Multimode cold-damping optomechanics with delayed feedback

Abstract

We investigate the role of time delay in cold-damping optomechanics with multiple mechanical resonances. For instantaneous electronic response, it was recently shown in \textit{Phys. Rev. Lett. \textbf{123}, 203605 (2019)}, that a single feedback loop is sufficient to simultaneously remove thermal noise from many mechanical modes. While the intrinsic delayed response of the electronics can induce single mode and mutual heating between adjacent modes, we propose to counteract such detrimental effects by introducing an additional time delay to the feedback loop. For lossy cavities and broadband feedback, we derive analytical results for the final occupancies of the mechanical modes within the formalism of quantum Langevin equations. For modes that are frequency degenerate collective effects dominate, mimicking behavior similar to Dicke super- and subradiance. These analytical results, corroborated with numerical simulations of both transient and steady state dynamics, allow to find suitable conditions and strategies for efficient single or multimode feedback optomechanics.

References in corpus (11)

• Ground-state cooling of a micromechanical oscillator: generalized framework for cold damping and cavity-assisted cooling schemes
• Feedback cooling of a cantilever's fundamental mode below 5 mK
• Multimode circuit optomechanics near the quantum limit
• High-sensitivity optical monitoring of a micro-mechanical resonator with a quantum-limited optomechanical sensor
• Cold Damping of an Optically Levitated Nanoparticle to micro-Kelvin Temperatures
• Nonreciprocal ground-state cooling of multiple mechanical resonators
• Multiple membrane cavity optomechanics
• Optimal Feedback Cooling of a Charged Levitated Nanoparticle with Adaptive Control
• Stochastic thermodynamics of Langevin systems under time-delayed feedback control: I. Second-law-like inequalities
• A controllable two-membrane-in-the-middle cavity optomechanical system
• Stochastic thermodynamics of Langevin systems under time-delayed feedback control: II. Nonequilibrium steady-state fluctuations