A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity

State-of-the-art laser frequency stabilization by high-finesse optical cavities is limited fundamentally by thermal noise-induced cavity length fluctuations. We present a novel design to reduce this thermal noise limit by an order of magnitude as well as an experimental realization of this new cavity system, demonstrating the most stable oscillator of any kind to date for averaging times of 0.1-10 s. The cavity spacer and the mirror substrates are both constructed from single-crystal silicon and are operated at 124 K, where the silicon thermal expansion coefficient is zero and the mechanical loss is small. The cavity is supported in a vibration-insensitive configuration, which, together with the superior stiffness of the silicon crystal, reduces the vibration-related noise. With rigorous analysis of heterodyne beat signals among three independent stable lasers, the silicon system demonstrates a fractional frequency instability of 1 x 10(-16) at short timescales and supports a laser linewidth of <40 mHz at 1.5 mu m.