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 2.5\,m Cryogenic sub-Hz cROss torsion-bar detector with quantum NOn-demolition Speed meter (CHRONOS), a triangular Sagnac speed-meter interferometer with power and signal recycling. Using ABCD-matrix analysis and \textsc{Finesse3} simulations, we optimize the optical configuration and achieve mode-matching efficiencies above 99.5\%. The optimized design reaches 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 \[ \mathcal{F}\simeq3.1\times10^{4}. \] Power-recycling detuning dominates the low-frequency quantum noise, while the optimal homodyne angle, $ζ\simeq46^{\circ}$, provides the best sensitivity around 1\,Hz. Assuming cryogenic operation at 10\,K with an end-mirror reflectivity of $99.9999\%$, CHRONOS provides a laboratory-scale demonstration of quantum-noise-limited cryogenic interferometry for future sub-hertz gravitational-wave detectors. The projected science reach includes intermediate-mass black-hole binaries with total masses of $10^{2}$--$10^{5}\,M_{\odot}$ out to approximately $271\,\mathrm{Mpc}$, stochastic gravitational-wave backgrounds down to $Ω_{\rm GW}\simeq4.7\times10^{-4}$, Yukawa-type deviations from Newtonian gravity down to $|α|\sim2\times10^{-5}$, and prompt gravity-gradient signals from nearby M5.2 earthquakes within approximately $90\,\mathrm{km}$.