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Physical Review A

Spatial control of spontaneous parametric down-conversion photon pairs through the use of apertured Bessel-Gauss pump beams

Dalia Gutiérrez-López, Mónica Maldonado-Terrón, Raul Josue Hernandez, Verónica Vicuña-Hernández, Roberto Ramírez-Alarcón, Héctor Cruz-Ramírez, Rocío Jáuregui, Alfred B. U’Ren

Published Jul 2, 2019• 7 citations
Publisher

Abstract

We demonstrate, both experimentally and theoretically, a method that allows us to modify the spatial properties of photon pairs produced by the process of spontaneous parametric down-conversion (SPDC) with an apertured, zeroth-order Bessel-Gauss beam. Concentrating on the use of a half-plane aperture, we show that the phase-matching conditions for non-paraxial pump beams can be controlled by simply changing the aperture orientation. Partially blocking the pump beam, leads to a selection of either one of two individual cones that form a dual-cone SPDC angular spectrum, or a portion of both of them. We can likewise determine the shape and orientation of the conditional angular spectrum. This control of the SPDC spatial properties could be useful for quantum information processing protocols.

DOI
10.1103/physreva.100.013802

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 14, 2005•0 citations
We demonstrate, both experimentally and theoretically, a method that allows us to modify the spatial properties of photon pairs produced by the process of spontaneous parametric down-conversion (SPDC) with an apertured, zeroth-order Bessel-Gauss beam. Concentrating on the use of a half-plane aperture, we show that the phase-matching conditions for non-paraxial pump beams can be controlled by simply changing the aperture orientation. Partially blocking the pump beam, leads to a selection of either one of two individual cones that form a dual-cone SPDC angular spectrum, or a portion of both of them. We can likewise determine the shape and orientation of the conditional angular spectrum. This control of the SPDC spatial properties could be useful for quantum information processing protocols.
We present an experimental and theoretical study of type I, frequency-degenerate spontaneous parametric down-conversion (SPDC) with a Bessel-Gauss pump in which we include both paraxial and nonparaxial pump beam configurations. We present measurements of the SPDC angular spectrum (AS), of the conditional angular spectrum (CAS) of signal-mode single photons as heralded by the detection of an idler photon, and of the transverse wave-vector signal-idler correlations (TWC). We show that as the pump is made increasingly nonparaxial, the AS acquires a nonconcentric double-cone structure, with the CAS shape depending on the azimuthal location of the heralding detector, while the signal-idler wave-vector correlation region splits into characteristic doublet stripes, representing as yet unexplored nontrivial, nonlocal quantum correlations between the signal and idler photons. Our work provides further understanding of SPDC with a particular class of structured pump beams, and we believe that the controlled presence of double wave-vector correlations represents an interesting resource for photon-pair quantum-state engineering.
We demonstrate experimental generation of spatially entangled photon pairs by spontaneous parametric down-conversion (SPDC) using a partial spatially coherent pump beam. By varying the spatial coherence of the pump, we show its influence on the down-converted photon's spatial correlations and on its degree of entanglement, in excellent agreement with theory. We then exploit this property to produce pairs of photons with a specific degree of entanglement by tailoring of the pump coherence length. This work thus unravels the fundamental transfer of coherence occurring in SPDC processes, and provides a simple experimental scheme to generate photon pairs with a well-defined degree of spatial entanglement, which may be useful for quantum communication and information processing.
Spontaneous parametric down-conversion (SPDC) has been a reliable process for the generation of entangled photon pairs. In this process, a nonlinear quadratic crystal is pumped by a laser field in order to convert (high-energy) photons into correlated photon pairs whose efficient control plays an essential role in various applications of quantum information processing. In particular, the amount of entanglement has been successfully controlled by adjusting the spatial structure of the incident pump field. Here, we theoretically analyze how the entanglement of the down-converted two-photon state can be further enhanced by using Ince-Gaussian beams with well-defined ellipticity $\ensuremath{\epsilon}$, i.e., solutions of the paraxial wave equation in elliptical coordinates. These spatially structured beams are quite universal as they include both the Laguerre-Gaussian beams for $\ensuremath{\epsilon}\ensuremath{\rightarrow}0$ as well as the Hermite-Gaussian beams for $\ensuremath{\epsilon}\ensuremath{\rightarrow}\ensuremath{\infty}$. We demonstrate that the entanglement of the generated photon pairs in SPDC can be maximized by a proper choice of $\ensuremath{\epsilon}$ and that such an enhanced entanglement can be observed experimentally in terms of the Schmidt number.
We propose a method for directly producing radially and azimuthally polarized photon pairs through spontaneous parametric downconversion (SPDC). This method constitutes a novel geometry for SPDC, in which a radially polarized Bessel-Gauss pump beam is directed into a nonlinear crystal, with the central propagation direction parallel to the crystal axis. The phasematching conditions are controlled by changing the opening angle of the pump beam; as the crystal axis cannot be tuned, we refer to this process as super-critical phasematching. We model and plot the spatial and polarization output distributions for Type-I and Type-II super-critical phasematching.
We propose a method for directly producing radially and azimuthally polarized photon pairs through spontaneous parametric downconversion (SPDC). This method constitutes a novel geometry for SPDC, in which a radially polarized Bessel-Gauss pump beam is directed into a nonlinear crystal, with the central propagation direction parallel to the crystal axis. The phasematching conditions are controlled by changing the opening angle of the pump beam; as the crystal axis cannot be tuned, we refer to this process as super-critical phasematching. We model and plot the spatial and polarization output distributions for Type-I and Type-II super-critical phasematching.
We elucidate the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric down-conversion (SPDC) in different non-collinear geometries. To date, most investigations addressed SPDC in nearly collinear phase-matching geometries, where the pump, the signal and idler photons propagate coaxially almost along the same direction. However, non-collinear geometries introduce a variety of new features. The OAM of the entangled photons strongly depend on the propagation direction of the photons. Here we show that locally paraxial measurements of the OAM conducted with entangled photons generated in non collinear geometries, they do not comply with the known selection rules for the spiral index of the pump, signal and idler mode functions (Mair et al., Nature 412, 313 (2001)). In particular, we find the orbital angular momentum of entangled pairs generated in purely transverse-emitting configurations, where the entangled photons counter-propagate perpendicularly to the direction of propagation of the pump beam. In transverse emitting configurations, the spatial shape of the down converted in one transverse dimensions strongly depends on the corresponding spatial shape of the input pump beam, while in the other transverse dimension, the shape is tailored by the longitudinal phase matching. The spatial walk-off of all interacting waves in the parametric process also determines the OAM content of the down-converted photons, and here its influence is also revealed.