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

arXiv:1603.02045 · Optical Engineering

Relative-phase and time-delay maps all over the emission cone of hyperentangled photon source

Salem F. Hegazy, Yahia Abdel-hamid Badr, Salah S. A. Obayya

Published Feb 16, 2017• 14 citations
arXivHTMLPDF

Abstract

Realizing high flux of hyperentangled photons requires collecting photon pairs simultaneously entangled in multiple degrees of freedom over relatively wide spectral and angular emission ranges. We consider the hyperentangled photons produced by superimposing noncollinear spontaneous parametric down conversion (SPDC) emissions of two crossed and coherently pumped nonlinear crystals. We present an approach for determining the directional-spectral relative-phase and time-delay maps of hyperentangled photons all over the SPDC emission cone. A vectorial representation is adopted for all parameters of concern. This enables us to examine unconventional arrangements such as the autocompensation of relative-phase and time-delay via oblique pump incidence. While prior works often adopt first-order approximation, it is shown that the actual directional relative-phase map is very well approximated by a quadratic function of the polar angle of the two-photon emission while negligibly varying with the azimuthal angle.

DOI
10.1117/1.oe.56.2.026114

Related papers

Accurate relative-phase and time-delay maps all over the emission cone of hyperentangled photon source

Salem F. Hegazy, Jala M. El-Azab, Yehia A. Badr +1 more

High flux of hyperentangled photons entails collecting the two-photon emission over relatively wide extent in frequency and transverse space within which the photon pairs are simultaneously entangled in multiple degrees of freedom. In this paper, we present a numerical approach to determining the spatial-spectral relative-phase and time-delay maps of hyperentangled photons all over the spontaneous parametric down conversion (SPDC) emission cone. We consider the hyperentangled-photons produced by superimposing noncollinear SPDC emissions of two crossed and coherentlypumped nonlinear crystals. We adopt a vectorial representation for all parameters of concern. This enables us to study special settings such as the self-compensation via oblique pump incidence. While rigorous quantum treatment of SPDC emission requires Gaussian state representation, in low-gain regime (like the case of the study), it is well approximated to the first order to superposition of vacuum and two-photon states. The relative phase and time-delay maps are then calculated between the two-photon wavepackets created along symmetrical locations of the crystals. Assuming monochromatic plane-wave pump field, the mutual signal-idler relations like energy conservation and transversemomentum conservation define well one of the two-photon with reference to its conjugate. The weaker conservation of longitudinal momentum (due to relatively thin crystals) allows two-photon emission directions coplanar with the pump beam while spreading around the perfect phase-matching direction. While prior works often adopt first-order approximation, it is shown that the relative-phase map is a very well approximated to a quadratic function in the polar angle of the two-photon emission while negligibly varying with the azimuthal angle.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 27, 2016•1 citation

Extended source of indistinguishable polarization-entangled photons over wide angles of emission

Salem F. Hegazy, Salah S. A. Obayya

The generation of high-fidelity polarization-entangled photon pairs, to date, has been demonstrated on specific spatial modes or over relatively narrow apertures. We put forward and demonstrate an experimental scheme to extend the temporal and spatial indistinguishability of polarization-entangled photons over wide emission angles, which can be applied to cover the whole spontaneous parametric downconversion (SPDC) cone. Over such a wide angular extent, while the time-delay map is almost flat which renders the conventional compensation via a birefringent element an appropriate approach, the relative-phase map—verified as a quadratic function—necessitates a tunable compensation paradigm. Here, to do so, we employ a phase-only two-dimensional spatial light modulator (2D SLM) loaded by the complementary of the relative phase map to equalize the phase variations for one third of the noncollinear SPDC emission. After eliminating the temporal and spatial distinguishability over the 2D SLM area, a 97% polarization visibility is verified for the entangled photon pairs scattered widely across the SPDC cone.

