Exploiting Symmetry in the Production and Measurement of Photon Pairs

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.\ud \ud 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