The thermal fluctuation of mirror surfaces is the fundamental limitation for interferometric gravitational wave (GW) detectors. Here, we experimentally demonstrate for the first time a reduction in a mirrors thermal fluctuation in a GW detector with sapphire mirrors from the Cryogenic Laser Interferometer Observatory at 17,K and 18,K. The detector sensitivity, which was limited by the mirrors thermal fluctuation at room temperature, was improved in the frequency range of 90,Hz to 240,Hz by cooling the mirrors. The improved sensitivity reached a maximum of $2.2 times 10^{-19},textrm{m}/sqrt{textrm{Hz}}$ at 165,Hz.
We achieved for the first time a direct measurement of the thermal fluctuation of a pendulum in an off-resonant region using a laser interferometric gravitational wave detector. These measurements have been well identified for over one decade by an agreement with a theoretical prediction, which was derived by a fluctuation-dissipation theorem. Thermal fluctuation is dominated by the contribution of resistances in coil-magnet actuator circuits. When we tuned these resistances, the noise spectrum also changed according to a theoretical prediction. The measured thermal noise level corresponds to a high quality factor on the order of 10^5 of the pendulum.
