Quantum noise of light is known to induce fundamental limits in high-sensitivity optical measurements, such as shot noise or back-action noise due to radiation pressure. In the case of gravitational-wave resonant detectors such as dual spheres with optical readout, the sensitivity can be strongly improved by a back-action cancellation effect related to the specific geometry of this kind of detectors. We report the observation of such a back-action cancellation. Our experiment is based on a high-finesse Fabry-Perot cavity where the displacements of both mirrors are monitored by sending a very stable laser beam in the cavity and measuring the phase of the reflected beam with an homodyne detection. Between 100 kHz and 4 MHz, the sensitivity is only limited by the shot noise at a level of 5 10{sup}(-20) m/√Hz. We have performed an exhaustive study of the internal thermal noise of mirrors and optomechanical properties of internal acoustic modes: resonance frequency, quality factor, effective mass, and spatial structure. To observe the back-action cancellation, we have injected an additional intense light beam in the cavity, with a classical intensity modulation to mimic the quantum radiation-pressure noise. Fig. 2 shows the modulation spectrum obtained near two mechanical resonances corresponding to individual modes of both mirrors of the cavity. Curve a displays a specific mechanical resonance of the output mirror, measured with an auxiliary intensity-modulated beam, reflected from the back on the end mirror of the cavity. Curve b presents the radiation pressure noise of both mirrors and exhibits a destructive interference between the out-of-phase responses of the two modes, in between the two resonances. A similar back-action cancellation is observed at higher frequency (right dip) due to the interference between the resonances and the background of all other vibration modes. As compared to the individual mirror responses, one gets a reduction of the back-action effects due to radiation pressure by a factor 200. Curve c presents the measured signal corresponding to the radiation pressure force of the auxiliary beam, in presence of back-action noise: the sensitivity of the weak force measurement is clearly increased due to the back-action cancellation effect.
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