Torque cancellation effect of Intensity noise for Cryogenic sub-Hz cROss torsion bar detector with quantum NOn-demolition Speed meter (CHRONOS)

TL;DR

The study advances sub-Hz gravitational-wave detection by proposing CHRONOS, a cryogenic torsion-bar Sagnac speed-meter. It develops an analytic and numerical intensity-noise model that incorporates photon-pressure torques, local-oscillator intensity noise, and beam-position misalignment, and uses FEA and FINESSE to compute the bar transfer functions and the readout sensing function. The results show torque cancellation and balanced-homodyne readout significantly suppress laser-intensity coupling, enabling a 2.5 m CHRONOS prototype to reach $S_h(1\ omega) \approx 2.9\times10^{-20}$ Hz$^{-1/2}$, and indicate feasible RIN requirements for longer-arm configurations. This work provides a framework for evaluating and mitigating intensity noise in torsion-bar speed-meter GW detectors, supporting the pursuit of sub-Hz GW astronomy and IMBH-merger science.

Abstract

Detection of sub-Hz gravitational waves is of significant importance for astrophysics. It enables the observation of intermediate-mass black hole mergers, the issuance of early alerts for gravitational-wave events, and the exploration of the stochastic gravitational-wave background. The Cryogenic sub-Hz cROss torsion-bar detector with quantum NOn-demolition Speed meter (CHRONOS) is a proposed gravitational-wave detector based on a Sagnac speed-meter topology that uses torsion bars as test masses. Its prototype design aims to achieve a strain sensitivity of $3 \times 10^{-18}~\mathrm{Hz}^{-1/2}$ at 1~Hz and thus enable the detection of $\mathcal{O}(10^4),M_\odot$ intermediate-mass black hole mergers at 100~Mpc with a signal-to-noise ratio of 3. We show that the torsion-bar-based speed meter can suppress noise originating from laser intensity fluctuations by canceling the net torque on the bar and by using a balanced homodyne readout. We further present, for the first time, an analytic intensity-noise model for a gravitational-wave detector employing a torsion-bar Sagnac speed-meter configuration. Using this model, we evaluate the expected performance of a 2.5~m arm-length CHRONOS prototype. The projected laser-intensity noise is $2.9 \times 10^{-20}~\mathrm{Hz}^{-1/2}$ at 1~Hz, which is sufficiently low to allow the detection of binary intermediate-mass black hole mergers.

Figures (6)

• Figure 1: Simplified optical path of CHRONOS. One torsion bar and balanced-homodyne detection part are shown.
• Figure 2: Mode shapes of the first and second bulk deformation modes of CHRONOS torsion bar calculated by COMSOL. Arrows indicate direction of surface displacement at each area. The circles of black line at left and right sides represent mirrors. (a) Vertical bending mode at 667 Hz. (b) Horizontal bending mode at 1238 Hz.
• Figure 3: Transfer functions from photon force to surface displacement at the mirrors. The CHRONOS 2.5-m option was assumed. Simulated by COMSOL. ( Solid black) Mean value of left or right beam injection at the designed position; ( Solid green) Mean value of left or right beam injection. The left beam was at 1 mm outward while the right beam was at the designed position; ( Solid orange) Model function given in Eq. (\ref{['eq:H_TF']}). The moment of inertia was $I=19.9 \ {\rm kg\cdot m^2}$, the mean horizontal position of the beams was $\bar{x}=0.5373 \ {\rm m}$, and the residual parameter was $\mu=0.35$; ( Dashed blue) Differential of left and right mirrors when two beams are simultaneously injected at the respective designed positions; ( Dashed red) Differential when the left beam shifted for 1 mm outward; ( Solid cyan) Model function given in Eq. (\ref{['eq:Delta_H_TF']}). The beam position mismatch was $a=0.0021$, $1/f^2$ residual parameter was $\nu=-0.0019$, and the $1/f^4$ magnitude parameter was $\delta=0.0022$.
• Figure 4: Sensing function of CHRONOS calculated by FINESSE3.
• Figure 5: Intensity noise of the CHRONOS 2.5-m option and its noise budget in the unit of spacetime strain. ( Solid black) Total intensity noise; ( Solid red) Term of classic photon pressure which pushes the bar; ( Solid blue) Term of local oscillator's beam power; ( Solid green) Target sensitivity CHRONOS.