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Classical and Quantum Gravity

Feasibility of loop-gain tuning for general measurement systems inspired by quantum locking for DECIGO

Tomohiro Ishikawa, Yuki Kawasaki, Kenji Tsuji, Ryuma Shimizu, Kurumi Umemura, Bin Wu, Shoki Iwaguchi, Yuta Michimura, Koji Nagano, Yutaro Enomoto, Kentaro Komori, Shinji Doki, Akira Furusawa, Seiji Kawamura

Published Sep 18, 2024• 1 citation
Publisher

Abstract

Abstract A series of quantum locking theories have been proposed to enhance the quantum-noise-limited target sensitivity of the DECi-hertz Interferometer Gravitational wave Observatory. The quantum locking that uses a square completion optimizes the sensitivity across all frequencies. However, a substantial amount of data-series must be post-processed since the square completion is a form of signal processing technique. This paper approaches the optimal sensitivity across all frequencies from an alternative perspective: by optimizing the frequency dependence of a servo gain in a feedback loop. The optimal servo gain is formulated by comparing the alternative method with the square completion method for the same optical setup. This will be shown in general noise issues extending the framework of the quantum locking. We find that the optimal servo gain forms a non-feasible filter but has certain characteristics. We also find that the noise of the measurement signal deteriorates proportionally to the noise measured in the feedback loop when the servo gain is slightly imperfect.

DOI
10.1088/1361-6382/ad7cb6

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Abstract A series of quantum locking theories have been proposed to enhance the quantum-noise-limited target sensitivity of the DECi-hertz Interferometer Gravitational wave Observatory. The quantum locking that uses a square completion optimizes the sensitivity across all frequencies. However, a substantial amount of data-series must be post-processed since the square completion is a form of signal processing technique. This paper approaches the optimal sensitivity across all frequencies from an alternative perspective: by optimizing the frequency dependence of a servo gain in a feedback loop. The optimal servo gain is formulated by comparing the alternative method with the square completion method for the same optical setup. This will be shown in general noise issues extending the framework of the quantum locking. We find that the optimal servo gain forms a non-feasible filter but has certain characteristics. We also find that the noise of the measurement signal deteriorates proportionally to the noise measured in the feedback loop when the servo gain is slightly imperfect.
Quantum locking using optical spring and homodyne detection has been devised to reduce the quantum noise that limits the sensitivity of the DECIGO, a space-based gravitational-wave antenna in the frequency band around 0.1 Hz for the detection of primordial gravitational waves. The reduction in the upper limit of energy density ΩGW from 2×10−15 to 1×10−16, as inferred from recent observations, necessitates improved sensitivity in the DECIGO to meet its primary science goals. To accurately evaluate the effectiveness of this method, this paper considers a detection mechanism that takes into account the influence of vacuum fluctuations on homodyne detection. In addition, an advanced signal processing method is devised to efficiently utilize signals from each photodetector, and design parameters for this configuration are optimized for the quantum noise. Our results show that this method is effective in reducing quantum noise, despite the detrimental impact of vacuum fluctuations on its sensitivity.
The sensitivity in interferometric measurements such as gravitational-wave detectors is ultimately limited by quantum noise of light. We discuss the use of feedback mechanisms to reduce the quantum effects of radiation pressure. Recent experiments have shown that it is possible to reduce the thermal motion of a mirror by cold damping. The mirror motion is measured with an optomechanical sensor based on a high-finesse cavity, and reduced by a feedback loop. We show that this technique can be extended to lock the mirror at the quantum level. In gravitational-waves interferometers with Fabry-Perot cavities in each arms, it is even possible to use a single feedback mechanism to lock one cavity mirror on the other. This quantum locking greatly improves the sensitivity of the interferometric measurement. It is furthermore insensitive to imperfections such as losses in the interferometer.
We study measurement-based feedback control of a damped harmonic oscillator, motivated by optomechanical and interferometric position measurements, in which feedback is synthesized from a displacement measurement. For a band-limited derivative controller, the loop shapes the mechanical susceptibility and reinjects measurement noise, creating a tradeoff between stabilization and noise amplification. We present a compact classical formulation that isolates this tradeoff in the closed-loop displacement spectrum and identifies the parameters governing resonance suppression versus noise-driven actuation. We then extend the same topology to a quantum-limited position detector, enforcing the imprecision-backaction constraint and introducing finite measurement bandwidth that regularizes high-frequency noise reinjection and adds phase lag in the feedback path. In the high-QQQ regime we obtain an analytic design rule for the optimal feedback gain at fixed controller and measurement bandwidths and compare it with full-spectrum calculations. The comparison shows that a high mechanical quality factor alone does not guarantee quantitative agreement: the accuracy of the near-resonant approximation depends strongly on the controller and measurement bandwidths. Because finite measurement bandwidth changes both the magnitude and phase of the feedback loop, the analysis separates the near-resonant damping contribution from imprecision-noise reinjection and shows that positive near-resonant feedback damping requires the product of the controller cutoff and measurement bandwidth to exceed the square of the mechanical resonance frequency. Finally, we present a dimensionless map of the gain-optimized high-QQQ occupation and compare its predictions with full-spectrum optimization. All analytical gains evaluated in this map satisfy the full closed-loop stability criterion for these parameters.
The sensitivity in interferometric measurements such as gravitational-wave detectors is ultimately limited by quantum noise of light. We discuss the use of feedback mechanisms to reduce the quantum effects of radiation pressure. Recent experiments have shown that it is possible to reduce the thermal motion of a mirror by cold damping. The mirror motion is measured with anoptomechanical sensor based on a high-finesse cavity, and reduced by a feedback loop. We show that this technique can be extended to lock the mirror at the quantum level. In gravitational-waves interferometers with Fabry-Perot cavities in each arms, it is even possible to use a single feedback mechanism to lock one cavity mirror on the other. This quantum locking greatly improves the sensitivity of the interferometric measurement. It is furthermore insensitive to imperfections such as losses in the interferometer.
Quantum fluctuation of light limits the sensitivity of advanced laser interferometric gravitational-wave detectors. It is one of the principal obstacles on the way towards the next-generation gravitational-wave observatories. The envisioned significant improvement of the detector sensitivity requires using quantum non-demolition measurement and back-action evasion techniques, which allow us to circumvent the sensitivity limit imposed by the Heisenberg uncertainty principle. In our previous review article (Danilishin and Khalili in Living Rev Relativ 15:5, 2012 ), we laid down the basic principles of quantum measurement theory and provided the framework for analysing the quantum noise of interferometers. The scope of this paper is to review novel techniques for quantum noise suppression proposed in the recent years and put them in the same framework. Our delineation of interferometry schemes and topologies is intended as an aid in the process of selecting the design for the next-generation gravitational-wave observatories.
Interferometric detection of gravitational waves at a level of astrophysical interest is expected to require measurement of optical phase differences of < or = 10(-10) rad. A fundamental limit to the phase sensing is the statistics of photon detection--Poisson statistics for light in a coherent state. We have built a laboratory-scale interferometer to achieve and investigate the phase detection sensitivity required for the Laser Interferometer Gravitational-Wave Observatory. With 70 W of circulating power, we have obtained a phase sensitivity of 1.28 x 10(-10) rad/square root(Hz) at frequencies above 600 Hz, limited by quantum noise. Below 600 Hz, excess noise above the quantum limit is seen, and we present our investigations into the sources of this excess. Compared with the results of previous such experiments, the phase sensitivity over the full 100-Hz-10-kHz band of interest has been improved by factors of up to 100, with a factor-of-2.5 improvement in the quantum-limited level.