Measurement of sub-fm/Hz 1/2 displacement spectral densities in ultrahigh-Q single-crystal microcavities with hertz-level lasers

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 MgF 2 whispering-gallery-mode microcavity by frequency synchronization between a 1 Hz cavity-stabilized laser and a resonance of the 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 × 10 − 16 m / 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.