Ultra-low vibration pulse-tube cryocooler stabilized cryogenic sapphire oscillator with notation 10-16 fractional frequency stability

A low maintenance long-term operational cryogenic sapphire oscillator has been implemented at 11.2 GHz using an ultra-low-vibration cryostat and pulse-tube cryocooler. It is currently the world's most stable microwave oscillator employing a cryocooler. Its performance is explained in terms of temperature and frequency stability. The phase noise and the Allan deviation of frequency fluctuations have been evaluated by comparing it to an ultra-stable liquid-helium cooled cryogenic sapphire oscillator in the same laboratory. Assuming both contribute equally, the Allan deviation evaluated for the cryocooled oscillator is σ_-y 1 × 10 ^-15τ^-1/2 for integration times 1 < τ < 10 s with a minimum σ_y = 3.9 × 10^-16 at τ = 20 s. The long term frequency drift is less than 5 × 10^-14day. From the measured power spectral density of phase fluctuations, the single-sideband phase noise can be represented by L (f) = 10^-14.0/ f⁴+10^-11.6/f³+10^-10.0/f ²+10^-10.2/f+ 10^-11.0 rad²/Hz for Fourier frequencies 10^-3 < f < 10³ Hz in the single oscillator. As a result, L\approx -97.5 dBc/Hz at 1-Hz offset from the carrier.