  Thermodynamically induced length fluctuations of high-reflectivity mirror
coatings put a fundamental limit on sensitivity and stability of precision
optical interferometers like gravitational wave detectors and ultra-stable
lasers. The main contribution - Brownian thermal noise - is related to the
mechanical loss of the coating material. Owing to their low mechanical losses,
Al\textsubscript{0.92}Ga\textsubscript{0.08}As/GaAs crystalline mirror coatings
are expected to reduce this limit. At room temperature they have demonstrated
lower Brownian thermal noise than with conventional amorphous coatings.
%However, no detailed study on the noise constituents from these coatings in
optical interferometers has been conducted. We present a detailed study on the
spatial and temporal noise properties of such coatings by using them in two
independent cryogenic silicon optical Fabry-Perot resonators operated at 4 K,
16 K and 124 K. We confirm the expected low Brownian thermal noise, but also
discover two new noise sources that exceed the Brownian noise: birefringent
noise that can be canceled via polarization averaging and global excess noise
(10 dB above Brownian noise). These new noise contributions are a barrier to
improving ultra-stable lasers and the related performance of atomic clocks, and
potentially limit the sensitivity of third-generation gravitational wave
detectors. Hence, they must be considered carefully in precision interferometry
experiments using similar coatings based on semiconductor materials.
