Inductive detection of sideband effects and mechanical noise in strongly driven membrane resonators

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Micro- and nanoscale mechanical resonators bear rich potential for applications in a broad range of areas. A particularly interesting realization of nanomechanical resonators are driven membranes that allow to visualize their vibration state giving important spatial information in addition to studies in the frequency and time domain. While in the past mostly linear effects have been used in applications, nonlinear phenomena came into focus only recently. These include distinct properties in system fluctuations, frequency response spectra and vibration patterns as well as new “quasi modes” produced by breaking the time translational symmetry of the nonlinear mechanical system, which have been predicted theoretically or found experimentally. However, most of these studies were limited to the (weakly nonlinear) Duffing regime. In this project, we will involve two important effects beyond the Duffing regime, namely spatial modulation and strong flexural mode coupling effects, into the studies of sideband effects related with quasi modes and noise properties of nonlinear membrane resonators. These two nonlinear effects have been reported to generate higher harmonic response as has been phenomenologically described by a theoretical model. In our preliminary results, the sidebands related with the quasi modes have shown unique properties in the frequency spectra including a wiggling dependence of their frequency and intensity enhancement on the drive power, avoided crossing and self-oscillation. However, the origin of these pronounced sideband effects is still unclear. In this project, we will systematically study these sideband effects in the spatial modulation and mode coupling states by employing a straightforward detection method, i.e. inductive detection. A theoretical model for the origin and properties of the quasi modes and their response to fluctuations (noise-induced sidebands) will be extended from the Duffing regime to the strongly nonlinear regime. In addition, the role of mode coupling in the appearance of avoided crossing and self-oscillation of the quasi modes will be explored by using different combinations of coupled flexural modes and stress-tuning structures to separate the mode coupling from other nonlinear effects. Moreover, the vibration patterns of membranes will be simultaneously monitored by using multiple probes in inductive detection and integrating Imaging White Light Interferometry into the inductive detection platform, which allows us to record a spatial image of the studied sidebands. Finally, the noise-induced sidebands can reveal squeezing effects and give information about the intensity of the mechanical noise, two important aspects to fully characterize mechanical systems and their large-amplitude vibration state. We will explore o derive a general understanding of the origin of the sidebands and noise squeezing and to elucidate the role of spatial modulation and flexural mode coupling on the noise properties.