标题： 模态耦合影响参数正则模态分裂：量化纳米机械谐振器的可调模态耦合 显示英文标题

标题： Modal coupling impacts the parametric normal mode splitting: Quantifying the tunable mode coupling of a nanomechanical resonator

摘要： 两个混合正常模态或振荡器之间的模态耦合强度的估计仍然是一个难以实现的任务。 然而，通过观察系统在能量注入后的动态行为，可以揭示耦合效应。 这种方法的一个表现是使用参数激励产生的正常模态分裂。 在本研究中，提出了一种严格且通用的数学公式，用于任何两模态动力系统中的参数正常模态分裂。 该方法能够在弱耦合和强耦合区域中估计耦合强度，并且与模态之间的混合程度无关。 该方法应用于可调纳米弦谐振器中的纳米机械两模态系统的振动。 我们发现实验结果与理论模型之间有良好的一致性，并能够根据施加的偏置电压量化纳米弦的模态耦合。 显示英文摘要

摘要： The estimation of the modal coupling strength between two hybridized normal modes or oscillators remains a hard task to achieve. However, the coupling effects can be unearthed by observing the system's dynamic behaviour upon energy injection. One of the manifestations of this approach is the normal mode splitting generated using parametric excitation. In this contribution, a rigorous and generic mathematical formulation for the parametric normal mode splitting in any two-mode dynamical system is presented. It allows for estimating the coupling strength both in the weak and in the strong coupling regime, and irrespective of the degree of hybridization between the modes. The method is applied on the vibrations of a nanomechanical two-mode system implemented in a tunable nanostring resonator. We find good agreement between the experiment and the theoretical model, and are able to quantify the modal coupling of the nanostring as a function of the applied bias voltage.