PACS numbers:Recent experimental progress in table-top experiments [1,2] or gravitational-wave interferometers [3] has enlightened the unique displacement sensitivity offered by optical interferometry. As the mirrors move in response to radiation pressure, higher power operation, though crucial for further sensitivity enhancement, will however increase quantum effects of radiation pressure, or even jeopardize the stable operation of the detuned cavities proposed for next-generation interferometers [4,5,6]. The appearance of such optomechanical instabilities [7,8] is the result of the nonlinear interplay between the motion of the mirrors and the optical field dynamics. In a detuned cavity indeed, the displacements of the mirror are coupled to intensity fluctuations, which modifies the effective dynamics of the mirror. Such "optical spring" effects have already been demonstrated on the mechanical damping of an electromagnetic waveguide with a moving wall [9], on the resonance frequency of a specially designed flexure oscillator [10], and through the optomechanical instability of a silica micro-toroidal resonator [11]. We present here an experiment where a micro-mechanical resonator is used as a mirror in a very high-finesse optical cavity and its displacements monitored with an unprecedented sensitivity. By detuning the cavity, we have observed a drastic cooling of the microresonator by intracavity radiation pressure, down to an effective temperature of 10 K. We have also obtained an efficient heating for an opposite detuning, up to the observation of a radiation-pressure induced instability of the resonator. Further experimental progress and cryogenic operation may lead to the experimental observation of the quantum ground state of a mechanical resonator [12,13,14], either by passive [15] or active cooling techniques [16,17,18].The resonator is placed at the end of a linear cavity, along with a conventional coupling mirror (Fig. 1a). As we are only interested in the motion at frequencies Ω close to a resonance frequency Ω m of the resonator, the mirror dynamics can be approximated as the one of a single harmonic oscillator, with resonance frequency Ω m , mass M , damping Γ m and mechanical susceptibility:The resonator is submitted to a radiation pressure force F rad induced by the intracavity field. Depending on the detuning Ψ ≡ 4πL/λ [2π], where L is the cavity length and λ the laser wavelength, any small displacement x of the resonator induces a variation of the intracavity power P and of the radiation pressure (see Fig. 1b). As a consequence, the spring constant k = M Ω 2 m of the resonator is balanced by the radiation pressure force: for a positive detuning, the displacement creates a negative linear force and thereby an additional binding force, increasing the effective spring constant, whereas for a negative detuning, the force corresponds to a softening of the oscillator. Effects are null at resonance, maximum at half-width of the optical resonance, and proportional to the incident power. These effects hav...

We describe an experiment in which a mirror is cooled by the radiation pressure of light. A high-finesse optical cavity with a mirror coated on a mechanical resonator is used as an optomechanical sensor of the Brownian motion of the mirror. A feedback mechanism controls this motion via the radiation pressure of a laser beam reflected on the mirror. We have observed either a cooling or a heating of the mirror, depending on the gain of the feedback loop.PACS : 42.50.Lc, 04.80.Nn, 05.40.Jc Thermal noise is a basic limit for many very sensitive optical measurements such as interferometric gravitational-wave detection [1][2][3]. Brownian motion of suspended mirrors can be decomposed into suspension and internal thermal noises. The latter is due to thermally induced deformations of the mirror surface and constitutes the major limitation of gravitational-wave detectors in the intermediate frequency domain [4,5]. Observation and control of this noise have thus become an important issue in precision measurements [6][7][8]. In order to reduce thermal noise effects, it is not always possible to lower the temperature and other techniques have been proposed such as feedback control [9].In this letter we report the first experimental observation of the cooling of a mirror by feedback control. The principle of the experiment is to detect the Brownian motion of the mirror with an optomechanical sensor and then to freeze the motion by applying an electronically controlled radiation pressure on the mirror. Mechanical effects of light on macroscopic objects have already been observed, such as the dissipative effects of electromagnetic radiation [10], the optical bistability and mirror confinement in a cavity induced by radiation pressure [11], or the regulation of the mechanical response of a microcantilever by feedback via the photothermal force [12]. In our experiment the radiation pressure is driven by the feedback loop in such a way that a viscous force is applied to the mirror. It thus plays a role somewhat similar to the one in optical molasses for atoms.The cooling mechanism can be understood from the experimental setup shown in figure 1. The mirror is used as * e-mail : cohadon, heidmann or pinard@spectro.jussieu.fr † Laboratoire de l'Université Pierre et Marie Curie et de l'Ecole Normale Supérieure associé au Centre National de la Recherche Scientifique the rear mirror of a single-ended Fabry-Perot cavity. The phase of the field reflected by the cavity is very sensitive to changes in the cavity length [13][14][15]. For a resonant cavity, a displacement δx of the rear mirror induces a phase shift δϕ x of the reflected field on the order ofwhere F is the cavity finesse and λ is the optical wavelength. This signal is superimposed to the quantum phase noise of the reflected beam. Provided that the cavity finesse is high enough, this quantum noise is negligible and the Brownian motion of the mirror can be detected by measuring the phase of the reflected field [15].To cool the mirror we use an auxiliary laser beam reflected fro...

Because of radiation pressure, an optical cavity with harmonically bound mirrors has an intensitydependent length and behaves as an effective Kerr medium. We determine the quantum fluctuations of the field reflected by such a cavity" taking into account the input field fluctuations and the mirror Brownian motion. In the regions of parameter space close to bistability turning points, we obtain a significant quantum-noise reduction effect.PACS number(s): 42.50.Lc, 42.65.Vh