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Reviews of Modern Physics

Quantum nondemolition measurements: the route from toys to tools

Vladimir B. Braginsky, Farid Ya Khalili

Published Jan 1, 1996• 377 citations
Publisher

Abstract

The history of the theory of quantum nondemolition (QND) measurements from the 1920s until today is reviewed. The definition and main principles of QND measurements are outlined. Achievements in the experimental realization of QND measurements and several new promising schemes of QND measurements are described. A list of the most important problems (from the authors' point of view) in the area of QND measurements is presented. The problem of measurement of a quantum oscillator phase is considered. A new method of phase measurement is proposed. Examples of possible solutions of fundamental physical problems using QND methods are given.

DOI
10.1103/revmodphys.68.1

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The history of the theory of quantum nondemolition (QND) measurements from the 1920s until today is reviewed. The definition and main principles of QND measurements are outlined. Achievements in the experimental realization of QND measurements and several new promising schemes of QND measurements are described. A list of the most important problems (from the authors' point of view) in the area of QND measurements is presented. The problem of measurement of a quantum oscillator phase is considered. A new method of phase measurement is proposed. Examples of possible solutions of fundamental physical problems using QND methods are given.
Quantum nondemolition—the phrase tumbles easily out of the brain and off the tounge. Too easily, in fact—one is left wondering what it could possibly mean. It could, for example refer to an unsuccessful laser weapon, or it might be a law prohibiting destruction of the buildings where the quantum theory was invented. Alas, it is neither of these, but what it does mean might be just as surprising. Quantum nondemolition refers to techniques for monitoring a weak force acting on a harmonic oscillator, the force being so weak that it changes the oscillator’s amplitude by an amount less than the amplitude of zero-point fluctuations. In these lecture notes I describe the current understanding of quantum nondemolition techniques and give a brief account of how that understanding developed. The references are intended to include a complete list of published work that bears directly on the quantum nondemolition problem.
This chapter discusses the type of measurement in the framework of the path-integral method. It begins from the simplest case of measurement of the linear momentum of a free particle, which allows one to see all the typical features characteristic of quantum nondemolition (QND) measurements. The idea of QND measurement is to measure a variable such that the unavoidable disturbance of the complementary one does not disturb the evolution of the chosen variable. The weight factor describes monitoring of the momentum, which for a free particle turns out to be a QND variable. This can be seen from the formula for the probability distribution of the measurement results. Usual relation between linear momentum and velocity is violated in the modified dynamics. From the physical point of view this is a consequence of measurement, of the influence of a measuring device.
Review of methods of measurement There are two different variants of the task of measuring electromagnetic energy: i) measuring the energy in a mode of an electromagnetic resonator, and ii) measuring the energy of a traveling electromagnetic wave. This chapter deals with the first variant; the next chapter, with the second. The general principles underlying QND measurements of energy were formulated in chapter IV. Let us recall that the main principles are: i) the response of the measuring device must be directly proportional to the energy (and not, for example, to the strength of the electric field or the charge on the capacitor); and ii) the response must contain no information about the phase of the electromagnetic oscillations. Chapter IV analyzed the simplest example of such a device: a ponderomotive sensor that registers the electromagnetic pressure on the resonator's wall. The weakness of the electromagnetic pressure produced by a small number of quanta makes it unlikely that this ponderomotive method can be realized in practice. Because of this, several other schemes for QND energy measurements have been proposed. Most are based on nonlinear effects in dielectrics. Their practical realization is a rather complicated task because, when the energy density is low, the nonlinear effects hardly work at all, and the response of the measuring device is correspondingly small.