Switching times in Fabry-Perot measurements

We show how to analyze the motion of very low dissipation suspended mirrors in a Fabry-Perot. The very precise measurements of the mirrors motion can be determined, also in the presence of a disturbing noise, by means of the sudden reflectivity changes in special points of the mirrors positions. When the mirrors cross such positions, the effective optomechanical potential that arises in the device is (roughly) at a maximum. We show that the motion cross such potential maxima is not only confused by the presence of noise, but also favoured by noise itself that induces hoppings. Thus, the measurements of the times at which the crossings occur can be exploited to identify the properties of the applied signal. We also show how to circumvent the difficulty of the extremely long transient that occur in the system analyzing the escape average time with two different methods: a direct sample average and the indirect estimate from the tail distribution. Numerical simulations and physical insight suggest that the indirect estimate, through the analysis of the distribution tails with an appropriated cut off is robust against the disturbances that arise from the presence of transient dynamics.