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

微纳米机械谐振器在许多领域具有广阔的应用前景。纳米机械谐振器的一个特别有趣的实现是驱动膜，其允许可视化其振动状态，除了在频域和时域中的研究之外，还提供重要的空间信息。虽然在过去大多数线性效应已被用于应用中，但非线性现象直到最近才成为焦点。这些特性包括系统波动、频率响应谱和振动模式的不同特性，以及通过打破非线性力学系统的时间平移对称性而产生的新的“准模式”，这些特性已经在理论上预测或在实验中发现。然而，大多数这些研究仅限于（弱非线性）Duffing制度。在本计画中，我们将把Duffing机制之外的两个重要效应，即空间调变效应与强弯模耦合效应，应用于非线性薄膜共振器中与准模相关的边带效应与噪声特性的研究。这两个非线性效应已被报道产生更高的谐波响应，已被描述的理论模型的现象。在我们的初步结果中，与准模相关的边带在频谱中显示出独特的性质，包括它们的频率和强度增强对驱动功率的摆动依赖性，避免交叉和自振荡。然而，这些明显的边带效应的起源仍然不清楚。在本计画中，我们将利用一种直接的侦测方法，即感应侦测法，系统地研究空间调变与模式耦合状态下的这些边带效应。准模式的起源和性质及其对波动（噪声引起的边带）的响应的理论模型将从Duffing制度扩展到强非线性制度。此外，模式耦合的作用，避免交叉和自振荡的准模式的外观将探索通过使用不同的组合耦合弯曲模式和应力调谐结构，以分离模式耦合从其他非线性效应。此外，通过在感应检测中使用多个探针并将成像白色光干涉仪集成到感应检测平台中，可以同时监测膜的振动模式，这使我们能够记录所研究的边带的空间图像。最后，噪声引起的边带可以揭示压缩效应，并给出关于机械噪声强度的信息，这是充分表征机械系统及其大振幅振动状态的两个重要方面。我们将探索或得出一个一般性的理解的边带和噪声压缩的起源，并阐明空间调制和弯曲模耦合的噪声特性的作用。

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.