Advances in Quantum Nonlinear Optics: a nonclassical journey from the optimization of silicon photomultipliers for Quantum Optics to quantum second-harmonic generation

In this thesis, we present our experimental and theoretical work on modern and old topics of Nonlinear Quantum Optics. The thesis is structured as follows. In the first chapter, we provide a general introduction about the basis of this field, in particular about the main concepts and results that will be needed in the following. In the second and third chapters, we explain our research on the role of silicon photomultipliers in Quantum Optics experiments. After a specific characterization of the sensors, we used them to detect nonclassical states of light. Different strategies for the estimation of experimental quantities are suggested. In the fourth chapter, we propose our quantum description for the second-harmonic-generation process, based on well-known perturbative methods. After a general introduction on the state of the art, we immediately dive into the problem by explaining the employed methods and showing our analytical results. Finally, we resume the essence of our achievements and draw our conclusions.