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 Modern Optics

Entanglement of orbital angular momentum for the signal and idler beams in parametric down-conversion

Miles J. Padgett, Johannes Courtial, L.J. Allen, Sonja Franke‐Arnold, S. M. Barnett

Published Apr 1, 2002• 25 citations
Publisher

Abstract

We calculate the anticipated correlation between measurements of the orbital angular momentum of the signal and idler beams for parametric down-conversion. These calculations apply to the experiments where the orbital angular momentum state is measured by the use of computer-generated holograms. Displacement of these holograms with respect to the beam axis allows the measurement of superpositions of Laguerre—Gaussian modes. The correlations between such superposition modes of the signal and idler beams show their entanglement and could be used for Bell-type tests of nonlocality.

DOI
10.1080/09500340110108594

Related papers

Superpositions of the orbital angular momentum for applications in quantum experiments

Alipasha Vaziri, Gregor Weihs, Anton Zeilinger

Two different experimental techniques for preparing and analysing superpositions of Gaussian and Laguerre–Gaussian modes are presented. These involve exploiting an interferometric method in one case and using computer-generated holograms in the other. It is shown that by shifting a hologram with respect to an incoming Gaussian beam, different superpositions of the Gaussian and the Laguerre–Gaussian beam can be produced. An analytical expression connecting the relative phase, the amplitudes of the modes and the displacement of the hologram is given. The application of such orbital angular momenta superpositions in quantum experiments such as quantum cryptography is discussed.

arXiv:quant-ph/0111033•Journal of Optics B Quantum and Semiclassical Optics•Mar 1, 2002•211 citations

Orbital angular momentum correlations with a phase-flipped Gaussian mode pump beam

Jacquiline Romero, Daniel Giovannini, Melanie G. McLaren +3 more

We report orbital angular momentum (OAM) and angle correlations between signal and idler photons observed when the nonlinear crystal used in spontaneous parametric down-conversion is illuminated by a non-fundamental Gaussian pump beam. We introduce a π-phase step to the transverse profile of the pump, before it impinges on the crystal to create a phase-flipped Gaussian mode, which is a close approximation to an HG10 Hermite–Gaussian-like beam. The correlations in OAM and angular position are then measured holographically using two separate spatial light modulators in the signal and idler arms. We show the transfer of the OAM spectrum of the pump to the down-converted fields, manifested as a redistribution in the OAM correlations consistent with OAM conservation. This corresponds to a modulation of the angular position correlations consistent with the Fourier relationship between the OAM and angle.

Journal of Optics•Aug 1, 2012•29 citations

Orbital angular momentum of the down converted photons

Xi‐Feng Ren, Guo‐Ping Guo, Bo Yu +2 more

We calculate the relative amplitude of orbital angular momentum (OAM) entangled photon pairs from the spontaneous parametric down conversion. The results show that the amplitude depends on both the two Laguerre indices l, p. We also discuss the influences of the mostly used holograms and mono-mode fibers for mode analyzation. We conclude that only a few dimensions can be explored from the infinite OAM modes of the down-converted photon pairs.

arXiv:quant-ph/0309044•Sep 4, 2003•1 citation

The orbital angular momentum of down-converted photons

Xi‐Feng Ren, Guo‐Ping Guo, Bo Hao Yu +2 more

We calculate the relative amplitude of the orbital angular momentum (OAM) of entangled photon pairs from the spontaneous parametric down-conversion of a thin quadratic nonlinear crystal. The results show that the amplitude depends on both of the two Laguerre indices l , p . We also discuss the influences of the commonly used holograms and mono-mode fibres for mode analysis. We conclude that only a few dimensions can be explored from the infinite OAM modes of down-converted photon pairs.

