Phase dependence of non-classical photon number correlations in coupled optical processes

In this paper, the authors investigate the coupling of the radiations generated by a non-degenerate three-level cascade laser and a parametric oscillator in a cavity coupled with a two-mode squeezed vacuum reservoir, using a $50:50$ beam splitter. They analyze the quantum statistical properties of the light superposed via the standard beam splitter with phase shift $\varphi$. When the beams of light superpose in phase ($\varphi =0$) and operate above threshold, they demonstrate that the mean and variance of photon number increase initially and remain constant over time. They also show that these quantities significantly rise with the linear gain coefficient when more atoms are initially prepared in the top energy level, and, regardless of the initial atomic preparation, increase with the driving amplitude of the parametric oscillator. Furthermore, at steady state and above threshold, the authors reveal that the superposed radiation, despite exhibiting super-Poissonian statistics, displays non-classical photon number correlations due to strong cross-correlations between the cavity modes of the coupled systems.