Crystalline optical cavity at 4 K with thermal noise limited instability and ultralow drift

Crystalline optical cavities are the foundation of today's state-of-the-art ultrastable lasers. Building on our previous silicon cavity effort, we now achieve the fundamental thermal noise-limited stability for a 6 cm long silicon cavity cooled to 4 Kelvin, reaching $6.5\times10^{-17}$ from 0.8 to 80 seconds. We also report for the first time a clear linear dependence of the cavity frequency drift on the incident optical power. The lowest fractional frequency drift of $-3\times10^{-19}$/s is attained at a transmitted power of 40 nW, with an extrapolated drift approaching zero in the absence of optical power. These demonstrations provide a promising direction to reach a new performance domain for stable lasers, with stability better than $1\times10^{-17}$ and fractional linear drift below $1\times10^{-19}$/s.