Cryogenic sub-Hz cROss torsion bar detector with quantum NOn-demolition Speed meter (CHRONOS) for gravitational wave detection

Abstract

We present the optical design and sensitivity modeling of the Cryogenic sub-Hz cROss torsion-bar detector with quantum NOn-demolition Speed meter (CHRONOS), a triangular Sagnac speed-meter interferometer incorporating power and signal recycling. Using ABCD-matrix analysis and \textsc{Finesse3} simulations, we obtain stable optical eigenmodes with mode-matching efficiencies above 99.5%. The optimized configuration achieves a quantum-noise-limited strain sensitivity of $h \simeq 3\times10^{-18},\mathrm{Hz^{-1/2}}$ at 1 Hz, with a ring-cavity finesse of $\mathcal{F}\simeq3.1\times10^{4}$ and a round-trip Gouy phase of $\psi\approx153^{\circ}$. The low-frequency quantum noise is primarily governed by the power-recycling cavity detuning, while the signal-recycling cavity produces an approximately uniform quadrature rotation. An optimal homodyne angle of $\zeta\simeq46^{\circ}$ provides the best sensitivity near 1 Hz. Assuming an end-mirror reflectivity of $R_{\mathrm{ETM}}=99.9999%$ at 10 K, CHRONOS can achieve quantum-noise-limited performance on a laboratory scale. Its projected science reach includes intermediate-mass black-hole binaries out to approximately $271,\mathrm{Mpc}$, a 10-year stochastic-background sensitivity of $\Omega_{\mathrm{GW}}\simeq4.7\times10^{-4}$ at $2.15,\mathrm{Hz}$, constraints on Yukawa-type deviations from Newtonian gravity, and prompt gravity-gradient signals from nearby earthquakes.