arXiv:2106.07025•Applied Physics Letters•Dec 14, 2020•2 citations

Tunable spatial–spectral phase compensation of type-I (ooe) hyperentangled photons

Salem F. Hegazy, Salah S. A. Obayya

The two-photon state generated by overlapping the noncollinear spontaneous parametric down conversion (SPDC) emissions of two coherently pumped type-I crystals undergoes spatial and spectral decoherence precluding the capture of high pair counts with high state fidelity. Here we present a tunable compensation method for tackling the rising state decoherence in the two degrees of freedom in the case of crystals with negative birefringence. We determine the directional-spectral phase function of the two-photon state initially and after compensation, taking into account the finite spectral width of the pump beam. Subsequently, the optimal characteristics of the compensation crystals are computed by criteria of flat phase function in spectrum and space. The results of our model are compared with measurements of some recent experiments.

Journal of the Optical Society of America B•Feb 18, 2015•17 citations

Parallel preparation of a set of arbitrary path-polarization hyperentangled states

Hussien Garalnaby, Salem F. Hegazy, Salah Hasab Elnaby

The simultaneous production of a set of arbitrary hyperentangled states is crucial for quantum machines running variant quantum protocols concurrently, like universal quantum computers and quantum communication hubs. We present an experimental method to prepare a set of arbitrary path-polarization hyperentangled states concurrently using non-collinear spontaneous parametric down-conversion (SPDC). A cascaded pair of type-I crystals are pumped by 405-nm diagonally-polarized beam to produce a noncollinear stream of photon pairs. Compensation crystals are inserted to correct for the angular slope of the relative phase of the produced polarization entangled state. The pathentangled states are created over four pairs of slits positioned at conjugate locations to the pump beam. The local relative-phases of the path and polarization states can be independently tailored by intercepting the SPDC emission by tiltable birefringent and glass plates. The amplitudes of the polarization states is controlled by the manipulation of the polarization state of the pump. Also, the amplitudes of the path states is accessed by translating the slits over the SPDC cone. Here, while a pure state describes the whole SPDC emission, the produced states can be deemed an independent set by avoiding paths balanced to less than the coherence-length.

Advances in Photonics of Quantum Computing, Memory, and Communication•Mar 4, 2019•0 citations

Compact generation scheme of path–frequency hyperentangled photons using 2D periodical nonlinear photonic crystal

Yang-He 洋河 Chen 陈, Bo 波 Ji 季, Nian-Qin 念芹 Li 李 +6 more

Hyperentanglement is a promising resource for achieving high capacity quantum communication. Here, we propose a compact scheme for the generation of path–frequency hyperentangled photon pairs via spontaneous parametric down-conversion (SPDC) processes, where six different paths and two different frequencies are covered. A two-dimensional periodical χ (2) nonlinear photonic crystal (NPC) is designed to satisfy type-I quasi-phase-matching conditions in the plane perpendicular to the incident pump beam, and a perfect phase match is achieved along the pump beam’s direction to ensure high conversion efficiency, with theoretically estimated photon flux up to 2.068 × 105 pairs⋅s−1⋅mm−2. We theoretically calculate the joint-spectral amplitude (JSA) of the generated photon pair and perform Schmidt decomposition on it, where the resulting entropy S of entanglement and effective Schmidt rank K reach 3.2789 and 6.4675, respectively. Our hyperentangled photon source scheme could provide new avenues for high-dimensional quantum communication and high-speed quantum information processing.

