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 techniques. Using ABCD-matrix analysis and Finesse3 simulations, we show that stable eigenmodes are obtained with optimized mirror curvatures and focal placements, achieving mode-matching efficiencies above 99.5%. The configuration reaches a quantum-noise-limited strain sensitivity of h ≃ 1 × 10 − 18 Hz − 1 / 2 at 2 Hz, with a ring-cavity finesse F ≃ 3.1 × 10 4 and a round-trip Gouy phase ψ ≈ 153 ∘ . The power-recycling cavity detuning ϕ p = 5 ∘ dominates the low-frequency quantum noise, while the signal-recycling cavity detuning ϕ s = 0 ∘ mainly introduces a uniform quadrature rotation. The optimal homodyne angle ( ζ ≃ 46 ∘ ) balances shot noise and radiation-pressure effects to give the best sensitivity near 1 Hz. Assuming an end-mirror reflectivity R ETM = 99.9999 % under cryogenic operation at 8 K, CHRONOS can achieve quantum-noise-limited performance on a laboratory scale and serve as a testbed for future long-baseline cryogenic interferometers probing sub-hertz gravitational waves. The projected science reach includes the detection of intermediate-mass black-hole binaries with total masses of 10 2 – 10 5 M ⊙ , reaching a maximum detection distance of ∼ 271 Mpc for binaries with total masses around 9 × 10 3 M ⊙ SNR = 1. The detector also achieves a best power-integrated sensitivity to stochastic gravitational-wave backgrounds of Ω GW ≃ 4.7 × 10 − 4 at 2.15 Hz after 10 years of observation, probes Yukawa-type deviations from Newtonian gravity down to | α | ∼ 2 × 10 − 5 , and can detect prompt gravity-gradient signals from nearby M5.2 earthquakes out to distances of approximately 90 km .