Towards a Robust and Stand-Alone Ultra-Stable Laser System Based on a 124 K Si Resonator with an Instability of $4\times 10^{-17}$

Ultra-stable laser systems are needed for precision measurements, e.g. with optical clocks, where the performance directly depends on the lasers' fractional frequency instability. This instability is fundamentally limited by the thermal noise in the systems' ultra-stable resonators. To reach the thermal noise floor, the technical noise of the laser system must be reduced below the thermal noise limit. This includes, noise resulting from laser power fluctuations, from residual amplitude modulation in the PDH servo or from seismic noise acting on the cavity.