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

TL;DR

This paper presents the optical design and sensitivity modeling of CHRONOS, a 2.5 m triangular Sagnac speed-meter interferometer with dual recycling. By combining ABCD-matrix analysis with Finesse3 simulations, the authors achieve stable, high-efficiency mode matching (>$99.5\%$) and a quantum-noise-limited strain sensitivity of $h \approx 3\times10^{-18}\ \text{Hz}^{-1/2}$ at $1\ \text{Hz}$, with a ring-cavity finesse of $\mathcal{F} \approx 3.1\times10^{4}$ and Gouy phase $\psi_{\text{rt}} \approx 153^{\circ}$. The low-frequency noise is dominated by power-recycling detuning ($\phi_p=-85^{\circ}$), while signal-recycling detuning ($\phi_s=0^{\circ}$) mainly rotates the readout quadrature; an optimal homodyne angle of $\zeta_{\text{opt}}\approx46^{\circ}$ achieves the best balance between shot noise and radiation pressure. Assumed end-mirror reflectivity ($R_{\text{ETM}}=99.9999\%$) under cryogenic operation, CHRONOS serves as a laboratory testbed to validate quantum-noise suppression strategies and informs designs for future long-baseline, cryogenic detectors probing sub-hertz gravitational waves; coating absorption and mechanical loss remain the main practical challenges for achieving ultimate sensitivity. The work demonstrates how careful optical design, detuning control, and high-precision mode matching enable quantum-noise-limited performance at sub-hertz frequencies in a compact facility.

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 $h \simeq 3\times10^{-18},\mathrm{Hz^{-1/2}}$ at 1 Hz, with a ring-cavity finesse $\mathcal{F}\simeq3.1\times10^{4}$ and round-trip Gouy phase $ψ_{\mathrm{rt}}\approx153^{\circ}$. The power-recycling cavity detuning ($φ_p=-85^{\circ}$) dominates the low-frequency quantum noise, while the signal-recycling cavity detuning ($φ_s=0^{\circ}$) mainly introduces a uniform quadrature rotation. The optimal homodyne angle ($ζ_{\mathrm{opt}}\simeq46^{\circ}$) 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.

Figures (14)

• Figure 1: Schematic of the bar-shaped test masses. Each bar has dimensions of $1100\,\mathrm{mm}$ in length, $200\,\mathrm{mm}$ in width, and $220\,\mathrm{mm}$ in height. Two orthogonal bars (X and Y) are suspended at the center to realize differential torsional readout.
• Figure 2: Schematic optical layout of the CHRONOS 2.5 m test facility. After pre-stabilization, the input laser beam passes through the PSL and IMC and is split into the X and Y arms by the IBS. Each arm contains an identical triangular Sagnac ring cavity formed by ITM, MTM, and ETM. For mode matching, the ETMs and CMs are given finite radii of curvature. The laser injection point is offset by about 0.5 m from the geometric center, and this asymmetry determines the closed optical path of the ring cavity. The returning beams are recombined at the OBS and pass through the SRM and OMC before being finally read out by BHD.
• Figure 3: Comparison of shot noise and radiation-pressure noise for varying ETM reflectivity.
• Figure 4: Radiation-pressure noise at low frequencies, illustrating degradation of QND suppression with reduced $r_{\mathrm{ifo}}$.
• Figure 5: Total quantum-noise spectra including shot noise, radiation-pressure noise, and other technical noise sources. Coating effects dominate the sensitivity in the 0.1-10 Hz band. The intensity noise is calculated elsewhere Tanabe:inprep.