Interferometric Gravitational Wave Research Articles

Quantum Measurement Theory in 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.

Wavefront aberration compensation with a thermally deformable mirror

First generation gravitational wave interferometer performances were affected by thermal effects and non-optimal coupling of the light into several optical cavities. Slow thermally induced beam-wavefront distortions can be compensated using deformable mirrors driven by thermal actuators. We propose a new device, where the set of heating actuators is placed in direct contact with the reflecting surface of the mirror, enabling an efficient control of its refractive index and shape. This system is particularly useful for an in-vacuum environment, where low noise remote actuation is required. It is therefore well suited for Advanced Gravitational Wave Detectors where many optical cavities will require active optimal coupling for optimizing their quantum noise sensitivity without producing motion of the rest of the optics, which could interrupt the control acquisition sequence. In this paper, a prototype for such a thermally deformable mirror is described, and first results are presented. The proposed system promises to perform with good stability and efficiency.

The effect of parametric oscillatory instability in a Fabry-Perot cavity of the Einstein telescope

The nonlinear effect of a parametric oscillatory instability in a Fabry-Perot cavity of the Einstein Telescope is investigated. Unstable combinations of elastic and optical modes are calculated for two possible configurations of the third-generation gravitational-wave detector. The results are compared with those for the LIGO gravitational-wave interferometer.

Angular and frequency response of the gravitational wave interferometers in the metric theories of gravity

We analyze detector responses of gravitational wave detectors for gravitational waves with arbitrary polarizations predicted in the metric theories of gravity. We present the general formulas for the frequency responses valid in various interferometric arrangements including Michelson, Delay-Line and Fabry-Perot detectors. We analyze the angular and frequency behavior and the sensitivity patterns of the responses for each polarization mode.

Active noise cancellation in a suspended interferometer

We demonstrate feed-forward vibration isolation on a suspended Fabry-Perot interferometer using Wiener filtering and a variant of the common least mean square adaptive filter algorithm. We compare the experimental results with theoretical estimates of the cancellation efficiency. Using data from the recent Laser Interferometer Gravitational Wave Observatory (LIGO) Science Run, we also estimate the impact of this technique on full scale gravitational wave interferometers. In the future, we expect to use this technique also to remove acoustic, magnetic, and gravitational noise perturbations from the LIGO interferometers. This noise cancellation technique is simple enough to implement in standard laboratory environments and can be used to improve signal-to-noise ratio for a variety of high precision experiments.

WHAT IS THE MOST PROMISING ELECTROMAGNETIC COUNTERPART OF A NEUTRON STAR BINARY MERGER?

The final inspiral of double neutron star and neutron star-black hole binaries are likely to be detected by advanced networks of ground-based gravitational wave (GW) interferometers. Maximizing the science returns from such a discovery will require the identification and localization of an electromagnetic (EM) counterpart. Here we critically evaluate and compare several possible counterparts, including short-duration gamma-ray bursts (SGRBs), "orphan" optical and radio afterglows, and ~day-long optical transients powered by the radioactive decay of heavy nuclei synthesized in the merger ejecta ("kilonovae"). We assess the promise of each counterpart in terms of four "Cardinal Virtues": detectability, high fraction, identifiability, and positional accuracy. Taking into account the search strategy for typical error regions of ~10s degs sq., we conclude that SGRBs are the most useful to confirm the cosmic origin of a few GW events, and to test the association with NS mergers. However, for the more ambitious goal of localizing and obtaining redshifts for a large sample of GW events, kilonovae are instead preferred. Off-axis optical afterglows will be detectable for at most ~10% of all events, while radio afterglows are promising only for the unique combination of energetic relativistic ejecta in a high density medium, and even then will require hundreds of hours of EVLA time per event. Our main recommendations are:(i) an all-sky gamma-ray satellite is essential for temporal coincidence detections, and for GW searches of gamma-ray triggered events; (ii) LSST should adopt a 1-day cadence follow-up strategy, ideally with ~0.5 hr per pointing to cover GW error regions (the standard 4-day cadence and depth will severely limit the probability of a unique identification); and (iii) radio searches should only focus on the relativistic case, which requires observations for a few months.

Arm-length stabilisation for interferometric gravitational-wave detectors using frequency-doubled auxiliary lasers

Residual motion of the arm cavity mirrors is expected to prove one of the principal impediments to systematic lock acquisition in advanced gravitational-wave interferometers. We present a technique which overcomes this problem by employing auxiliary lasers at twice the fundamental measurement frequency to pre-stabilise the arm cavities' lengths. Applying this approach, we reduce the apparent length noise of a 1.3 m long, independently suspended Fabry-Perot cavity to 30 pm rms and successfully transfer longitudinal control of the system from the auxiliary laser to the measurement laser.

