Multimode cold-damping optomechanics with delayed feedback

TL;DR

This paper explores how introducing a deliberate time delay in feedback loops can mitigate the negative effects of electronic response delays in multimode optomechanical systems, enhancing noise reduction and collective behavior.

Contribution

It proposes a method to counteract electronic delay effects in multimode optomechanics by adding an intentional delay, supported by analytical and numerical analysis.

Findings

Counteracting electronic delays improves mode cooling efficiency

Analytical expressions for mode occupancies are derived

Collective effects akin to Dicke super- and subradiance are observed

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.