Chinese Physics B•Oct 24, 2023•1 citation

Spectral and spatial effects in spontaneous parametric down-conversion with a focused pump

Warren P. Grice, Ryan S. Bennink, Zhi Gao Zhao +3 more

Photons produced in the process of spontaneous parametric down-conversion (SPDC) are typically entangled in multiple degrees of freedom. Although polarization is often the parameter of interest, the presence of spectral or spatial entanglement can complicate experiments, either by reducing the visibility of certain interference effects or by reducing collection efficiency. Several recent works have shown that the collection efficiency can be improved by focusing the pump beam. This approach has the added benefit of increasing the bandwidths of the emitted photons. We show that, in the case of type II SPDC, a focused pump can result in different spatial profiles for the signal and idler. If the crystal is configured for emission of polarization-entangled photon pairs, this effect will reduce the fidelity of that entanglement. Moreover, this spatial asymmetry leads to different spectral profiles for the two photons, even when the pump is monochromatic. The spectral and spatial asymmetries can be attributed to the difference in the angular dispersion (walk-off) of the two polarizations, along with a strong correlation between wavelength and emission direction. We also examine the link between spatial entanglement and single-mode coupling efficiency. We find that efficiency is maximized when spatial entanglement can be eliminated. For the case in which walk-off does not play a role, this can be accomplished by properly focusing the pump.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 1, 2008•3 citations
Realizing high flux of hyperentangled photons requires collecting photon pairs simultaneously entangled in multiple degrees of freedom over relatively wide spectral and angular emission ranges. We consider the hyperentangled photons produced by superimposing noncollinear spontaneous parametric down conversion (SPDC) emissions of two crossed and coherently pumped nonlinear crystals. We present an approach for determining the directional-spectral relative-phase and time-delay maps of hyperentangled photons all over the SPDC emission cone. A vectorial representation is adopted for all parameters of concern. This enables us to examine unconventional arrangements such as the autocompensation of relative-phase and time-delay via oblique pump incidence. While prior works often adopt first-order approximation, it is shown that the actual directional relative-phase map is very well approximated by a quadratic function of the polar angle of the two-photon emission while negligibly varying with the azimuthal angle.
High flux of hyperentangled photons entails collecting the two-photon emission over relatively wide extent in frequency and transverse space within which the photon pairs are simultaneously entangled in multiple degrees of freedom. In this paper, we present a numerical approach to determining the spatial-spectral relative-phase and time-delay maps of hyperentangled photons all over the spontaneous parametric down conversion (SPDC) emission cone. We consider the hyperentangled-photons produced by superimposing noncollinear SPDC emissions of two crossed and coherentlypumped nonlinear crystals. We adopt a vectorial representation for all parameters of concern. This enables us to study special settings such as the self-compensation via oblique pump incidence. While rigorous quantum treatment of SPDC emission requires Gaussian state representation, in low-gain regime (like the case of the study), it is well approximated to the first order to superposition of vacuum and two-photon states. The relative phase and time-delay maps are then calculated between the two-photon wavepackets created along symmetrical locations of the crystals. Assuming monochromatic plane-wave pump field, the mutual signal-idler relations like energy conservation and transversemomentum conservation define well one of the two-photon with reference to its conjugate. The weaker conservation of longitudinal momentum (due to relatively thin crystals) allows two-photon emission directions coplanar with the pump beam while spreading around the perfect phase-matching direction. While prior works often adopt first-order approximation, it is shown that the relative-phase map is a very well approximated to a quadratic function in the polar angle of the two-photon emission while negligibly varying with the azimuthal angle.
The generation of high-fidelity polarization-entangled photon pairs, to date, has been demonstrated on specific spatial modes or over relatively narrow apertures. We put forward and demonstrate an experimental scheme to extend the temporal and spatial indistinguishability of polarization-entangled photons over wide emission angles, which can be applied to cover the whole spontaneous parametric downconversion (SPDC) cone. Over such a wide angular extent, while the time-delay map is almost flat which renders the conventional compensation via a birefringent element an appropriate approach, the relative-phase map—verified as a quadratic function—necessitates a tunable compensation paradigm. Here, to do so, we employ a phase-only two-dimensional spatial light modulator (2D SLM) loaded by the complementary of the relative phase map to equalize the phase variations for one third of the noncollinear SPDC emission. After eliminating the temporal and spatial distinguishability over the 2D SLM area, a 97% polarization visibility is verified for the entangled photon pairs scattered widely across the SPDC cone.
