A simplified cryogenic optical resonator apparatus providing ultra-low frequency drift

A system providing an optical frequency with an instability comparable to that of a hydrogen maser is presented. It consists of a $5$ $\mathrm{cm}$ long, vertically oriented silicon optical resonator operated at temperatures between $1.5$ $\mathrm{K}$ and $3.6$ $\mathrm{K}$ in a closed-cycle cryostat with low-temperature Joule-Thomson stage. We show that with a standard cryostat, a simple cryogenic optomechanical setup, no active or passive vibration isolation, a minimum frequency instability of $2.5\times10^{-15}$ at $\tau=1500$ $\mathrm{s}$ integration time can be reached. The influence of pulse-tube vibrations was minimized by using a resonator designed for low acceleration sensitivity. With reduced optical laser power and interrogation duty cycle an ultra-low fractional frequency drift of $-2.6\times10^{-19}$/$\mathrm{s}$ is reached. At $3.5$ $\mathrm{K}$ the resonator frequency exhibits a vanishing thermal sensitivity and an ultra-small temperature derivative $8.5\times10^{-12}/\mathrm{K}^{2}$. These are favorable properties that should lead to high performance also in simpler cryostats not equipped with a Joule-Thomson stage.