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Physical Review A

Quantum-nondemolition measurement of light by a piezoelectric crystal

M. Pinard, Claude Fabre, A. Heidmann

Published Mar 1, 1995• 27 citations
Publisher

Abstract

We show that an optical cavity made of mirrors coated on a piezoelectric crystal can provide a quantum-nondemolition measurement of the intensity of a light beam. Due to radiation pressure, the crystal length is sensitive to the light intensity and can be measured by an electric circuit. The intensity fluctuations are not modified by reflection on such a cavity and the quantum correlations between these fluctuations and the output current of the electric circuit can be made very large even at nonzero temperature.

DOI
10.1103/physreva.51.2443

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We show that an optical cavity made of mirrors coated on a piezoelectric crystal can provide a quantum-nondemolition measurement of the intensity of a light beam. Due to radiation pressure, the crystal length is sensitive to the light intensity and can be measured by an electric circuit. The intensity fluctuations are not modified by reflection on such a cavity and the quantum correlations between these fluctuations and the output current of the electric circuit can be made very large even at nonzero temperature.
According to quantum mechanics, if we keep observing a continuous variable we generally disturb its evolution. For a class of observables, however, it is possible to implement a so-called quantum nondemolition measurement: by confining the perturbation to the conjugate variable, the observable is estimated with arbitrary accuracy, or prepared in a well-known state. For instance, when the light bounces on a movable mirror, its intensity is not perturbed (the effect is just seen on the phase of the radiation), but the radiation pressure allows one to trace back its fluctuations by observing the mirror motion. In this work, we implement a cavity optomechanical experiment based on an oscillating micromirror, and we measure correlations between the output light intensity fluctuations and the mirror motion. We demonstrate that the uncertainty of the former is reduced below the shot-noise level determined by the corpuscular nature of light.
According to quantum mechanics, there exists a class of observables for which is possible to confine the perturbation produced by a continuous measurement to the conjugate variable. Therefore, it is possible to devise experimental schemes that allow estimating the observed variable with arbitrary accuracy, or preparing it in a well-known state. Such schemes are referred to as quantum non-demolition measurements (QND). Among these observables there is the amplitude of the light field. Indeed, it is possible to exploit a movable mirror to implement a QND scheme [1]. Intensity fluctuations of an optical field impinging on it are not affected by the interaction. However, the movable mirror is excited by the associated radiation pressure. This, in turn, affects the phase of the field.
We analyze the coupling between the fluctuations of an atomic beam incident on an evanescent wave mirror and the fluctuations of the laser beam producing the evanescent potential barrier. We show that this coupling is equivalent to a crossed Kerr effect between an atomic field and a light field, and that the consistency of the theory requires that both fields be subject to symmetrical commutation relations and quantum fluctuations. We show in particular that the phase shift undergone by the light field during the atomic reflection process permits a quantum nondemolition measurement of the incident atomic intensity.
A modified Michelson interferometer in which one of the mirrors is driven by a piezoelectric crystal connected to a Gaussian random-noise generator has been used to phase modulate a light beam from a Spectra Physics 119 model laser. The recombination of the modulated and the unmodulated beam reflected by a stationary prism generates a randomly varying interference pattern whose intensity distribution has been analyzed by means of a standard photon-counting technique. The experimental data agree with the theoretical semiclassical predictions in the range of linearity of the piezoelectric crystal. Deviations from the theory have been detected and correlated with the hysteresis of the crystal for large root-mean-square voltages applied to it.