Enhanced gravitational-wave detection of black hole quasi-normal modes using optically diluted optomechanical filters

Black hole quasi-normal modes (QNM) are powerful probes of the mass and spin of black holes created from coalescence events. The characteristic frequency scales inversely with black hole mass. The sensitivity of Advanced LIGO-type detectors degrades at high frequency due to shot noise, thereby restricting their sensitivity to QNM produced by black holes lower in mass than those that have been currently observed. In this paper we show the requirements for a negative dispersion optomechanical filter to be used in practice to realize broadband sensitivity enhancement at high frequency. The improved sensitivity can be achieved by using a very low frequency cat-flap resonator stiffened by a stable optical spring trap. We show that an optical trap combined with an AlGaAs catflap resonator can achieve a $T\cdot Q_m^{-1}$ factor $\sim 2 \times 10^{-9}$, sufficient to improve the 2 kHz sensitivity of Advanced LIGO detectors by approximately 3-fold compared to the 800 kW design sensitivity. This will allow high sensitivity to stellar mass black hole QNMs and binary neutron stars, enabling much better characterization of their population.