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arXiv:1903.09378 · Physical review. D/Physical review. D.

Fundamental relations between measurement, radiation, and decoherence in gravitational wave laser interferometer detectors

Belinda Pang, Yanbei Chen

Published Jun 11, 2019• 10 citations
arXivHTMLPDF

Abstract

As laser interferometer gravitational wave (GW) detectors become quantum noise dominated, understanding the fundamental limit on measurement sensitivity imposed by quantum uncertainty is crucial to guide the search for further noise reduction. Recent efforts have included applying ideas from quantum information theory to GW detection---specifically the quantum Cramer-Rao bound, which is a minimum bound on error in parameter estimation using a quantum state and is determined by the state's quantum Fisher information (QFI) with respect to the parameter [Helstrom, J. Stat. Phys. 1, 231 (1969)]. Identifying the QFI requires knowing the interaction between the quantum probe and the signal, which was rigorously derived for GW interferometer detectors in Pang and Chen [Phys. Rev. D 98, 124006 (2018)]. In this paper, we calculate the QFI and fundamental quantum limit (FQL) for GW detection, and furthermore we derive explicit reciprocity relations involving the QFI that summarize information exchange between the detector and a surrounding weak quantum GW field. Specifically, we show that the GW power radiation by the detector's quantum fluctuations are proportional to the QFI, and therefore are inversely proportional to its FQL. Similarly, the detector's decoherence rate in a white noise GW bath can be explicitly related to the QFI/FQL. These relations are fundamental and appear generalizable to a broader class of quantum measurement systems.

DOI
10.1103/physrevd.99.124016

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As laser interferometer gravitational wave (GW) detectors become quantum noise dominated, understanding the fundamental limit on measurement sensitivity imposed by quantum uncertainty is crucial to guide the search for further noise reduction. Recent efforts have included applying ideas from quantum information theory to GW detection---specifically the quantum Cramer-Rao bound, which is a minimum bound on error in parameter estimation using a quantum state and is determined by the state's quantum Fisher information (QFI) with respect to the parameter [Helstrom, J. Stat. Phys. 1, 231 (1969)]. Identifying the QFI requires knowing the interaction between the quantum probe and the signal, which was rigorously derived for GW interferometer detectors in Pang and Chen [Phys. Rev. D 98, 124006 (2018)]. In this paper, we calculate the QFI and fundamental quantum limit (FQL) for GW detection, and furthermore we derive explicit reciprocity relations involving the QFI that summarize information exchange between the detector and a surrounding weak quantum GW field. Specifically, we show that the GW power radiation by the detector's quantum fluctuations are proportional to the QFI, and therefore are inversely proportional to its FQL. Similarly, the detector's decoherence rate in a white noise GW bath can be explicitly related to the QFI/FQL. These relations are fundamental and appear generalizable to a broader class of quantum measurement systems.
Laser interferometers are quantum instruments. This chapter presents the quantum theory of laser interferometer gravitational wave detectors. We show the basics for analysing the quantum noise in the detector, and for deriving the associated standard quantum limit (SQL) for the sensitivity. By providing different perspectives on the origin of the SQL, we illustrate the motivations behind different approaches for surpassing the SQL. Introduction The most difficult challenge in building a laser interferometer gravitational wave (GW) detector is isolating the test masses from the rest of the world (e.g. random kicks from residual gas molecules, seismic activities, acoustic noises, thermal fluctuations, etc.) whilst keeping the device locked around the correct point of operation (e.g. pitch and yaw angles of the mirrors, locations of the beam spots, resonance condition of the cavities, and darkport condition for the Michelson). Once all these issues have been solved, we arrive at the issue that we are going to analyse in this chapter: the fundamental noise that arises from quantum fluctuations in the system. A simple estimate (following the steps of Braginsky, 1968) will already lead us into the quantum world – as it will turn out, the superb sensitivity of gravitational wave detectors will be constrained by the standard quantum limit (SQL), which relates to the fundamental heisenberg uncertainty principle . Further improvements of detector sensitivity beyond this require us to manipulate the quantum coherence of light to our advantage. In this chapter, we will introduce how to analyse GW detectors quantum mechanically, and will describe several advanced configurations to surpass the SQL.
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 fundamental quantum limit, or the quantum Cramér-Rao bound, defines the sensitivity limit for quantum measurements. For linear measurement systems, such as gravitational-wave detectors, it is inversely proportional to the noise spectrum of the dynamical variable that couples to the measured signal. Defining a physically meaningful spectrum, however, requires that the system is stable and a steady state exists. We relax such a stability requirement and prove that the fundamental quantum limit can be derived simply by considering the open-loop dynamics in the Fourier domain.
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
Interferometric gravitational wave detectors (such as advanced LIGO) employ high-power solid-state lasers to maximize their detection sensitivity and hence their reach into the universe. These sophisticated light sources are ultra-stabilized with regard to output power, emission frequency and beam geometry; this is crucial to obtain low detector noise. However, even when all laser noise is reduced as far as technically possible, unavoidable quantum noise of the laser still remains. This is a consequence of the Heisenberg Uncertainty Principle, the basis of quantum mechanics: in this case, it is fundamentally impossible to simultaneously reduce both the phase noise and the amplitude noise of a laser to arbitrarily low levels. This fact manifests in the detector noise budget as two distinct noise sources—photon shot noise and quantum radiation pressure noise—which together form a lower boundary for current-day gravitational wave detector sensitivities, the standard quantum limit of interferometry. To overcome this limit, various techniques are being proposed, among them different uses of non-classical light and alternative interferometer topologies. This article explains how quantum noise enters and manifests in an interferometric gravitational wave detector, and gives an overview of some of the schemes proposed to overcome this seemingly fundamental limitation, all aimed at the goal of higher gravitational wave event detection rates. This article is part of a discussion meeting issue ‘The promises of gravitational-wave astronomy’.
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.