A pair of optical cavities are designed and set up so as to be insensitive to both temperature fluctuations and mechanical vibrations. With the influence of these perturbations removed, a fundamental limit to the frequency stability of the optical cavity is revealed. The stability of a laser locked to the cavity reaches a floor < 2 X 10(-15) for averaging times in the range 0.5-100 s. This limit is attributed to Brownian motion of the mirror substrates and coatings.
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