Squeezed light at 1550 nm with a quantum noise reduction of 123 dB

Continuous-wave squeezed states of light at the wavelength of 1550 nm have recently been demonstrated, but so far the obtained factors of noise suppression still lag behind today's best squeezing values demonstrated at 1064 nm. Here we report on the realization of a half-monolithic nonlinear resonator based on periodically-poled potassium titanyl phosphate which enabled the direct detection of up to 12.3 dB of squeezing at 5 MHz. Squeezing was observed down to a frequency of 2 kHz which is well within the detection band of gravitational wave interferometers. Our results suggest that a long-term stable 1550 nm squeezed light source can be realized with strong squeezing covering the entire detection band of a 3rd generation gravitational-wave detector such as the Einstein Telescope.

Backscatter tolerant squeezed light source for advanced gravitational-wave detectors

We report on the performance of a dual-wavelength resonant, traveling-wave optical parametric oscillator to generate squeezed light for application in advanced gravitational-wave interferometers. Shot noise suppression of 8.6±0.8 dB was measured across the detection band of interest to Advanced LIGO, and controlled squeezing measured over 5900 s. Our results also demonstrate that the traveling-wave design has excellent intracavity backscattered light suppression of 47 dB and incident backscattered light suppression of 41 dB, which is a crucial design issue for application in advanced interferometers.

First results from the ‘Violin-Mode’ tests on an advanced LIGO suspension at MIT

This paper describes the first results from ‘Violin-Mode’ measurements made on the four suspension fibres of a fully suspended 40 kg test mass. These measurements were made at the LIGO lab, Gravitational Wave Observatory test facility, at MIT. Here, an aluminium-alloy (dummy) test mass, simulating an advanced LIGO (Laser Interferometer Gravitational Wave Observatory) test mass/mirror, had been suspended in air from a test suspension by four fused-silica suspension fibres, each measuring 400 µm in diameter × 600 mm long. Violin-Mode measurements were made on these highly tensioned fibres by retrofitting a prototype system of four novel shadow sensors to the test suspension, one per fibre, these sensors having, collectively, a displacement sensitivity of (6.9 ± 1.3) × 10−11 m (rms) Hz−1/2, at 500 Hz, over a measuring span of ±0.1 mm. Violin-Mode fundamental resonances were detected in all four fibres: with frequencies ∼ 485 Hz when the test mass was supported lightly from below, and at ∼500 Hz when it was fully suspended. In the latter case the Violin-Mode detection took place whilst the test mass, together with its suspension fibres, was undergoing relatively large-amplitude ‘pendulum-mode’ motion, at ∼0.6 Hz. This motion was measured to have a peak–peak amplitude at one of the suspension fibres of up to ∼140 µm (35 µm, rms)—the shadow sensors each having subsidiary outputs for monitoring such low-frequency, large amplitude, motion. Under fully suspended conditions, a calibrated Violin-Mode ‘free-oscillation’ amplitude of 430 ± 20 picometres, rms, was measured at 500.875 Hz, in the same suspension fibre which was found to be undergoing, simultaneously, the ∼140 µm peak–peak motion. Over the bandwidth monitored (dc to 3.2 kHz), Violin-Mode harmonics up to the sixth were recorded in an evoked response. It was concluded that the prototype system had demonstrated amply its practical viability as a detector of Violin-Mode resonances in the test-mass suspension fibres of gravitational wave interferometers, such as those of advanced LIGO.

Detection of slow geophysical perturbations in gravitational-wave interferometers

Techniques for measuring quasistatic geophysical perturbations with gravitational-wave laser interferometers are studied. The transfer function for this kind of apparatus with destructive interference (the dark spot regime) is calculated taking the natural asymmetry of the lengths of the arms of the Fabry–Perot optical cavities into account. Equations are derived for estimating the modulation in the power of the output signal at the photon circulation frequency in the arms of the interferometer owing to geophysical perturbations. These estimates are compared with observations on the LIGO interferometer.

A state observer for the Virgo inverted pendulum

We report an application of Kalman filtering to the inverted pendulum (IP) of the Virgo gravitational wave interferometer. Using subspace method system identification techniques, we calculated a linear mechanical model of Virgo IP from experimental transfer functions. We then developed a Kalman filter, based on the obtained state space representation, that estimates from open loop time domain data, the state variables of the system. This allows the observation (and eventually control) of every resonance mode of the IP mechanical structure independently.

Binary Systems As Gravitational Wave Sources

AbstractBinary systems with compact components and some newly discovered systems with relatively short orbital periods are studied as gravitational-wave sources. The gravitational wave amplitudes of these systems have been compared with the limit of gravitational wave interferometers (e.g. LISA, LIGO, and VIRGO).

Towards the experimental demonstration of quantum radiation pressure noise

Abstract Quantum radiation pressure noise has never been experimentally demonstrated, though it has been predicted for more than thirty years. It is, however, expected to limit the low-frequency sensitivity of second generation gravitational-wave interferometers. We have demonstrated classical radiation-pressure-induced correlations between two optical beams sent into the same high-finesse cavity with a moving mirror. Our two-beam scheme can be used to retrieve quantum noise embedded in an overwhelming classical noise, and has applications both in high-sensitivity measurements and in quantum optics.

