Effective description of a suspended mirror coupled to cavity light -Limitations of Q-enhancement due to normal mode splitting by an optical spring-

Abstract

Pendulums have long been used as force sensors due to their ultimately low dissipation (high-quality factor) characteristic. They are widely used in the measurement of the gravitational constant, detection of gravitational waves, and determination of ultralight dark matter. Furthermore, it is expected that the quantum nature of gravity will be demonstrated by performing quantum control for macroscopic pendulums. Recently, we have demonstrated that quantum entanglement between two pendulums can be generated using an optical spring [D. Miki, N. Matsumoto, A. Matsumura, T. Shichijo, Y. Sugiyama, K. Yamamoto, and N. Yamamoto, arXiv:2210.13169 (2022)]; however, we have ignored that an optical spring can reduce the quality factor (Q-factor) by applying normal-mode splitting between the pendulum and rotational modes possessing relatively high dissipation. Herein, we analyze a system composed of a cylinder suspended using a beam (a suspended mirror, i.e., a pendulum) and an optical spring to consider normal-mode splitting. The reduction in Q-factor is determined only by the beam parameters: the ratio of the radius of the mirror to the length of the beam, and the ratio of the frequency of the rotational mode to the pendulum mode in the absence of cavity photons. In our analysis, we find that the reduction factor $4.38$ is reproduced, which is consistent with the experimental result in Matsumoto \textit{et al.} [N. Matsumoto, S. B. Catan$\tilde{\text{o}}$-Lopez, M. Sugawara, S. Suzuki, N. Abe, K. Komori, Y. Michimura, Y. Aso, and K. Edamatsu, Phys. Rev. Lett. 122, 071101 (2019)]. Our analysis shows that low dissipation (high quality) can be reached using an optical spring for the realistic pendulum system considering the rotational degree of freedom.

arXiv comment13pages, 5 figures

References in corpus (32)

• Cavity Optomechanics
• A Spin Entanglement Witness for Quantum Gravity
• Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity
• Ground-state cooling of a micromechanical oscillator: generalized framework for cold damping and cavity-assisted cooling schemes
• Phase noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion
• Macroscopic Quantum Mechanics: Theory and Experimental Concepts of Optomechanics
• Dark Matter Direct Detection with Accelerometers
• Quantum Superposition of Massive Objects and the Quantization of Gravity
• Optical dilution and feedback cooling of a gram-scale oscillator to 6.9 mK
• Tabletop experiments for quantum gravity: a user's manual
• Observable quantum entanglement due to gravity
• Gravitationally Mediated Entanglement: Newtonian Field vs. Gravitons
• A Simple Pendulum Determination of the Gravitational Constant
• A micromechanical proof-of-principle experiment for measuring the gravitational force of milligram masses
• Direct limits for scalar field dark matter from a gravitational-wave detector
• Non-Gaussianity as a signature of a quantum theory of gravity
• An Optomechanical Quantum Cavendish Experiment
• Quantum correlation of light mediated by gravity
• Gravity-induced entanglement in optomechanical systems
• Ultralight dark matter detection with mechanical quantum sensors
• Enhancement of mechanical Q-factors by optical trapping
• Demonstration of displacement sensing of a mg-scale pendulum for mm- and mg- scale gravity measurements
• High Q mg-scale monolithic pendulum for quantum-limited gravity measurements
• Entanglement and decoherence of massive particles due to gravity
• Signatures of the quantum nature of gravity in the differential motion of two masses
• Quantum sensing with milligram scale optomechanical systems
• Generating quantum entanglement between macroscopic objects with continuous measurement and feedback control
• Leggett-Garg inequalities for testing quantumness of gravity
• Non-Gaussian entanglement in gravitating masses: the role of cumulants
• An optically trapped mirror for reaching the standard quantum limit
• Consistency between causality and complementarity guaranteed by the Robertson inequality in quantum field theory
• Effects of photon field on entanglement generation in charged particles

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