300 μs optical cavity storage time and $\mathbf{10^{-7}}$ active RAM cancellation for $\mathbf{10^{-19}}$ laser frequency stabilisation

Abstract: Frequency stabilisation of lasers to optical reference cavities is an established method to achieve state-of-the-art stability. The strengths of this method are the high discriminator coefficient of optical cavities, and the low-noise extraction of the stabilisation signal using modulation techniques. In this Letter we report beyond state-of-the-art performance on both of these fundamentals, unlocking $10^{-19}$ fractional frequency laser stabilisation. We employ a 68 cm long cavity to realise an optical storage time of 300 microseconds, achieving ultrahigh frequency discrimination. We develop a simple and robust scheme to actively cancel residual amplitude modulation (RAM) at the $10^{-7}$ level in an annealed-proton-exchanged lithium-niobate waveguide electro-optic-modulator (EOM).