Journal of Optics B Quantum and Semiclassical Optics•Mar 26, 2004•31 citations

Effect of high-dimensional entanglement of Laguerre-Gaussian modes in parametric downconversion

Daisuke Kawase, Yoko Miyamoto, Mitsuo Wada Takeda +2 more

We calculate the coincidence count probabilities when the photon pairs entangled in orbital angular momentum generated via spontaneous parametric downconversion are measured by using holograms with an m-fold dislocation, considering the nonzero crystal length. We find that the coincidence probabilities related to azimuthal changes in hologram positions deviate significantly from a sinusoidal curve, which has often been assumed in simple analyses. It is found that the main cause of this effect is the high-dimensional entanglement in Laguerre-Gaussian modes. We also find that the crystal length causes the hologram positions to change for the maximum coincidence probabilities.

Journal of the Optical Society of America B•Mar 26, 2009•14 citations

Indistinguishability of orbital angular-momentum modes in spontaneous parametric down-conversion

Geraldo Alexandre Barbosa

Identification of light modes usually requires careful considerations of the collecting geometry. This is particularly true for states carrying orbital angular-momentum modes from spontaneous parametric down-conversion due to the entanglement of the signal and idler fields. A detailed understanding of the generated modes in a general case allows the design of efficient detection setups. This is true for distinct cases, e.g., when multiple samplings are performed by repeated state generation or in single-photon cryptography or quantum computation, where a photon state is generated within a short-time window and a single measurement is performed. Aspects of nonorthogonality of signal and idler modes and effects of restrictions on the collecting geometry are discussed in this work.

Physical Review A•May 8, 2009•1 citation
We calculate the anticipated correlation between measurements of the orbital angular momentum of the signal and idler beams for parametric down-conversion. These calculations apply to the experiments where the orbital angular momentum state is measured by the use of computer-generated holograms. Displacement of these holograms with respect to the beam axis allows the measurement of superpositions of Laguerre—Gaussian modes. The correlations between such superposition modes of the signal and idler beams show their entanglement and could be used for Bell-type tests of nonlocality.
Two different experimental techniques for preparing and analysing superpositions of Gaussian and Laguerre–Gaussian modes are presented. These involve exploiting an interferometric method in one case and using computer-generated holograms in the other. It is shown that by shifting a hologram with respect to an incoming Gaussian beam, different superpositions of the Gaussian and the Laguerre–Gaussian beam can be produced. An analytical expression connecting the relative phase, the amplitudes of the modes and the displacement of the hologram is given. The application of such orbital angular momenta superpositions in quantum experiments such as quantum cryptography is discussed.
We report orbital angular momentum (OAM) and angle correlations between signal and idler photons observed when the nonlinear crystal used in spontaneous parametric down-conversion is illuminated by a non-fundamental Gaussian pump beam. We introduce a π-phase step to the transverse profile of the pump, before it impinges on the crystal to create a phase-flipped Gaussian mode, which is a close approximation to an HG10 Hermite–Gaussian-like beam. The correlations in OAM and angular position are then measured holographically using two separate spatial light modulators in the signal and idler arms. We show the transfer of the OAM spectrum of the pump to the down-converted fields, manifested as a redistribution in the OAM correlations consistent with OAM conservation. This corresponds to a modulation of the angular position correlations consistent with the Fourier relationship between the OAM and angle.
We calculate the coincidence count probabilities when the photon pairs entangled in orbital angular momentum generated via spontaneous parametric downconversion are measured by using holograms with an m-fold dislocation, considering the nonzero crystal length. We find that the coincidence probabilities related to azimuthal changes in hologram positions deviate significantly from a sinusoidal curve, which has often been assumed in simple analyses. It is found that the main cause of this effect is the high-dimensional entanglement in Laguerre-Gaussian modes. We also find that the crystal length causes the hologram positions to change for the maximum coincidence probabilities.
Identification of light modes usually requires careful considerations of the collecting geometry. This is particularly true for states carrying orbital angular-momentum modes from spontaneous parametric down-conversion due to the entanglement of the signal and idler fields. A detailed understanding of the generated modes in a general case allows the design of efficient detection setups. This is true for distinct cases, e.g., when multiple samplings are performed by repeated state generation or in single-photon cryptography or quantum computation, where a photon state is generated within a short-time window and a single measurement is performed. Aspects of nonorthogonality of signal and idler modes and effects of restrictions on the collecting geometry are discussed in this work.