Thermomechanical Two-Mode Squeezing in an Ultrahigh- Q Membrane Resonator

We realize a quantum-compatible multimode interaction in an ultrahigh Q mechanical resonator via a reservoir-mediated parametric coupling. We use this interaction to demonstrate nondegenerate parametric amplification and thermomechanical noise squeezing, finding excellent agreement with a theoretical model of this interaction over a large dynamic range. This realization of strong multimode nonlinearities in a mechanical platform compatible with quantum-limited optical detection and cooling makes this a powerful system for nonlinear approaches to quantum metrology, transduction between optical and phononic fields, and the quantum manipulation of phononic degrees of freedom.