The random thermal motion of two distinct modes of a large membrane resonator are brought 'in sync' by creating a nonlinear interaction between the modes. Such 'two-mode squeezed states' present new opportunities for quantum metrology.
We realize a nondegenerate parametric amplifier in an ultrahigh Q mechanical membrane resonator and demonstrate two-mode thermomechanical noise squeezing. Our measurements are accurately described by a two-mode model that attributes this nonlinear mechanical interaction to a substrate-mediated process which is dramatically enhanced by the quality factors of the individual modes. 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.