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.
Highlights
A widespread technique for the removal of thermal noise from a given mechanical degree of freedom involves electronic feedback loops
Extending the analytical approach that we have previously introduced in Ref. [19] to include a delay time τ, we show that analytical solutions are still possible to some degree in the fast-feedback lossy-cavity (FFLC) regime
The dynamics is generally non-Markovian as the task is to solve a system of coupled integro-differential equations; for relatively small time delay, we introduce the weak and the strong Markovian approximations, which simplify the task by turning the dynamics into a set of coupled linear differential equations
Summary
A widespread technique for the removal of thermal noise from a given mechanical degree of freedom involves electronic feedback loops. We show that a single feedback loop can very efficiently couple to a bright collective mode which, in the near-degeneracy case where all mechanical modes lie within a very narrow frequency window, can be up to N times faster damped to a N times lower occupancy than a single mode This is reminiscent of the superradiance effect as in an increase in the collective radiative rate for a system of N quantum emitters coupled to a single bosonic mode, as in the Dicke model in quantum optics [40,41].
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