Measurement of the mechanical loss of a cooled reflective coating for gravitational wave detection

We have measured the mechanical loss of a dielectric multilayer reflective coating (ion-beam sputtered SiO${}_2$ and Ta${}_2$O${}_5$) in cooled mirrors. The loss was nearly independent of the temperature (4 K $\sim$ 300 K), frequency, optical loss, and stress caused by the coating, and the details of the manufacturing processes. The loss angle was $(4\sim 6)\times {10}^{-4}$. The temperature independence of this loss implies that the amplitude of the coating thermal noise, which is a severe limit in any precise measurement, is proportional to the square root of the temperature. Sapphire mirrors at 20 K satisfy the requirement concerning the thermal noise of even future interferometric gravitational wave detector projects on the ground, for example, LCGT.