Three-mode optoacoustic parametric interactions with a coupled cavity

We theoretically analyze three-mode optoacoustic parametric interactions in a coupled Fabry-Perot cavity, where one acoustic mode interacts with two optical modes. We show explicitly that extra degrees of freedom in a coupled cavity allow explorations of both parametric instability and cooling regimes with high parametric gain in a single table top experiment. This work can motivate experimental realizations of the three-mode parametric instability which might be an issue in next-generation gravitational-wave detectors with high optical-power cavities, helping in the development of better models, and in developing techniques for controls. In addition, we show that the same scheme can be implemented in the resolved-sideband acoustic-mode cooling.