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Register a new userQuantum Measurement Theory in Gravitational-Wave Detectors
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Added by
Stefan Danilishin L.
Publication date
2012
fields
Physics
and research's language is
English
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The fast progress in improving the sensitivity of the gravitational-wave (GW) detectors, we all have witnessed in the recent years, has propelled the scientific community to the point, when quantum behaviour 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 round the corner, and finding the 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 Standard Quantum Limit and the methods of its surmounting.
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The quantum nature of the electromagnetic field imposes a fundamental limit on the sensitivity of optical precision measurements such as spectroscopy, microscopy, and interferometry. The so-called quantum limit is set by the zero-point fluctuations of the electromagnetic field, which constrain the precision with which optical signals can be measured. In the world of precision measurement, laser-interferometric gravitational wave (GW) detectors are the most sensitive position meters ever operated, capable of measuring distance changes on the order of 10^-18 m RMS over kilometer separations caused by GWs from astronomical sources. The sensitivity of currently operational and future GW detectors is limited by quantum optical noise. Here we demonstrate a 44% improvement in displacement sensitivity of a prototype GW detector with suspended quasi-free mirrors at frequencies where the sensitivity is shot-noise-limited, by injection of a squeezed state of light. This demonstration is a critical step toward implementation of squeezing-enhancement in large-scale GW detectors.
Space-based gravitational wave detectors based on the Laser Interferometer Space Antenna (LISA) design operate by synthesizing one or more interferometers from fringe velocity measurements generated by changes in the light travel time between three spacecraft in a special set of drag-free heliocentric orbits. These orbits determine the inclination of the synthesized interferometer with respect to the ecliptic plane. Once these spacecraft are placed in their orbits, the orientation of the interferometers at any future time is fixed by Keplers Laws based on the initial orientation of the spacecraft constellation, which may be freely chosen. Over the course of a full solar orbit, the initial orientation determines a set of locations on the sky were the detector has greatest sensitivity to gravitational waves as well as a set of locations where nulls in the detector response fall. By artful choice of the initial orientation, we can choose to optimize or suppress the antennas sensitivity to sources whose location may be known in advance (e.g., the Galactic Center or globular clusters).
Earth-based gravitational-wave detectors will be limited by quantum noise in a large part of their spectrum. The most promising technique to achieve a broadband reduction of such noise is the injection of a frequency dependent squeezed vacuum state from the output port of the detector, whit the squeeze angle rotated by the reflection off a Fabry-Perot filter cavity. One of the most important parameters limiting the squeezing performance is represented by the optical losses of the filter cavity. We report here the operation of a 300 m filter cavity prototype installed at the National Astronomical Observatory of Japan (NAOJ). The cavity is designed to obtain a rotation of the squeeze angle below 100 Hz. After achieving the resonance of the cavity with a multi-wavelength technique, the round trip losses have been measured to be between 50 ppm and 90 ppm. This result demonstrates that with realistic assumption on the input squeeze factor and on the other optical losses, a quantum noise reduction of at least 4 dB in the frequency region dominated by radiation pressure can be achieved.
Long-baseline laser-interferometer gravitational-wave detectors are operating at a factor of 10 (in amplitude) above the standard quantum limit (SQL) within a broad frequency band. Such a low classical noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the new possibility of experimentally probing macroscopic quantum mechanics (MQM) - quantum mechanical behavior of objects in the realm of everyday experience - using gravitational-wave detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometers classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the classical noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum state preparation, and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses, and the performance of the planned Advanced LIGO interferometers in quantum-state preparation.
Future ground-based gravitational-wave detectors are slated to detect black hole and neutron star collisions from the entire stellar history of the universe. To achieve the designed detector sensitivities, frequency noise from the laser source must be reduced below the level achieved in current Advanced LIGO detectors. This paper reviews the laser frequency noise suppression scheme in Advanced LIGO, and quantifies the noise coupling to the gravitational-wave readout. The laser frequency noise incident on the current Advanced LIGO detectors is $8 times 10^{-5}~mathrm{Hz/sqrt{Hz}}$ at $1~mathrm{kHz}$. Future detectors will require even lower incident frequency noise levels to ensure this technical noise source does not limit sensitivity. The frequency noise requirement for a gravitational wave detector with arm lengths of $40~mathrm{km}$ is estimated to be $7 times 10^{-7}~mathrm{Hz/sqrt{Hz}}$. To reach this goal a new frequency noise suppression scheme is proposed, utilizing two input mode cleaner cavities, and the limits of this scheme are explored. Using this scheme the frequency noise requirement is met, even in pessimistic noise coupling scenarios.
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