The two-photon state generated by overlapping the noncollinear spontaneous parametric down conversion (SPDC) emissions of two coherently pumped type-I crystals undergoes spatial and spectral decoherence precluding the capture of high pair counts with high state fidelity. Here we present a tunable compensation method for tackling the rising state decoherence in the two degrees of freedom in the case of crystals with negative birefringence. We determine the directional-spectral phase function of the two-photon state initially and after compensation, taking into account the finite spectral width of the pump beam. Subsequently, the optimal characteristics of the compensation crystals are computed by criteria of flat phase function in spectrum and space. The results of our model are compared with measurements of some recent experiments.
The simultaneous production of a set of arbitrary hyperentangled states is crucial for quantum machines running variant quantum protocols concurrently, like universal quantum computers and quantum communication hubs. We present an experimental method to prepare a set of arbitrary path-polarization hyperentangled states concurrently using non-collinear spontaneous parametric down-conversion (SPDC). A cascaded pair of type-I crystals are pumped by 405-nm diagonally-polarized beam to produce a noncollinear stream of photon pairs. Compensation crystals are inserted to correct for the angular slope of the relative phase of the produced polarization entangled state. The pathentangled states are created over four pairs of slits positioned at conjugate locations to the pump beam. The local relative-phases of the path and polarization states can be independently tailored by intercepting the SPDC emission by tiltable birefringent and glass plates. The amplitudes of the polarization states is controlled by the manipulation of the polarization state of the pump. Also, the amplitudes of the path states is accessed by translating the slits over the SPDC cone. Here, while a pure state describes the whole SPDC emission, the produced states can be deemed an independent set by avoiding paths balanced to less than the coherence-length.
Hyperentanglement is a promising resource for achieving high capacity quantum communication. Here, we propose a compact scheme for the generation of path–frequency hyperentangled photon pairs via spontaneous parametric down-conversion (SPDC) processes, where six different paths and two different frequencies are covered. A two-dimensional periodical χ (2) nonlinear photonic crystal (NPC) is designed to satisfy type-I quasi-phase-matching conditions in the plane perpendicular to the incident pump beam, and a perfect phase match is achieved along the pump beam’s direction to ensure high conversion efficiency, with theoretically estimated photon flux up to 2.068 × 105 pairs⋅s−1⋅mm−2. We theoretically calculate the joint-spectral amplitude (JSA) of the generated photon pair and perform Schmidt decomposition on it, where the resulting entropy S of entanglement and effective Schmidt rank K reach 3.2789 and 6.4675, respectively. Our hyperentangled photon source scheme could provide new avenues for high-dimensional quantum communication and high-speed quantum information processing.
Photons produced in the process of spontaneous parametric down-conversion (SPDC) are typically entangled in multiple degrees of freedom. Although polarization is often the parameter of interest, the presence of spectral or spatial entanglement can complicate experiments, either by reducing the visibility of certain interference effects or by reducing collection efficiency. Several recent works have shown that the collection efficiency can be improved by focusing the pump beam. This approach has the added benefit of increasing the bandwidths of the emitted photons. We show that, in the case of type II SPDC, a focused pump can result in different spatial profiles for the signal and idler. If the crystal is configured for emission of polarization-entangled photon pairs, this effect will reduce the fidelity of that entanglement. Moreover, this spatial asymmetry leads to different spectral profiles for the two photons, even when the pump is monochromatic. The spectral and spatial asymmetries can be attributed to the difference in the angular dispersion (walk-off) of the two polarizations, along with a strong correlation between wavelength and emission direction. We also examine the link between spatial entanglement and single-mode coupling efficiency. We find that efficiency is maximized when spatial entanglement can be eliminated. For the case in which walk-off does not play a role, this can be accomplished by properly focusing the pump.