Realization and characterization of an entangled photon source

The present work starts with a historical and conceptual introduction of the foundation of the entanglement, from the idea of Einstein to the formulation of Bohm, much more experimentally accessible. For the formation of an entangled state, the description of the nonlinear physical process SPDC (Spontaneous Parametric Down-Conversion) was given, starting from the classical Hamiltonian and performing the quantization of the fields exiting the crystal. It was possible to determine the general structure of the wave function by perturbing the vacuum state. The basic properties of the density matrix and the qubit, the fundamental unit of quantum computation, have also been recalled as a prerequisite to the measurements of Bell Inequality and Quantum Tomography. The second chapter is focusing on the apparatus. This can be thought as divided into two independent parts. The first, formed by the laser, the temporal precompensation system and the non-linear crystal, is responsible for the production of entangled photons. The second, formed by the spatial compensation system, the waveplates, and the beam splitter, can be described as an operator, according to Jones's matrix calculation, which acts on the wavefunction produced by the source. Measuring entanglement means detect coincidences, then we explain the dependence of the counting rate from the apparatus and how we optimized the coincidence rate. Finally, in order to verify the quantum character of the source, a Bell test was performed and the value of S is extracted. The reconstruction of the density matrix is presented in the last chapter, using an analytical analysis of the Bloch hypersphere, from which we found a starting point for a numerical optimization of the density matrix that better represents our system. In the last, we characterized the degree of entanglement of the source.