Hybrid and Macroscopic Quantum Systems

The eigenmodes of micromechanical resonators are usually only visualized in the linear regime. The nonlinear dynamics are far less explored and recent reports showed emerging spatial structures in strongly-driven micromechanical devices. Using an extension of our efficient mode mapping technique, we spatially resolve the nonlinear behavior of a high-stress silicon nitride membrane. Its modes have widely different quality factors Q allowing us to not only distinguish between the intrinsic and the readout nonlinearity, but also map these in a single resonator. The (2,2) mode already becomes nonlinear for small amplitudes and follows a regular Duffing response. In contrast, the (1,1) mode requires a much larger amplitude and has a strongly deformed response. Still, by fitting the phase, we can determine the mechanical nonlinearity reliably. We find that for both modes the Duffing parameter is position independent and that the distorted resonances due to nonlinear readout. A hallmark signature of the latter are overtones and we see up to 25 harmonics. Their spatial maps show characteristic annuli of alternating positive and negative regions. All results can be reproduced using analytical models. Our results provide novel insights in the interplay between intrinsic and readout nonlinearities in nano- and micromechanical devices.