Nonlinear frequency transduction of nanomechanical Brownian motion

Abstract

We report on experiments addressing the nonlinear interaction between a nanomechanical mode and position fluctuations. The Duffing nonlinearity transduces the Brownian motion of the mode and of other nonlinearly coupled ones into frequency noise. This mechanism, ubiquitous to all weakly nonlinear resonators thermalized to a bath, results in a phase diffusion process altering the motion: two limit behaviors appear, analogous to motional narrowing and inhomogeneous broadening in NMR. Their crossover is found to depend nontrivially on the ratio of the frequency noise correlation time to its magnitude. Our measurements obtained over an unprecedented range covering the two limits match the theory of Y. Zhang and M. I. Dykman [Phys. Rev. B 92, 165419 (2015)], with no free parameters. We finally discuss the fundamental bound on frequency resolution set by this mechanism, which is not marginal for bottom-up nanostructures.