Sub-Hz line width diode lasers by stabilization to vibrationally and   thermally compensated ULE Fabry-Perot cavities
  We achieved a 0.5 Hz optical beat note line width with ~ 0.1 Hz/s frequency drift at 972 nm between two external cavity diode lasers independently stabilized to two vertically mounted Fabry-Perot (FP) reference cavities. Vertical FP reference cavities are suspended in mid-plane such that the influence of vertical vibrations to the mirror separation is significantly suppressed. This makes the setup virtually immune for vertical vibrations that are more difficult to isolate than the horizontal vibrations. To compensate for thermal drifts the FP spacers are made from Ultra-Low-Expansion (ULE) glass which possesses a zero linear expansion coefficient. A new design using Peltier elements in vacuum allows operation at an optimal temperature where the quadratic temperature expansion of the ULE could be eliminated as well. The measured linear drift of such ULE FP cavity of 63 mHz/s was due to material aging and the residual frequency fluctuations were less than 40 Hz during 16 hours of measurement. Some part of the temperature-caused drift is attributed to the thermal expansion of the mirror coatings. High-frequency thermal fluctuations that cause vibrations of the mirror surfaces limit the stability of a well designed reference cavity. By comparing two similar laser systems we obtain an Allan instability of 2*10-15 between 0.1 and 10 s averaging time, which is close to the theoretical thermal noise limit. 
J. Alnis, A. Matveev, N. Kolachevsky, T. Wilken, Th. Udem, and T.W.   Haensch