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arXiv:2106.07025 · Applied Physics Letters

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

Salem F. Hegazy, Salah S. A. Obayya

Published Dec 14, 2020• 2 citations
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Abstract

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.

DOI
10.1063/5.0022646

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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 polarization entangled state produced via spontaneous parametric downconversion (SPDC) has relativephase maps in frequency and momentum domains which give an almost complete picture about the distinguishability and purity loss in the conjugate time and space domains. We demonstrate experimentally the tunable compensation of directional relative-phase profile for entangled photons generated by two cascaded / crossed crystals and captured over ultra-wide spatial window. We use a phase-only spatial light modulator (SLM) programmable via a personal computer to flatten (or correct for) the spatial relative-phase profile and also to add on-demand spatial phase profile. A fast, yet accurate, technique is introduced for frequent relative-phase measurements based on the tilt angle of a quarter wave plate (QWP) acting on the diagonally polarized pump beam and nulling the relative-phase of the entangled state at that direction. Our experimental measurements verify previous theoretical models for tunable compensation of the polarization two-photon state produced by the cascaded crystals arrangement.
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.
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.
We demonstrate a broadband entangled photon source based on a single-pass, type-0 phase-matched, non-collinear spontaneous parametric down-conversion (SPDC) process. By spatially multiplexing the intrinsically random transverse momentum states of biphotons emitted in an annular spatial distribution from a single-frequency-pumped, 2-mm-long periodically poled KTP crystal, we generate polarization-entangled pair photons with a spectral bandwidth of ∼130 nm centered at 810 nm. The negligible group-velocity mismatch of the co-polarized near-degenerate photons in single-pass and low birefringence of standard optical components preserves indistinguishability across the broadband emission without phase compensation, enabling high-quality polarization entanglement over the entire emission bandwidth. The source achieves a brightness of 0.57 Mpairs/s/mW and a two-photon coherence length of 6.97 μm, while exhibiting an interference visibility exceeding 95%, a Bell–CHSH parameter of 2.526 ± 0.005 that remains stable over 12 h of continuous operation and violates the Bell inequality by more than 100 standard deviations, and a state fidelity of 96.3%. The generic scheme providing the broadest bandwidth entangled biphotons at 810 nm, to our knowledge, can readily be used for other wavelengths as required for multiparty quantum networks and quantum sensing applications.
We demonstrate a broadband entangled photon source based on a single-pass, type-0 phase-matched, non-collinear spontaneous parametric down-conversion (SPDC) process. By spatially multiplexing the intrinsically random transverse momentum states of biphotons emitted in an annular spatial distribution from a single-frequency-pumped, 2-mm-long periodically poled KTP crystal, we generate polarization-entangled pair photons with a spectral bandwidth of ∼130 nm centered at 810 nm. The negligible group-velocity mismatch of the co-polarized near-degenerate photons in single-pass and low birefringence of standard optical components preserves indistinguishability across the broadband emission without phase compensation, enabling high-quality polarization entanglement over the entire emission bandwidth. The source achieves a brightness of 0.57 Mpairs/s/mW and a two-photon coherence length of 6.97 μm, while exhibiting an interference visibility exceeding 95%, a Bell–CHSH parameter of 2.526 ± 0.005 that remains stable over 12 h of continuous operation and violates the Bell inequality by more than 100 standard deviations, and a state fidelity of 96.3%. The generic scheme providing the broadest bandwidth entangled biphotons at 810 nm, to our knowledge, can readily be used for other wavelengths as required for multiparty quantum networks and quantum sensing applications.
Entanglement-based quantum key distribution (QKD) relies on the distribution of high-fidelity maximally entangled Bell states, typically generated via spontaneous parametric down-conversion (SPDC). In practical systems, unwanted relative phases arise from birefringence, pump-beam contributions, imperfect photon-pair generation, transmission through physical channels, and collection, transforming Bell states into phase-shifted states. This degrades interference visibility, increases the quantum bit error rate (QBER), and limits secure key generation. Conventional compensation techniques, such as birefringent crystals, interferometric stabilization, and spatial light modulators, are often impractical in real-world deployments. Here, we demonstrate a simple and versatile phase-compensation scheme that can be implemented at either the source or the receiver to eliminate arbitrary relative phases in Bell states. We theoretically and experimentally quantify the dependence of QBER in the BBM92 protocol on the relative phase and show that geometric-phase-based control can effectively restore entanglement quality. In a proof-of-concept experiment using a nondegenerate polarization Bell state, we achieve a fidelity exceeding 95% and reduce QBER below the 11% security threshold required for secure QKD. This robust approach enables practical phase control in entangled-photon systems and can be extended to time-bin QKD via time-polarization mapping, offering a promising route toward stable, low-QBER quantum communication.