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Physical Review A

Nonideal quantum nondemolition measurements

Murray Holland, Matthew J. Collett, Daniel F. Walls, M. D. Levenson

Published Sep 1, 1990• 140 citations
Publisher

Abstract

The process of making a measurement on a quantum-mechanical system introduces quantum noise to that system. A quantum nondemolition measurement scheme seeks to make a measurement of an observable to better than this quantum limit, by feeding all the introduced noise into a conjugate variable to that under consideration. In this paper three quantitative criteria are suggested for the evaluation of nonideal quantum nondemolition measurements. The application of these criteria is illustrated using both a simple beam splitter and the ${\mathrm{\ensuremath{\chi}}}^{3}$ interaction in a Raman-active medium.

DOI
10.1103/physreva.42.2995

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The process of making a measurement on a quantum-mechanical system introduces quantum noise to that system. A quantum nondemolition measurement scheme seeks to make a measurement of an observable to better than this quantum limit, by feeding all the introduced noise into a conjugate variable to that under consideration. In this paper three quantitative criteria are suggested for the evaluation of nonideal quantum nondemolition measurements. The application of these criteria is illustrated using both a simple beam splitter and the \ensuremathχ3{\mathrm{\ensuremath{\chi}}}^{3}\ensuremathχ3 interaction in a Raman-active medium.
We show theoretically that optical phase conjugation via four-wave mixing can satisfy the quantitative criteria [Holland et al., Phys. Rev. A 42, 2995 (1990)] for performing quantum nondemolition measurements of a signal field despite the fact that this measurement scheme introduces noise into the signal field and thus does not perform a true quantum nondemolition measurement. The criteria can be satisfied under conditions in which the vacuum field injected in the rear of the phase-conjugate mirror is quadrature squeezed. Using this measurement scheme, it is possible to obtain values of the total information transfer coefficient that are as large as those that can be achieved using quantum nondemolition measurements.
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.