Thermal frequency noise in micromechanical resonators due to nonlinear mode coupling

Nonlinear coupling between different normal modes of a mechanical resonator is a relevant issue in nanomechanical resonators with high aspect ratio, as well as in very low mass resonators based on graphene and nanotube resonators or in trapped nanoparticles. Here we demonstrate that nonlinear coupling between the two orthogonal flexural modes of a high aspect ratio microcantilever results in measurable effects down to the thermal noise level at liquid helium temperature. In particular, thermal amplitude fluctuations of the first mode are mapped into frequency fluctuations of the second mode. Furthermore, we point out non-Gaussian features in the frequency noise due to a single individual mode, an effect which is a direct consequence of the nonlinear coupling. Finally, we discuss possible implications of nonlinear thermal frequency noise in ultrasensitive force microscopy technologies.