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Physical Review A

Quantum-nondemolition measurement of photon number using radiation pressure

Kurt A. Jacobs, Paolo Tombesi, Matthew J. Collett, Daniel F. Walls

Published Mar 1, 1994• 95 citations
Publisher

Abstract

We propose a quantum-nondemolition measurement of the amplitude quadrature and the photon-number statistics by using the effect of radiation pressure on a freely suspended mirror. We propose to measure the momentum fluctuations of the mirror which will give us a readout of the amplitude quadrature fluctuations. The scheme we propose is able to avoid the back-action noise leaving the state of the field after the measurement practically undegraded.

DOI
10.1103/physreva.49.1961

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We propose a quantum-nondemolition measurement of the amplitude quadrature and the photon-number statistics by using the effect of radiation pressure on a freely suspended mirror. We propose to measure the momentum fluctuations of the mirror which will give us a readout of the amplitude quadrature fluctuations. The scheme we propose is able to avoid the back-action noise leaving the state of the field after the measurement practically undegraded.
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.
Radiation pressure exerted by light in interferometric measurements is responsible for displacements of mirrors which appear as an additional back-action noise and limit the sensitivity of the measurement. We experimentally study these effects by monitoring in a very highfinesse optical cavity the displacements of a mirror with a sensitivity at the 10-20 m/√Hz level. This unique sensitivity is a step towards the first observation of the fundamental quantum effects of radiation pressure and the resulting standard quantum limit in interferometric measurements. Our experiment may become a powerful facility to test quantum noise reduction schemes, and we already report the first experimental demonstration of a back-action noise cancellation. Using a classical radiation-pressure noise to mimic the quantum noise of light, we have observed a drastic improvement of sensitivity both in position and force measurements.
Radiation pressure exerted by light in interferometric measurements is responsible for displacements of mirrors which appear as an additional back-action noise and limit the sensitivity of the measurement. We experimentally study these effects by monitoring in a very high-finesse optical cavity the displacements of a mirror with a sensitivity at the 10-20m/√Hz level. This unique sensitivity is a step towards the first observation of the fundamental quantum effects of radiation pressure and the resulting standard quantum limit in interferometric measurements. Our experiment may become a powerful facility to test quantum noise reduction schemes, and we already have demonstrated radiation-pressure induced correlations between two optical beams sent into the same moving mirror cavity. Our scheme can be extended down to the quantum level and has applications both in high-sensitivity measurements and in quantum optics.
We analyze schemes for performing quantum nondemolition (QND) measurements in optical cavities. We consider three schemes: (1) measurement of a quadrature phase amplitude using a parametric process, (2) measurement of a quadrature phase amplitude using the optical Kerr effect in a nonlinear fiber, and (3) measurement of the photon number also using the Kerr effect in a fiber. We show that in the second scheme an enhancement of the QND effect may be obtained by making the cavity finesse for the signal larger than that for the probe.