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We report on the relative length fluctuation of two fixed-spacer Fabry-Perotcavities with mirrors fabricated from silica/tantala dielectric coatings onfused silica substrates. By locking a laser to each cavity and reading out thebeat note $\hat{\nu} = \nu_1 - \nu_2$ of the transmitted beams, we find that,for frequencies from 10 Hz to 1 kHz, the amplitude spectral density of beatnote fluctuation is $\sqrt{S_\hat{\nu}(f)} = (0.5\,\mathrm{Hz})/f^{1/2}$. Bycareful budgeting of noise sources contributing to the beat note, we find thatour measurement is consistent with the fluctuation in this band being dominatedby the Brownian noise of the mirror coatings. Fitting for the coating lossangle $\phi_\mathrm{c}$, we find it equal to $4\times10^{-4}$. We then use aBayesian analysis to combine our measurement with previous observations, andthereby extract estimates for the individual loss angles of silica and tantala.It is hoped that the testbed described in this article can be used in thefuture to measure the length noise of cavities formed with novel mirrormaterials and geometries.

Broadband Measurement of Coating Thermal Noise in Rigid Fabry-Perot Cavities