Recent experimental progress in cavity optomechanics has allowed cooling of mesoscopic mechanical oscillators via dynamic backaction provided by the parametric coupling to either an optical or an electrical resonator. Here we analyze the occurrence of normal-mode splitting in backaction cooling at high input power. We find that a hybridization of the oscillator's motion with the fluctuations of the driving field occurs and leads to a splitting of the mechanical and optical fluctuation spectra. Moreover, we find that cooling experiences a classical limitation through the cavity lifetime.

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We present an optomechanical displacement transducer, that relies on three cavity modes parametrically coupled to a mechanical oscillator and whose frequency spacing matches the mechanical resonance frequency. The additional resonances allow to reach the standard quantum limit at substantially lower input power (compared to the case of only one resonance), as both, sensitivity and quantum backaction are enhanced. Furthermore, it is shown that in the case of multiple cavity modes, coupling between the modes is induced via reservoir interaction, e.g., enabling quantum backaction noise cancellation. Experimental implementation of the schemes is discussed in both the optical and microwave domain. Introduction.-High frequency nano-and micromechanical oscillators have received a high degree of attention recently. They have been used as sensitive detectors, e.g. for spin [1] or particle mass [2], but also carry an intrinsic interest in the study of small scale dissipation of mechanical systems [3], quantum limited motion detection [18], and backaction cooling of vibrational modes [4]. These studies have in common that a sensitive motion transduction is required, which can be implemented by parametric coupling to an optical, electrical, or microwave resonator. The ideal transducer should i) have a high sensitivity and possibly operate at the standard quantum limit(SQL), and ii) should operate at low power. The latter is experimentally advantageous, as high power may cause excess heating due to intrinsic losses. The former pertains to the minimum uncertainty in motion detection and arises from the trade off between measurement imprecision, inherent to the meter (i.e., detector shot noise), and (for linear continuous measurements) inevitable quantum backaction (QBA) [5,6]. These processes are characterized by the displacement spectral densityS xx (Ω) and the QBA force spectral densityS F F (Ω) [28]. For a parametric motion transducer, where a single cavity mode (with frequency ω 0 and energy decay rate κ) is parametrically coupled to a mechanical oscillator [7], the spectral densities are given bȳ

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