Experimental upper limit on the estimated thermal noise at low frequencies in a gravitational wave detector

The mirror relative motion of a suspended Fabry-Perot cavity is studied in the frequency range 3-100 Hz. The experimental measurements presented in this paper have been performed at the Low Frequency Facility, a high finesse optical cavity 1 cm long suspended to a mechanical seismic isolation system like the one of the VIRGO gravitational wave antenna. Because of the radiation pressure between the two mirrors of the cavity, the dynamic behavior of the system is characterized by the optical spring stiffness. In the frequency region above 3 Hz, where seismic noise contamination is negligible, the mirror displacement noise is stationary and its statistical distribution is Gaussian. Using a simplified mechanical model of the suspended system and applying the fluctuation dissipation theorem, we show that the measured power spectrum is reproduced in the frequency region 3-90 Hz. Since the contribution coming from different sources of the system to the total noise budget turns out to be negligible, we conclude that the relative displacement power spectrum of this opto-mechanical system is compatible with a system at thermal equilibrium within its environment. In the region 3-10 Hz this measurement gives so far the best upper limit for the thermal noise of the suspension for a gravitational wave interferometer.