Spectral narrowing of parametrically pumped thermomechanical noise

We derive the displacement noise spectrum of a parametrically pumped resonator below the onset for self-excited oscillations. We extend the fluctuation-dissipation response of a thermomechanical-noise-driven resonator to the case of degenerate parametric pumping as a function of pump magnitude and frequency while properly accounting for the quadrature-dependence of the parametric thermal noise squeezing. We use measurements with a microelectromechanical cantilever to corroborate our model. (C) 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).