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Advanced series in applied physics

Quantum Nondemolition Measurements

Carlton M. Caves

Published Jan 1, 1997• 2 citations
Publisher

Abstract

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.

DOI
10.1142/9789812819895_0010

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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.
The complex amplitude ${X}_{1}+i{X}_{2}\ensuremath{\equiv}(x+\frac{\mathrm{ip}}{m\ensuremath{\omega}}){e}^{i\ensuremath{\omega}t}$ of a harmonic oscillator is constant in the absence of driving forces. Although the uncertainty principle forbids precise measurements of X1{X}_{1}X1​ and X2{X}_{2}X2​ simultaneously ($\ensuremath{\Delta}{X}_{1}\ensuremath{\Delta}{X}_{2}>~\frac{\ensuremath{\hbar}}{2m\ensuremath{\omega}}$), X1{X}_{1}X1​ alone can be measured precisely and continuously ("quantum nondemolition measurement"). Examples are given of measuring systems that do this job. Such systems might play a crucial role in gravitational-wave detection and elsewhere.
Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves et al., 1980, Rev. Mod. Phys. 52, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. [S0034-6861(96)00103-1]
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.
The limitations of the detectability of extremely weak signals (gravitational radiation for instance) imposed by Heisenberg's uncertainty principle on the sequential determination of those signals have been explored recently. A variety of schemes have been proposed to circumvent these limitations. Although all of the earlier attempts have been proven fruitless a recent proposal seems to be quite promising. The scheme, consisting of two harmonic oscillators interacting with each other in a peculiar way, allows for an exact analytical solution which is derived here. If it can be assumed that the expectation value of one of the canonical variables of the total system suffices to monitor the weak signal it can be shown that, in the absence of thermal noise, arbitrarily weak signals can in principle be measured without interference from the uncertainty principle.