Testing the intrinsic noise of a coil–magnet actuator for cryogenic gravitational wave interferometers

The third generation gravitational wave interferometers that will operate underground and at cryogenic temperatures will need a complex and sophisticated control system to satisfy the requirements on the alignment and position of its optics and keep the detector at its working point. The force actuators of the control systems of the present interferometers are for the most part coil–magnet actuators. To check the possibility of using these actuators also at low temperature we have tested the magnetization and the magnetization noise of an SmCo magnet at 4.2 K. The magnetization loss, measured with a fluxgate magnetometer, is 7%. The magnetization noise has been measured with a superconducting quantum interference device magnetometer. The application of dc and ac (0.1 Hz) magnetic fields of an amplitude comparable to that needed to produce on the magnet a force large enough for the control system does not change the measured noise. The equivalent maximum force noise produced by the actuator as a result of the magnetization noise of the magnet has been evaluated. Its effect on the sensitivity of a third generation interferometer (Einstein Telescope) is negligible with respect to the most relevant fundamental noise contributions.

A cryogenic payload for the 3rd generation of gravitational wave interferometers

Thermal noise is a limiting factor of interferometric gravitational wave detectors sensitivity in the low and intermediate frequency range. A concrete possibility for beating this limit, is represented by the development of a cryogenic last stage suspension to be integrated within a complex seismic isolation system. To this purpose a last stage payload prototype has been designed and built. It has been suspended within a dedicated cryostat with the same technique adopted for the VIRGO payload and making use of two thin wires in a cradle configuration to support a mirror made of silicon. The cooling strategy, the thermal behaviour and the system mechanical response have been deeply studied while a measurement characterization campaign has been performed both at room temperature and at cryogenic temperature. In this paper, the preliminary results obtained together with the first cooling down of the 300 kg overall mass payload at about 25 K, are reported. This study will play a driving role in the design of the third generation gravitational wave detector.

Toward a new generation of low-loss mirrors for the advanced gravitational waves interferometers

The new generation of advanced interferometer needs fused silica mirrors having better optical and mechanical properties. This Letter describes the way to reduce the ion beam sputtering coating absorption at 1064 nm and to improve the layer thickness uniformity in order to coat two large mirrors (diameter 35 cm) at the same time.

Long gravitational-wave transients and associated detection strategies for a network of terrestrial interferometers

Searches for gravitational waves (GWs) traditionally focus on persistent sources (e.g., pulsars or the stochastic background) or on transients sources (e.g., compact binary inspirals or core-collapse supernovae), which last for time scales of milliseconds to seconds. We explore the possibility of long GW transients with unknown waveforms lasting from many seconds to weeks. We propose a novel analysis technique to bridge the gap between short $\mathcal{O}(\mathrm{s})$ ``burst'' analyses and persistent stochastic analyses. Our technique utilizes frequency-time maps of GW strain cross power between two spatially separated terrestrial GW detectors. The application of our cross power statistic to searches for GW transients is framed as a pattern recognition problem, and we discuss several pattern-recognition techniques. We demonstrate these techniques by recovering simulated GW signals in simulated detector noise. We also recover environmental noise artifacts, thereby demonstrating a novel technique for the identification of such artifacts in GW interferometers. We compare the efficiency of this framework to other techniques such as matched filtering.

Note: Discharging fused silica test masses with ionized nitrogen

We have developed a technique for discharging fused silica test masses in a gravitational-wave interferometer with nitrogen ionized by an electron beam. The electrons are produced from a heated filament by thermionic emission in a low-pressure region to avoid contamination and burnout. Some electrons then pass through a small aperture and ionize nitrogen in a higher-pressure region, and this ionized gas is pumped across the test mass surface, neutralizing both polarities of charge. The discharge rate varies exponentially with charge density and filament current, quadratically with filament potential, and has an optimal working pressure of ∼8 mT. Adapting the technique to larger test mass chambers is also discussed.

The Seismic Superattenuators of the Virgo Gravitational Waves Interferometer

The Virgo experiment, located near Pisa, Italy, is a large laser Michelson interferometer aiming at the first direct detection of gravitational waves. The interferometer monitors the relative distance of its mirrors placed at the ends of two 3 km-long perpendicular arms. The goal is to measure spectral differential variations of the arm lengths of 10−18 m/Hz1/2 in the frequency range from 10 Hz to 10 kHz. Avoiding spurious motions of the optical components is therefore essential to detect gravitational waves. Since the ground motion is 9 orders of magnitude larger than the arm length variations induced by gravitational waves, the seismic noise is the dominant low frequency noise source for terrestrial gravitational wave interferometers. The seismic isolation is obtained suspending the mirrors by an 8-meter tall chain of cascaded mechanical filters, called “Superattenuator” (SA). The Superattenuator is a passive device acting as a low pass filter in all six degrees of freedom, capable of attenuating the ground motion by more than 10 orders of magnitude, starting from a few Hz. To further reduce the seismic disturbances, the filter chain is suspended from an actively stabilized platform that compensates for low frequency and large amplitude oscillations caused by the mechanical resonances of the chain. In this article we describe the Superattenuator together with its control system, and we report about its performance.