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 $h\simeq 3\times 10^{-18},\mathrm{H}{\mathrm{z}}^{-1/2}$ at 1 Hz, with a ring-cavity finesse of $\mathcal{F}\simeq 3.1\times 10^4$ and a round-trip Gouy phase of $\ddot{I}ˆ\approx 153^{\circ }$. 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 $\hat{I}\P \simeq 46^{\circ }$ 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 $\hat{I}{\text{c◯}}_{\mathrm{GW}}\simeq 4.7\times 10^{-4}$ at $2.15,\mathrm{Hz}$, constraints on Yukawa-type deviations from Newtonian gravity, and prompt gravity-gradient signals from nearby earthquakes.

35 page, 17 figures