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Exploiting Symmetry in the Production and Measurement of Photon Pairs

Rebecca Y. Saaltink

Published Jan 1, 2017• 0 citations
Publisher

Abstract

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.

DOI
10.20381/ruor-668

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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 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.
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.
This thesis deals with the production of entangled photons using spontaneous parametric down-conversion (SPDC). We start with a short overview of some important theoretical concepts. First we provide a brief reminder of the theory of entanglement. We then discuss how the state of quantum systems can be determined using quantum state tomography. We also explain SPDC, the physical process which we use to produce entangled photons. Finally, we give an overview of the methods which have been used to produce entangled photons in the past, both for two- and three-photon entanglement. \n \nThe first experiment is the design of an efficient source of entangled photon pairs based on a polarizing Sagnac interferometer configuration. With this configuration, we can use quasi-phasematched materials which allow for higher efficiencies than standard bulk nonlinear materials. The source is pumped by a low-power continuous-wave laser diode, and produces degenerate photon pairs at 809nm. It has a spectral brightness of 87,500 pairs/(s mW nm), and the fidelity of the produced quantum states with a Bell state is 98.9%. The source is used for experiments in quantum key distribution, cluster state quantum computing, remote state preparation, state discrimination, and entanglement-enhanced classical communication. \n \nThe second experiment discussed in this thesis is the generation of photon triplets using cascaded SPDC. In this experiment, a primary SPDC source is pumped with a low-power, continuous-wave laser diode, producing photon pairs. Single photons from these pairs serve as the pump for a second down-conversion, resulting in photon triplets. This is the first demonstration of the direct production of photon triplets, and the first observation of SPDC at the single photon level. This method could potentially be used to produce entangled photon triplets without post-selection, and as a source of triggered Bell pairs.
The experimental realization of optimal symmetric phase-covariant $1\ensuremath{\rightarrow}2$ cloning of qubit states is presented. The qubits are represented by polarization states of photons generated by spontaneous parametric down-conversion. The experiment is based on the interference of two photons on a custom-made beam splitter with different splitting ratios for vertical and horizontal polarization components. From the measured data we have estimated the implemented cloning transformation using the maximum-likelihood method. The result shows that the realized transformation is very close to the ideal one and the map fidelity reaches 94%.