people don't appreciate 1e-18 fractional accuracy enough. It took decades of development pushing many things to the extreme. For example, let's take a look at the optical cavity used for stabilizing the laser used for these atomic clocks. The most recent fight they had with the cavity is replacing the dielectric coating (sputtered SiO2/Ta2O5 or TiO2), which is amorphous, to stacks of crystalline GaAs/AlGaAs, because crystals have lower thermal mechanical noise than amorphous materials, and they got a cavity with 2.5e-17 stability with such quieter mirror coatings. [Lee2026] How good is 2.5e-17? When you are here, you are at the extreme opposite of "nothing ever happens". Everything is happening, and everything affects you. Temperature? It gives you at least two big headaches, (temperature fluctuation) * (thermal expansion), and thermal noise itself. So you optimize the cavity shape, you use single crystal for both the mirror spacer as well as the mirrors themselves so they are less lossy and thus less noisy, and you bond them together along the same crystal orientation as closely as possible. You also cooldown the cavity to reduce thermal noise, not only that, but you also operate at the CTE zero crossing point so temperature fluctuation matters less, thats why you see 124 K and 17 K for silicon cavities. Even with zero CTE, you still need few mK temperature control. Away from zero CTE, it may need to be stabilized to sub uK level. If you glance into cavities working at 4 K (i.e. small but not at zero CTE), you'll see crazy thermal damping systems to smooth out the temperature fluctuation of the 4 K cryostat (~20 mK), as well as find claims like "we now require only mK level control of the room temperature enclosure". [Zhang2017, Robinson2019] (they said "only" because some older cavities were at room T and controlled to sub mK [Ludlow2007], and they got tricks to reduce effects from room T.) (temperature gradient also gives you headache, which is why they choose silicon over glass, for its much higher thermal conductivity) Next is vibration/acceleration. Nothing is rigid, the cryostat vibrates, the earth rotates, and your cavity changes shape. Thats another motivation for silicon over glass, for its higher Young's modulus. So you make the cavity shape as symmetric as possible, and make the mounting fixture as symmetric as possible, and align them with the crystal axis because silicon's Youngs modulus not isotropic . Thus you also choose the optical axis to be the crystal axis with the highest Young's modulus. [Kessler2012] You also gotta align the mechanical axis with the optical axis and with the crystal axis, otherwise longitudinal acceleration would tilt the mirrors and change cavity length. The spacer shape is also a double cone so that it sags less and bends less under transverse acceleration. [Millo2009] Any mechanical resonance would be bad, so you also gotta use PEEK instead of PTFE for supporting the mounting ring, and push the lowest mechanical resonance to be as high freq as possible. Remember silicon's crystal structure? Remember its 3-fold rotational symmetry? That's why your support structure also has the same 3-fold symmetry. [Matei2016] If you have done all these properly, congratulations, now you might be ready to start fighting thermal noise in the dielectric mirror coatings. Harry2002: [Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings](doi.org/10.1088/0264-9381/19…) Numata2004: [Thermal-Noise Limit in the Frequency Stabilization of Lasers with Rigid Cavities](doi.org/10.1103/PhysRevLett.…) Ludlow2007: [Compact, thermal-noise-limited optical cavity for diode laser stabilization at 1e-15](doi.org/10.1364/OL.32.000641) Millo2009: [Ultrastable lasers based on vibration insensitive cavities](doi.org/10.1103/PhysRevA.79.…) Hopcroft2010: [What is the Young's Modulus of Silicon?](doi.org/10.1109/JMEMS.2009.2…) Kessler2012: [A sub-40-mHz-linewidth laser based on a silicon single-crystal optical cavity](doi.org/10.1038/nphoton.2012…) Matei2016: [A second generation of low thermal noise cryogenic silicon resonators](doi.org/10.1088/1742-6596/72…) Zhang2017: [Ultrastable Silicon Cavity in a Continuously Operating Closed-Cycle Cryostat at 4 K](doi.org/10.1103/PhysRevLett.…) Robinson2019: [Crystalline optical cavity at 4 K with thermal-noise-limited instability and ultralow drift](doi.org/10.1364/OPTICA.6.000…) Lee2026: [Frequency Stability of 2.5×10^−17 from a Si Cavity with AlGaAs Crystalline Mirrors](doi.org/10.1103/zgrm-cjbb)