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Crystalline optical cavities are the foundation of today's state-of-the-artultrastable lasers. Building on our previous silicon cavity effort, we nowachieve the fundamental thermal noise-limited stability for a 6 cm long siliconcavity 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 cavityfrequency drift on the incident optical power. The lowest fractional frequencydrift of $-3\times10^{-19}$/s is attained at a transmitted power of 40 nW, withan extrapolated drift approaching zero in the absence of optical power. Thesedemonstrations provide a promising direction to reach a new performance domainfor stable lasers, with stability better than $1\times10^{-17}$ and fractionallinear drift below $1\times10^{-19}$/s.

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