Classical and quantum-linearized descriptions of degenerate optomechanical parametric oscillators

Recent advances in the development of modern quantum technologies have opened the possibility of studying the interplay between spontaneous parametric down-conversion and optomechanics, two of the most fundamental nonlinear optical processes. Apart from practical reasons, such scenario is very interesting from a fundamental point of view, because it allows exploring the optomechanical interaction in the presence of a strongly quantum-correlated field, the spontaneously down-converted mode. In this work we analyze such problem from two approximate but valuable perspectives: the classical limit and the limit of small quantum fluctuations. We show that, in the presence of optomechanical coupling, the well-known classical phase diagram of the optical problem gets modified by the appearance of new dynamical instabilities. As for the quantum-mechanical description, we prove the ability of the squeezed down-converted field to cool down the mechanical motion not only to thermal but also to squeezed thermal mechanical states, and in a way that can be much less sensitive to parameters (e.g., detuning of the driving laser) than standard sideband cooling.