Tracing a resonance frequency of a high quality factor (Q) optical cavity facilitates subpicometer displacement measurements of the optical cavity via Pound–Drever–Hall (PDH) locking scheme, tightly synchronizing a laser frequency to the optical cavity. Here we present observations of subfemtometer displacements on a ultrahigh-Q single-crystal ${\mathrm{MgF}}_2$ whispering-gallery-mode microcavity by frequency synchronization between a 1 Hz cavity-stabilized laser and a resonance of the ${\mathrm{MgF}}_2$ cavity using PDH laser-cavity locking. We characterize not only the displacement spectral density of the microcavity with a sensitivity of $1.5\times {10}^{-16}\mathrm{m}/{\mathrm{Hz}}^{1/2}$ over the Fourier offset frequency ranging from 15 mHz to 100 kHz but also a 1.77 nm displacement fluctuation of the microcavity over 4500 s. Such measurement capability not only supports the analysis of integrated thermodynamical and technical cavity noise but allows for minute displacement measurements using laser-cavity locking for ultraprecise positioning, metrology, and sensing.

中文翻译：

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用赫兹级激光器测量超高 Q 单晶微腔中的亚 fm/Hz1/2 位移谱密度

通过 Pound-Drever-Hall (PDH) 锁定方案跟踪高质量因数 ( Q ) 光学腔的共振频率有助于光学腔的亚皮米位移测量，从而将激光频率与光学腔紧密同步。在这里，我们展示了超高Q单晶上亚飞米位移的观察结果${\mathrm{氟化镁}}_2$回音壁模式微腔通过 1 Hz 腔稳定激光器和谐振腔之间的频率同步${\mathrm{氟化镁}}_2$腔使用PDH激光腔锁定。我们不仅表征了微腔的位移谱密度，其灵敏度为$1.5\times {10}^{-16}\mathrm{米}/{\mathrm{赫兹}}^{1/2}$在从 15 mHz 到 100 kHz 的傅里叶偏移频率范围内，而且在 4500 秒内微腔的位移波动为 1.77 nm。这种测量能力不仅支持集成热力学和技术腔噪声的分析，而且允许使用激光腔锁定进行微小位移测量，以实现超精密定位、计量和传感。