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Super-critical phasematching for photon pair generation in structured light modes

Rebecca Y. Saaltink, Lambert Giner, Robert W. Boyd, Ebrahim Karimi, Jeff S. Lundeen

Published Jan 1, 2016• 3 citations
Publisher

Abstract

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.

DOI
10.20381/ruor-23234

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Journal of the Optical Society of America B•May 1, 1997•38 citations
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 present two projects that exploit symmetry to produce and measure photon pairs. In the first project, 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. We model and plot the spatial and polarization distributions for Type-I and Type-II phasematching. In the second project, we demonstrate experimentally a method to measure the polarization state of single photons through direct measurements performed on optimal quantum clones. We produce these optimal quantum clones on a non-polarizing beam splitter and interfere the outputs of this beam splitter in a displaced Sagnac interferometer. By performing orthogonal polarization measurements on these two photons, we reconstruct the density matrix for input states H and R.
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.
Spontaneous parametric downconversion is the primary source to generate entangled photon pairs in quantum photonics laboratories. Depending on the experimental design, the generated photon pairs can be correlated in the frequency spectrum, polarization, position-momentum, and spatial modes. Exploring the spatial modes' correlation has hitherto been limited to the polar coordinates' azimuthal angle, and a few attempts to study Walsh mode's radial states. Here, we study the full-mode correlation, on a Laguerre-Gauss basis, between photon pairs generated in a type-I crystal. Furthermore, we explore the effect of a structured pump beam possessing different spatial modes onto bi-photon spatial correlation. Finally, we use the capability to project over arbitrary spatial mode superpositions to perform the bi-photon state's full quantum tomography in a 16-dimensional subspace.
An analysis of the output polarization of a noncollinear type I optical parametric downconversion source is presented. Such a source can be made by pumping a nonlinear crystal with an extraordinary-polarized beam to produce pairs of ordinary-polarized photons. A polarization map of the output light illustrates dramatic variation in the polarization direction at large scattering angles. The effect of this variation in polarization direction is seen on a map of the nonlinear conversion efficiency. The apparent ambiguity in the polarization for the particular case in which one of the outputs propagates along the crystal optic axis is also discussed.