Advanced LIGO: length sensing and control in a dual recycled interferometric gravitational wave antenna

Length sensing and control is vital for Advanced LIGO and its goal of performing astrophysical searches. The current kilometer scale gravitational wave antennae are dual recycled Michelson interferometers enhanced with Fabry–Perot resonators in the arms. Observation requires the lengths of all optical cavities to be precisely servoed in the vicinity of a resonance using feedback controls. Simultaneously achieving robustness and low-noise is challenging due to cross-couplings between the multiple coupled optical resonators. We analytically derive the Advanced LIGO sensing and control scheme, calculate the effects of radiation pressure forces and review the current strategies of minimizing the coupling of noise into the gravitational wave readout. (paper)