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arXiv:1607.03724 · Journal of Physics B Atomic Molecular and Optical Physics

Quantum limits on the detection sensitivity of a linear detector with feedback

Yang Gao

Published Jan 13, 2017• 1 citation
arXivHTMLPDF

Abstract

Abstract We show that the detection sensitivity of a linear detector is lower bounded by some quantum limits. For the force sensitivity, which is relevant for atomic force microscopes, the lower bound is given by the so-called ultimate quantum limit (UQL). For the displacement sensitivity, which is relevant for detecting gravitational waves, a generalized lower bound that can overcome the usual UQL is obtained.

DOI
10.1088/1361-6455/aa5958

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Abstract We show that the detection sensitivity of a linear detector is lower bounded by some quantum limits. For the force sensitivity, which is relevant for atomic force microscopes, the lower bound is given by the so-called ultimate quantum limit (UQL). For the displacement sensitivity, which is relevant for detecting gravitational waves, a generalized lower bound that can overcome the usual UQL is obtained.
Ever since the inception of gravitational-wave detectors, limits imposed by quantum mechanics to the detection of time-varying signals have been a subject of intense research and debate. Drawing insights from quantum information theory, quantum detection theory, and quantum measurement theory, here we prove lower error bounds for waveform detection via a quantum system, settling the long-standing problem. In the case of optomechanical force detection, we derive analytic expressions for the bounds in some cases of interest and discuss how the limits can be approached using quantum control techniques.
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A fundamental peculiarity of gravitational waves is the fact that they couple very weakly to the matter. For this reason the response of a detector can be so small to be comparable with quantum undeterminations. An important limitation for the sensitivity of future generation interferometric detectors of gravitational waves is the so-called standard quantum limit, which makes impossible to do repeated, arbitrary precision measurements of the relevant observables. It can be explained as the consequence of the measurement process' back action on the detector's dynamics. A relevant theoretical and experimental effort has been done in these years in order to study the possibility of avoiding this limitation, which is no more considered a fundamental one. In this talk after a short introduction to the SQL problem from a general point of view I discuss some proposals for detection strategies designed to evade it.
The fast progress in improving the sensitivity of the gravitational-wave detectors, we all have witnessed in the recent years, has propelled the scientific community to the point at which quantum behavior of such immense measurement devices as kilometer-long interferometers starts to matter. The time when their sensitivity will be mainly limited by the quantum noise of light is around the corner, and finding ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of the Standard Quantum Limit and the methods of its surmounting. 1 ar
The quantum Cramér-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the standard quantum limit that arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum nondemolition measurement with the backaction evaded. Additionally, we show that the test mass is more a resource for improving measurement sensitivity than a victim of the quantum backaction, which suggests a new approach to enhancing the sensitivity of a broad class of sensors. We illustrate these points with laser interferometric gravitational-wave detectors.
The fast progress in improving the sensitivity of the gravitational-wave detectors, we all have witnessed in the recent years, has propelled the scientific community to the point at which quantum behavior of such immense measurement devices as kilometer-long interferometers starts to matter. The time when their sensitivity will be mainly limited by the quantum noise of light is around the corner, and finding ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of the Standard Quantum Limit and the methods of its surmounting.