The main scope of this thesis is the investigation of quantum properties of nonlinear, dissipative, optical and condensed matter systems. Compared with previous studies on this subjects, we reached several milestone of general interests for the theoretical and experimental community.
The main experimental platform we refer to in this thesis is microcavity polaritons: polaritons arise from the coupling of light with excitons in a quantum well, i.e., a 2D semiconductor material embedded in the microcavity. They have attracted the interest of the scientific community for their rich physics. Polaritons can form out-of-equilibrium Bose-Einstein condensates, they can experience superfluid phase transition and, due to their interaction via the excitonic component, they show a variety of phenomena which are typical of nonlinear physics, such as bistability and parametric scattering.
In particular, motivated by recent proposals about the generation of single photons from weakly nonlinear system, like the unconventional photon blockade, and by the production of squeezed states in polariton systems, we studied the possibility of obtaining antibunched light and other quantum states (like squeezed states and entangled states), when the nonlinear system shows some peculiar features: in particular we consider polariton soliton and cascade systems.
Finally, when considering nonlinear incoherent processes, we investigate the effect of the PT-symmetry and the PT-symmetry breaking on the quantum state of the emitted light.
Hence, this research work has two main objectives: first, from the fundamental physics point of view, to understand the interplay between nonlinear phenomena and quantum optics, second to provide useful tools for future technological applications. Specifically, for the latter case, we demonstrate a theorem that links the measurement of intensity correlations with the occurrence of certain phase transitions, and we propose a setup to maximize the non-classicality of the light emitted by weakly non-linear systems via a cascade configuration.