Resonant cascaded down-conversion

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 χ(2)-level oscillation thresholds that are therefore much lower than for a χ(3) OPO. This is promising for reaching the regime of an effective third-order nonlinearity well above both thresholds. Such a χ(2) 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.