High-sensitivity optical measurement of mechanical Brownian motion

Hadjar, Yassine; Cohadon, P.-F.; Aminoff, C.G.; Pinard, M.; Heidmann, A.

doi:10.1209/epl/i1999-00422-6

Cited by 90 publications

(110 citation statements)

References 24 publications

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“…Relevant examples are interferometers for the detection of gravitational waves [1] and atomic force microscopes [2]. Up to now, the major limitation to the implementation of sensitive optical measurements is given by thermal noise [3]. It has been proposed in Ref.…”

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Optomechanical scheme for the detection of weak impulsive forces

2001

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We show that a cooling scheme and an appropriate quantum nonstationary strategy can be used to improve the signal to noise ratio for the optomechanical detection of weak impulsive forces. PACS number(s): 03.65. Bz, 05.40.Jc, 04.80.Nn A mechanical oscillator coupled to an optical mode by the radiation pressure provides a sensitive device able to detect very weak forces. Relevant examples are interferometers for the detection of gravitational waves [1] and atomic force microscopes [2]. Up to now, the major limitation to the implementation of sensitive optical measurements is given by thermal noise [3]. It has been proposed in Ref.[4] to reduce thermal noise by means of a feedback loop based on homodyning the light reflected by the oscillator, playing the role of a cavity mirror. The proposed scheme is a sort of continuous version of the stochastic cooling technique used in accelerators [5], because the homodyne measurement provides a continuous monitoring of the oscillator's position, and the feedback continuously "kicks" the mirror in order to put it in its equilibrium position. This proposal has been experimentally realized in Ref.[6], using the "cold damping" technique [7], which is physically analogous to that proposed in Ref. [4] and which amounts to applying a viscous feedback force to the oscillating mirror.Both the "stochastic cooling" scheme of Ref.[4] and the cold damping scheme of Ref.[6] cool the mirror by overdamping it, thereby strongly decreasing its mechanical susceptibility at resonance. As a consequence, the oscillator does not resonantly respond to the thermal noise, yielding in this way an almost complete suppression of the resonance peak in the noise power spectrum, which is equivalent to cooling. However, the two feedback schemes cannot be directly applied to improve the detection of weak forces. In fact the strong reduction of the mechanical susceptibility at resonance means that the mirror does not respond not only to the noise but also to the signal, and we shall see that the signal to noise ratio (SNR) of the device in stationary conditions is actually never improved. Despite that, here we show how it is possible to design a nonstationary strategy able to significantly increase the SNR for the detection of impulsive classical forces acting on the oscillator. This may be of crucial importance in the field of metrology [8], as well as for the detection of gravitational waves [1]. We use a quantum treatment, allowing us to show why a classical approach provides an incomplete description of the optomechanical scheme.Let us consider a simplified system with a single mechanical mode, representing the movable mirror (with mass m and frequency ω m ) of a coherently driven optical cavity. The optomechanical coupling between the mirror and the cavity field is realized by the radiation pressure. In the adiabatic limit in which the mirror frequency is much smaller than the cavity free spectral range c/2L (L is the cavity length) [9], one can focus on one cavity mode only (with annihilation operato...

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Optomechanical scheme for the detection of weak impulsive forces

2001

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“…[12]. Moreover recent experiments have shown that classical laser noise can be made negligible in the relevant frequency range [8,9]. The adiabatic regime ω S ≪ c/2L we have assumed in Eq.…”

Section: The Dynamics Of the Systemmentioning

confidence: 97%

“…1 for a schematic description of the system). The mechanical oscillator, which may represent not only the center-of-mass degree of freedom of the mirror, but also a torsional degree of freedom as in [9], or an internal acoustic mode as in [8], undergoes Brownian motion caused by the uncontrolled coupling with other internal and external modes at the equilibrium temperature T .…”

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Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion

2001

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We study the dynamics of an optical mode in a cavity with a movable mirror subject to quantum Brownian motion. We study the phase noise power spectrum of the output light, and we describe the mirror Brownian motion, which is responsible for the thermal noise contribution, using the quantum Langevin approach. We show that the standard quantum Langevin equations, supplemented with the appropriate non-Markovian correlation functions, provide an adequate description of Brownian motion.

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Radiation-pressure cooling and optomechanical instability of a micromirror

Arcizet

Cohadon

Briant

et al. 2006

Nature

966

969

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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...

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High-sensitivity optical measurement of mechanical Brownian motion

Cited by 90 publications

References 24 publications

Optomechanical scheme for the detection of weak impulsive forces

Optomechanical scheme for the detection of weak impulsive forces

Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion

Radiation-pressure cooling and optomechanical instability of a micromirror

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