تعيين حالت كوانتومي خروجي بلور از BBO در آزمايش نامساوي بل به روش توموگرافي حالت كوانتومي

In this thesis, an experimental reconstruction an‎d theoretical analysis of optical quantum states generated via spontaneous parametric down-conversion (SPDC) in a beta-barium borate (BBO) crystal is presented. The main objective of this research is the accurate determination of the density matrix of the generated photon pairs an‎d a detailed investigation of their nonlocal properties through Bell inequality tests an‎d comparison with the predictions of quantum mechanics. In the theoretical part, fundamental concepts of quantum systems, including qubits an‎d the geometric representation of polarization states on the Poincaré sphere, are reviewed. Subsequently, the physical process of photon-pair generation is described. In the experiment, a pump laser beam with a wavelength of 405 nm an‎d diagonal polarization (45°) is incident on a nonlinear BBO crystal. Through type-II SPDC, pump photons are converted into signal an‎d idler photon pairs with a wavelength of 810 nm. Proper alignment of the crystal optical axes results in strong quantum correlations in the polarization degrees of freedom of the photon pairs, providing the basis for Bell inequality violation experiments. To fully characterize the generated quantum state, quantum state tomography (QST) is employed as a stan‎dard protocol for two-qubit systems. A complete set of polarization-resolved measurements is performed, an‎d the experimental data are analyzed using the maximum likelihood estimation (MLE) algorithm. This approach ensures the reconstruction of a physical density matrix satisfying the positive semi-definite condition an‎d yields the most accurate estimate of the actual quantum state. In the experimental implementation, the Bell inequality in the Clauser–Horne–Shimony–Holt (CHSH) form is realized. The photon-counting statistics yield an experimental Bell parameter of S=2.59. which clearly violates the classical bound of 2 an‎d confirms the presence of nonclassical correlations at the output of the BBO crystal. Analysis of the reconstructed density matrix shows a fidelity of 93% with respect to the ideal Bell state ϕ^+. Furthermore, applying the Horodecki criterion to the density matrix predicts a maximum theoretical Bell parameter of 2.65. The slight discrepancy between the experimental an‎d theoretical values is attributed to systematic optical imperfections an‎d statistical uncertainties. Overall, the results demonstrate the effectiveness of quantum state tomography in the precise reconstruction an‎d characterization of entangled photonic states.

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