the Optical Society of America B•Jun 1, 1989•91 citations
An interference experiment in which signal and idler photons from a parametric oscillator (paramp) were mixed by a beam splitter and the coincidence count rate was measured has been outlined by Ou Mandel , [ Phys. Rev. Lett.61, 50 ( 1988)]. The theory of the joint two-photon detection probability has been generalized to include nondegenerate photons and time delays between the photons at the beam splitter. Previously, two-photon Fock states were employed in this analysis. We consider the squeezed vacuum output of a paramp in a cavity. The results derived here reduce to the special case derived by Ou and Mandel. Furthermore, a cascade emission process is treated by using a rate equation approach.
The interference effects that can be observed in the two output arms of a lossless beam splitter are calculated for incident light in the form of a photon-pair excitation in the two input arms. The output state that occurs when the photon pair is excited in a single input arm resembles that expected for independent classical particles, whereas quantum interference effects occur when the photon pair is divided between the two input arms. Detailed output photocount correlation functions are calculated for two-photon input states produced by a two-atom light source, a degenerate or nondegenerate parametric oscillator in a high-Q cavity, and an atomic cascade emission light source.
Two-photon quantum interference at a beam splitter, commonly known as Hong–Ou–Mandel interference, is a fundamental demonstration of the quantum mechanical nature of electromagnetic fields and a key component of various quantum information processing protocols. The phenomenon was recently demonstrated with microwave-frequency photons by Lang et al (2013 Nature Phys. 9 345–8). This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the microwave fields at the outputs of the beam splitter using linear detectors. Here we present the calculation of these correlation functions for the cases of inputs corresponding to: (i) trains of pulsed Gaussian or Lorentzian single microwave photons and (ii) resonant fluorescent microwave fields from continuously driven circuit QED systems. In both cases, the signature of two-photon quantum interference is a suppression of the second-order cross-correlation function for small delays. The experiment described in Lang et al (2013) was performed with trains of Lorentzian single photons, and very good agreement with experimental data is obtained. The results are relevant not only to interference experiments using circuit QED systems, but any such setup with highly controllable sources and time-resolved detection.
Two-photon quantum interference at a beam splitter, commonly known as Hong–Ou–Mandel interference, is a fundamental demonstration of the quantum mechanical nature of electromagnetic fields and a key component of various quantum information processing protocols. The phenomenon was recently demonstrated with microwave-frequency photons by Lang et al (2013 Nature Phys. 9 345–8). This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the microwave fields at the outputs of the beam splitter using linear detectors. Here we present the calculation of these correlation functions for the cases of inputs corresponding to: (i) trains of pulsed Gaussian or Lorentzian single microwave photons and (ii) resonant fluorescent microwave fields from continuously driven circuit QED systems. In both cases, the signature of two-photon quantum interference is a suppression of the second-order cross-correlation function for small delays. The experiment described in Lang et al (2013) was performed with trains of Lorentzian single photons, and very good agreement with experimental data is obtained. The results are relevant not only to interference experiments using circuit QED systems, but any such setup with highly controllable sources and time-resolved detection.
Quantum mechanical models of beam splitters1 predict interesting fourth-order interference effects when nonclassical light is used. If indistinguishable one-photon states are simultaneously input into each port of a 50/50 beam splitter, the theory predicts that each output will contain either two photons or none. A naive (particle) theory would predict a mixture of two’s and one’s. The required |1,1〉 photon state can be selected in nondegenerate parametric downconversion experiments by photon-counting coincidence detection. The disappearance of this coincidence after a beam splitter has recently been studied,1-2 and the range of path length differences over which the effect can be seen is related by Fourier transform to the photon bandwidth. In our work the bandwidth is not limited by external filters, and we have developed a theory which relates the measured photon length to the geometry of the apparatus and the detailed phase matching conditions at the parametric crystal. This theory of phase matching viewed through a beam splitter produces some unexpected results when the beam splitter is tilted and when large aperture detectors are considered.
We report a violation of Bell's inequality using one photon from a parametric down-conversion source and a second photon from an attenuated laser beam. The two photons were entangled at a beam splitter using the postselection technique of Shih and Alley [Phys. Rev. Lett. 61, 2921 (1988)]]. A quantum interference pattern with a visibility of 91% was obtained using the photons from these independent sources, as compared with a visibility of 99.4% using two photons from a central parametric down-conversion source.
A two-photon state can be selected by coincidence detection of photon pairs created in parametric downconversion. We demonstrate a reduction in the coincidence-count rate when pairs of photons are combined in a beam splitter. This reduction occurs only when photon wave functions overlap and can permit accurate (subpicosecond) relative timing measurements. We relate the width of the coincidence reduction to the bandwidth of the downconverted light and thence to the detailed phase-matching conditions in the parametric downconversion crystal. We also demonstrate that the loss of coincidences is associated with an increased probability of detection of photon pairs in each output of the beam splitter.