Optical design and sensitivity optimization of Cryogenic sub-Hz cROss torsion bar detector with quantum NOn-demolition Speed meter (CHRONOS)

arXiv:2510.24780v1 Announce Type: new
Abstract: We present the optical design and sensitivity modeling of the 2.5 m 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 resulting configuration reaches a quantum-noise-limited strain sensitivity of $h simeq 3times10^{-18},mathrm{Hz^{-1/2}}$ at 1 Hz, with a ring-cavity finesse $mathcal{F}simeq3.1times10^{4}$ and round-trip Gouy phase $psi_{mathrm{rt}}approx153^{circ}$. The power-recycling cavity detuning ($phi_p=-85^{circ}$) dominates the low-frequency quantum noise, while the signal-recycling cavity detuning ($phi_s=0^{circ}$) mainly introduces a uniform quadrature rotation. The optimal homodyne angle ($zeta_{mathrm{opt}}simeq46^{circ}$) balances shot-noise and radiation-pressure effects to give the best sensitivity near 1 Hz. Assuming end-mirror reflectivity $R_{mathrm{ETM}}=99.9999%$ under cryogenic operation at 10 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.