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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quantum nondemolition and gravity-wave detection

William George Unruh

Published May 15, 1979• 95 citations
Publisher

Abstract

A variety of quantum nondemolition measurement schemes are defined and examples are given to demonstrate their theoretical and practical possibilities. They show that the quantum limit of measurement of weak forces does not exist.
DOI
10.1103/physrevd.19.2888

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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 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.
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.
Optomechanical sensors are capable of transducing external perturbations to resolvable optical signals. A particular regime of interest is that of high-bandwidth force detection, where an impulse is delivered to the system over a short period of time. Exceedingly sensitive impulse detection has been proposed to observe very weak signals like those due to long-range interactions with dark matter that require much higher sensitivities than current sensors can provide. Quantum resources to go beyond the traditional standard quantum limit of these sensors include squeezing of the light used to transduce the signal, backaction evasion by measuring the optimal quadrature, and quantum nondemolition (QND) measurements that reduce backaction directly. These methods have been developed in the context of gravitational wave detection for target frequencies in the audio band range. Here, we provide the theoretical limits to quantum noise reduction for higher and broader frequency targets, such as those from dark matter signals, while combining quantum-enhanced readout techniques based on squeezed light and QND measurements with optomechanical sensors. We demonstrate that backaction evasion through QND techniques dramatically reduces the technical challenges presented when using squeezed light for broadband force detection, paving the way for combining multiple quantum noise reduction techniques for enhanced sensitivity in the context of impulse metrology.