Absolute Length Sensing in a Long-Baseline, High-Finesse Optical Cavity

Abstract: The relative phase between two lasers in transmission of an optical cavity can be used to continuously measure its absolute length with sub-micron precision. The first laser is kept on resonance with the cavity, while a second laser is phase-locked to the first with a frequency separation equal to an integer multiple of the cavity's initial free spectral range. As the free spectral range frequency changes due to cavity length changes, the second laser de-tunes slightly from resonance and gains an additional phase offset in transmission of the cavity. The cavity length changes can be calibrated in terms of this phase offset. This technique is applied to a high-finesse optical cavity with a length of 123 meters, transforming it into a strainmeter with an effective sensitivity to transient seismic events of $10^{-10} \, - \, 10^{-9}$ m/m. We report absolute length changes associated with anthropogenic noise, a distant earthquake, and the diurnal and semidiurnal earth tides.