Measurement of radiation-pressure-induced optomechanical dynamics in a suspended Fabry-Perot cavity

We report on experimental observation of radiation-pressure induced effects in a high-power optical cavity. These effects play an important role in next-generation gravitational wave detectors, as well as in quantum nondemolition interferometers. We measure the properties of an optical spring, created by coupling of an intense laser field to the pendulum mode of a suspended mirror, and also the parametric instability (PI) that arises from the coupling between acoustic modes of the cavity mirrors and the cavity optical mode. We measure an unprecedented optical rigidity of $K=(3.08\pm 0.09)\times {10}^4\mathrm{N}∕\mathrm{m}$, corresponding to an optical rigidity that is 6000 times stiffer than the mechanical stiffness, and PI strength $R\approx 3$. We measure the unstable nature of the optical spring resonance, and demonstrate that the PI can be stabilized by feedback to the frequency of the laser source.

Figure 1

(Color online) Schematic representation of the experiment, showing the $1\text{−}\mathrm{m}$-long Fabry-Perot cavity suspended in vacuum. $3\mathrm{W}$ of the $1064\mathrm{nm}$ Nd:YAG laser light is incident on the suspended cavity. The input mirror of the cavity has a transmission of 0.63%, giving a linewidth of $75\mathrm{kHz}$. EOM refers to electro-optic modulator, MX to mixer, PD to photodetector, and QWP to quarter-wave plate.

Figure 2

(Color online) The transfer function of applied force to displacement of the end mirror of the cavity, showing the optical spring resonance. The solid (red) curve is the theoretical prediction, based on measurement of the intracavity power, and the quadrangles are the measured data. An important feature is the increase in phase from 0° to 180° at the resonance, showing that the resonance is unstable. The dashed (gray) curve is the expected response of the mirror in the absence of the OS, illustrating modest noise suppression below the OS resonance.

Figure 3

(Color online) The instability measure $R$ is plotted as a function of detuning of the cavity from resonance, for fixed input power. The solid (gray) curve is the theoretical prediction, given by a numerical solution to Eq. (1) with no free parameters. The squares show the measured data; the error bars are explained in the text. The inset time series show $3\mathrm{s}$ of data along with fits for the ringup and ringdown.