Quantum optics of nonlinear systems in cascade

In this letter, we investigate the quantum optical properties of driven-dissipative nonlinear systems in a cascade configuration. We show that pumping a nonlinear system with a state having a noncoherent statistics, can improve the antibunching of the output state and, consequently, the nonclassicality of the whole system. Furthermore, we show that is possible to generate entanglement through dissipative coupling. These results applies to a broad category of physical systems with a Kerr-like non-linearity, from Rydberg atoms to exciton polaritons in microcavities.