零色散谐振腔的频率稳定和噪声引起的谱窄化
Frequency stabilization and noise-induced spectral narrowing in resonators with zero dispersion
摘要：
机械谐振器依赖于其本征频率的稳定性而被广泛用作精密时钟和灵敏检测器。相位噪声由不同的因素决定，从谐振器的热噪声和频率噪声到反馈电路中的噪声。增加振动幅度可以减轻这些影响中的一些，但是这种改善受到非线性的限制，非线性对于小型化的微机械和纳米机械系统特别强。在这里，我们设计了一个微机械谐振器与非单调依赖的本征振荡的频率上的能量。在本征频率的色散为零的极值附近，系统恢复了线性谐振器的某些特性，尽管振动幅度很大。当噪声强度增加时，谱峰经历反直观的变窄。利用谐振器作为反馈回路中的频率确定元件，在极值幅度处的相位噪声比传统的非线性区域小三倍。零色散现象为改进谐振传感器和频率基准提供了新的机会。
英文摘要：
Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors ranging from thermal noise and frequency noise of the resonator to noise in the feedback circuitry. Increasing the vibration amplitude can mitigate some of these effects but the improvements are limited by nonlinearities that are particularly strong for miniaturized micro- and nano-mechanical systems. Here we design a micromechanical resonator with non-monotonic dependence of the frequency of eigenoscillations on energy. Near the extremum, where the dispersion of the eigenfrequency is zero, the system regains certain characteristics of a linear resonator, albeit at large vibration amplitudes. The spectral peak undergoes counter-intuitive narrowing when the noise intensity is increased. With the resonator serving as the frequency determining element in a feedback loop, the phase noise at the extremum amplitude is three times smaller than the conventional nonlinear regime. Zero dispersion phenomena open new opportunities for improving resonant sensors and frequency references.
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