Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion

We study the dynamics of an optical mode in a cavity with a movable mirror subject to quantum Brownian motion. We study the phase-noise power spectrum of the output light, and we describe the mirror Brownian motion, which is responsible for the thermal-noise contribution, using the quantum Langevin approach. We show that the standard quantum Langevin equations, supplemented with the appropriate non-Markovian correlation functions, provide an adequate description of Brownian motion.