We analyze an optical parametric oscillator (OPO) in which cascaded down-conversion occurs inside a cavity resonant for all modes but the initial pump. Due to the resonant cascade design, the OPO presents two ${\chi }^{\left(2\right)}$-level oscillation thresholds that are therefore much lower than for a ${\chi }^{\left(3\right)}$ OPO. This is promising for reaching the regime of an effective third-order nonlinearity well above both thresholds. Such a ${\chi }^{\left(2\right)}$ cascaded device also has potential applications in frequency conversion to far-infrared regimes. But, most importantly, it can generate novel multipartite quantum correlations in the output radiation, which represent a step beyond squeezed or entangled light. The output can be highly non-Gaussian and therefore not describable by any semiclassical model. In this paper, we derive quantum stochastic equations in the positive-$P$ representation and undertake an analysis of steady-state and dynamical properties of this system.

• Received 23 December 2008

DOI:https://doi.org/10.1103/PhysRevA.85.033821