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Journal of Physics Conference Series

Improving the sensitivity of advanced gravitational-wave detectors using discrete sampling variation measurement technique

S. L. Danilishin

Published May 1, 2007• 1 citation
Publisher

Abstract

We propose new measurement concept that can be implemented in the third generation of gravitational-wave (GW) detectors: the discrete sampling variation measurement (DSVM). We demonstrate that this method allows to overcome the standard quantum limit (SQL) for free body and improve the sensitivity of interferometric gravitational wave detectors in wide frequency band. DSVM technique is based on well known method of quantum variation measurement that suggests to modulate in the optimal way the local oscillator phase in homodyne readout scheme of interferometric detector in order to measure such quadrature of the output light wave that has minimal uncertainty at the moment and therefore can be measured with precision, higher than SQL. The main disadvantage of variation measurement is the necessity to know a priori the form of detected signal in order to choose optimally the modulation function. It can be overcome if one modulates the local oscillator phase periodically with period less than sampling period required by Nyquist-Kotel'nikov-Shannon sampling theorem, and then fllters the output data using optimally chosen fllter functions.

DOI
10.1088/1742-6596/66/1/012059

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We propose new measurement concept that can be implemented in the third generation of gravitational-wave (GW) detectors: the discrete sampling variation measurement (DSVM). We demonstrate that this method allows to overcome the standard quantum limit (SQL) for free body and improve the sensitivity of interferometric gravitational wave detectors in wide frequency band. DSVM technique is based on well known method of quantum variation measurement that suggests to modulate in the optimal way the local oscillator phase in homodyne readout scheme of interferometric detector in order to measure such quadrature of the output light wave that has minimal uncertainty at the moment and therefore can be measured with precision, higher than SQL. The main disadvantage of variation measurement is the necessity to know a priori the form of detected signal in order to choose optimally the modulation function. It can be overcome if one modulates the local oscillator phase periodically with period less than sampling period required by Nyquist-Kotel'nikov-Shannon sampling theorem, and then fllters the output data using optimally chosen fllter functions.
We propose new gravitational wave detector design and new method of measurement that is based on principle of quantum non-demolition (QND) measurement. New design implies the so called "intracavity" measurement of the optical field parameters inside the cavity of interferometer without disturbing light quantum state. It is shown that using a technique called discrete sampling variation measurement (DSVM) in a local meter it is possible to overcome the standard quantum limit by an arbitrary amount limited only by the amount of optical energy circulating in the cavity of local meter and optical losses in the local meter mirrors. This technique being implemented will also be a demonstration of QND measurement and therefore can be used to demonstrate the detector moveable mirrors quantum behaviour.
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The intracavity topologies of laser gravitational-wave detectors proposed several years ago are the promising way to obtain sensitivity of these devices significantly better than the Standard Quantum Limit (SQL). In essence, the intracavity detector is a two-stage device where the end mirrors displacement created by the gravitational wave is transferred to the displacement of an additional local mirror by means of the optical rigidity. The local mirror positions have to be monitored by an additional local meter. It is evident that the local meter precision defines the sensitivity of the detector. To overcome the SQL, the quantum variational measurement can be used in the local meter. In this method a frequency-dependent correlation between the meter backaction noise and measurement noise is introduced, which allows us to eliminate the backaction noise component from the meter output signal. This correlation is created by means of an additional filter cavity. In this article the sensitivity limitations of this scheme imposed by the optical losses both in the local meter itself and in the filter cavity are estimated. It is shown that the main sensitivity limitation stems from the filter cavity losses. In order to overcome it, it is necessary to increase the filter cavity length. In a preliminary prototype experiment, an approximate 10 m long filter cavity can be used to obtain sensitivity approximately 2--3 times better than the SQL. For future Quantum Non-Demolition (QND) gravitational-wave detectors with sensitivity about 10 times better than the SQL, the filter cavity length should be within kilometer range.
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.
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
Gravitational waves manifest as a time varying straining of space: they arise from the accelerating motions of large bodies of mass and propagate across the universe at the speed of light as ripples in the fabric of space-time, a fleetingly weak effect so far eluding direct detection. The detection of gravitation waves is expected to yield a rich vein to observational astronomy, complementing existing electromagnetic surveys and revealing a hitherto unexplored range of phenomena. First generation interferometric gravitational wave detectors, notably Enhanced LIGO, achieved strain sensitivities of one part in ten to power twenty-one per square-root-Hertz at 100 Hz with an expected detection rate of 2-3 events per year. Commissioning of a new generation of Advanced LIGO interferometric detectors has concluded recently with a resultant ten-fold sensitivity improvement. Overall their potential event detection space has increased by a factor of 1000. The quantum nature of light within these detectors now limits their sensitivity over most of their frequency range. This quantum noise limit is driven by the vacuum quadrature fluctuations propagated through their open detection ports and represents a fundamental noise floor to their strain sensitivity. This thesis addresses two distinct approaches to quantum noise improvement for future upgrades to advanced detectors. The first addresses the issue of quantum noise by adopting a quantum non-demolition approach to detector readout variables, the so-called `speed-meter’ design. Such a modified instrument samples test mass momentum, a quantity for which time separated measurements commute and are therefore not bound by Heisenberg-like limits. A novel polarisation-folded sloshing cavity type speed-meter is proposed where readout fields are stored and delayed in the orthogonal polarisation of the interferometer’s arms cavities. Here frequency dependence is selected to cancel position like measurements so that only test mass momentum information remains. A quantum noise propagation model is developed and a sensitivity performance is demonstrated that beats the standard quantum limit below 100 Hz over a broad range of frequencies. A second approach to achieve quantum noise enhancement in advanced detectors involves injection of quadrature-squeezed states in the place of vacuum. This dissertation details the development of a prototype squeezed vacuum source suitable to the demanding enhancement requirements for an Advanced LIGO squeezing installation. The construction of a doubly resonant, bow-tie cavity source is presented. This employs a novel monolithic all-glass cavity construction and is vacuum compatible. This design demonstrates the viability of building a cavity using optical contacting as a construction technique for attaching mounting prisms to highly polished fused-silica breadboards. Such a design can be expected to have excellent length noise stability, provide low intrinsic phase noise and would be suitable to mount on seismic isolation stages within the LIGO vacuum envelope. Further, the travelling wave cavity design should provide excellent 50 dB intrinsic backscatter isolation. We demonstrate the first operation of such a complex non-linear device under vacuum, producing 8.6 dB of measured vacuum squeezing down to 10 Hz across the advanced LIGO ‘audio-band’ detection range.