Caves, Carlton M. and Thorne, Kip S. and Drever, Ronald W. P. and Sandberg, Vernon D. and Zimmermann, Mark (1980) On the measurement of a weak classical force coupled to a quantummechanical oscillator. I. Issues of principle. Reviews of Modern Physics, 52 (2). pp. 341392. ISSN 00346861. doi:10.1103/RevModPhys.52.341. https://resolver.caltech.edu/CaltechAUTHORS:20120719163130442

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Abstract
The monitoring of a quantummechanical harmonic oscillator on which a classical force acts is important in a variety of highprecision experiments, such as the attempt to detect gravitational radiation. This paper reviews the standard techniques for monitoring the oscillator, and introduces a new technique which, in principle, can determine the details of the force with arbitrary accuracy, despite the quantum properties of the oscillator. The standard method for monitoring the oscillator is the "amplitudeandphase" method (position or momentum transducer with output fed through a narrowband amplifier). The accuracy obtainable by this method is limited by the uncertainty principle ("standard quantum limit"). To do better requires a measurement of the type which Braginsky has called "quantum nondemolition." A well known quantum nondemolition technique is "quantum counting," which can detect an arbitrarily weak classical force, but which cannot provide good accuracy in determining its precise time dependence. This paper considers extensively a new type of quantum nondemolition measurement—a "backactionevading" measurement of the real part X_1 (or the imaginary part X_2) of the oscillator's complex amplitude. In principle X_1 can be measured "arbitrarily quickly and arbitrarily accurately," and a sequence of such measurements can lead to an arbitrarily accurate monitoring of the classical force. The authors describe explicit Gedanken experiments which demonstrate that X_1 can be measured arbitrarily quickly and arbitrarily accurately. In these experiments the measuring apparatus must be coupled to both the position (position transducer) and the momentum (momentum transducer) of the oscillator, and both couplings must be modulated sinusoidally. For a given measurement time the strength of the coupling determines the accuracy of the measurement; for arbitrarily strong coupling the measurement can be arbitrarily accurate. The "momentum transducer" is constructed by combining a "velocity transducer" with a "negative capacitor" or "negative spring." The modulated couplings are provided by an external, classical generator, which can be realized as a harmonic oscillator excited in an arbitrarily energetic, coherent state. One can avoid the use of two transducers by making "stroboscopic measurements" of X_1, in which one measures position (or momentum) at halfcycle intervals. Alternatively, one can make "continuous singletransducer" measurements of X_1 by modulating appropriately the output of a single transducer (position or momentum), and then filtering the output to pick out the information about X_1 and reject information about X_2. Continuous singletransducer measurements are useful in the case of weak coupling. In this case long measurement times are required to achieve good accuracy, and continuous singletransducer measurements are almost as good as perfectly coupled twotransducer measurements. Finally, the authors develop a theory of quantum nondemolition measurement for arbitrary systems. This paper (Paper I) concentrates on issues of principle; a sequel (Paper II) will consider issues of practice.
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Additional Information:  © 1980 American Physical Society. Supported in part by the National Aeronautics and Space Administration (NGR 05002256 and a grant from PACE) and by the National Science Foundation (Grant No. AST7680801 A02). The ideas and prose of this Appendix are due entirely to Carlton M. Caves, and constitute a portion of the material submitted by him to the California Institute of Technology in partial fulfillment of the requirements for the Ph.D. degree.  
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Issue or Number:  2  
DOI:  10.1103/RevModPhys.52.341  
Record Number:  CaltechAUTHORS:20120719163130442  
Persistent URL:  https://resolver.caltech.edu/CaltechAUTHORS:20120719163130442  
Official Citation:  Caves, C. M., K. S. Thorne, et al. (1980). "On the measurement of a weak classical force coupled to a quantummechanical oscillator. I. Issues of principle." Reviews of Modern Physics 52(2): 341392.  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  32597  
Collection:  CaltechAUTHORS  
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Deposited On:  20 Jul 2012 17:49  
Last Modified:  09 Nov 2021 21:28 
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