Statistical properties and quantum nature of light in optical cavities combining second- and third-order nonlinearities

The squeezing of light is a typical quantum effect arising in nonlinear systems, which is of great importance for quantum sensors and other applications. We investigate a scheme consisting of an optical cavity containing a pair of coupled quantum wells through electronic tunneling. Nonlinear excitonic interactions in the direct and indirect exciton fields are considered. Further, the cavity interacts with an optical parametric oscillator which results in the injection of squeezed photons inside the cavity. We show that the excitonic density in the quantum wells is increased by the external squeezed source. By analytically solving the quantum Langevin equations in the frequency domain and optimizing the noise spectrum of the transmitted light, we show that indirect exciton nonlinearity produces a stronger squeezing than direct exciton nonlinearity. In all scenarios, incorporating the parametric oscillator significantly increase the degree of squeezing. The impact of the second-order nonlinearity is much more noticeable in the weak coupling regime compared to excitonic nonlinearity. Nevertheless, the nonlinearity of the exciton produces higher squeezing than the optical parametric oscillator when the strong coupling regime is reached. We found also that the squeezing effect manifests a high resistance and stability against the thermal baths, in particular in the weak coupling regime. The proposed scheme offers possible applications by significantly reducing noise in a specific frequency range in a compact device.