Gravitational Wave Detection by Interferometry (Ground and Space)

Simultaneous measurement of displacement, pitch, and yaw angles of a cavity output mirror based on phase measuring deflectometry

Accurate and high dynamic range measurement of the three attitude variations (i.e., displacement, pitch, yaw angles) has been widely researched based on various approaches to meet different application requirements. However, none of the existing methods can detect these three attitude variations at the same time. This paper proposes a method based on a classical phase measuring deflectometry (PMD) system and a double iteration algorithm to simultaneously measure the three variations of the output mirror in a laser resonator. The relationship between the attitude variations and the lateral displacement parameters (LDP) of the imaged structural fringes is derived in the PMD system. Through the established relationship, the attitude variations could be calculated once the LDP are detected. Furthermore, a two-step measuring scheme combining the four-step shifting phase and the color-coded fringe is proposed to effectively detect the LDP. Finally, an experiment is conducted to verify the feasibility of the proposed method.

Flat mirror tilt and piston measurement based on structured light reflection

This paper presents a simple method for flat mirror tilt and piston measurement. The method only needs an LCD screen and a CCD camera. LCD screen displays structured light pattern, and camera takes the pattern's virtual image (VI) reflected by the mirror. Pose relationship between camera coordinate system and VI coordinate system can be calculated by camera calibration. Through coordinate transition, the relative tilt and piston of the mirror can be obtained. This method is simple in both structure and principle, and experiments prove that it can measure the flat mirror tilt for about 1″ accuracy and piston for less than 1um accuracy. And under the guidance of our method, a mirror can be adjusted to a specified pose.

Stabilized high-power laser system for the gravitational wave detector advanced LIGO

An ultra-stable, high-power cw Nd:YAG laser system, developed for the ground-based gravitational wave detector Advanced LIGO (Laser Interferometer Gravitational-Wave Observatory), was comprehensively characterized. Laser power, frequency, beam pointing and beam quality were simultaneously stabilized using different active and passive schemes. The output beam, the performance of the stabilization, and the cross-coupling between different stabilization feedback control loops were characterized and found to fulfill most design requirements. The employed stabilization schemes and the achieved performance are of relevance to many high-precision optical experiments.

Apparatus for dimensional characterization of fused silica fibers for the suspensions of advanced gravitational wave detectors

Detection of gravitational waves from astrophysical sources remains one of the most challenging problems faced by experimental physicists. A significant limit to the sensitivity of future long-baseline interferometric gravitational wave detectors is thermal displacement noise of the test mass mirrors and their suspensions. Suspension thermal noise results from mechanical dissipation in the fused silica suspension fibers suspending the test mass mirrors and is therefore an important noise source at operating frequencies between ∼10 and 30 Hz. This dissipation occurs due to a combination of thermoelastic damping, surface and bulk losses. Its effects can be reduced by optimizing the thermoelastic and surface loss, and these parameters are a function of the cross sectional dimensions of the fiber along its length. This paper presents a new apparatus capable of high resolution measurements of the cross sectional dimensions of suspension fibers of both rectangular and circular cross section, suitable for use in advanced detector mirror suspensions.

Cryogenic resonant acoustic spectroscopy of bulk materials (CRA spectroscopy)

The capability to measure Q factors at cryogenic temperatures enhances the ability to study relaxation processes in solids. Here we present a high-precision cryogenic setup with the ability to measure Q factors of at least 10(9). This level of sensitivity offers new potential for analyzing relaxation processes in solids and for correlating mode shape and relaxation strength. Our improved method of mechanical spectroscopy, cryogenic resonant acoustic spectroscopy of bulk materials, is verified by identifying relaxation processes in low-loss quartz crystals. For the first time, we observe additional damping peaks. The mechanical Q factors of different modes of cylindrical crystalline quartz substrates were measured from 300 down to 6 K. Resonant modes with frequencies between 10 and 325 kHz were excited without contact to the substrates and the ring down of the amplitudes was recorded using an interferometric vibration readout.

Analytic Black Hole Perturbation Approach to Gravitational Radiation

We review the analytic methods used to perform the post-Newtonian expansion of gravitational waves induced by a particle orbiting a massive, compact body, based on black hole perturbation theory. There exist two different methods of performing the post-Newtonian expansion. Both are based on the Teukolsky equation. In one method, the Teukolsky equation is transformed into a Regge-Wheeler type equation that reduces to the standard Klein Gordon equation in the flat-space limit, while in the other method (which was introduced by Mano, Suzuki, and Takasugi relatively recently, the Teukolsky equation is used directly in its original form. The former's advantage is that it is intuitively easy to understand how various curved space effects come into play. However, it becomes increasingly complicated when one goes to higher and higher post-Newtonian orders. In contrast, the latter's advantage is that a systematic calculation to higher post-Newtonian orders can be implemented relatively easily, but otherwise, it is so mathematical that it is hard to understand the interplay of higher order terms. In this paper, we review both methods so that their pros and cons may be seen clearly. We also review some results of calculations of gravitational radiation emitted by a particle orbiting a black hole.

Towards quantum superpositions of a mirror

We propose an experiment for creating quantum superposition states involving of the order of 10(14) atoms via the interaction of a single photon with a tiny mirror. This mirror, mounted on a high-quality mechanical oscillator, is part of a high-finesse optical cavity which forms one arm of a Michelson interferometer. By observing the interference of the photon only, one can study the creation and decoherence of superpositions involving the mirror. A detailed analysis of the requirements shows that the experiment is within reach using a combination of state-of-the-art technologies.

The Cosmological Constant

This is a review of the physics and cosmology of the cosmological constant. Focusing on recent developments, I present a pedagogical overview of cosmology in the presence of a cosmological constant, observational constraints on its magnitude, and the physics of a small (and potentially nonzero) vacuum energy.

Initial Data for Numerical Relativity

Initial data are the starting point for any numerical simulation. In the case of numerical relativity, Einstein's equations constrain our choices of these initial data. We will examine several of the formalisms used for specifying Cauchy initial data in the 3 + 1 decomposition of Einstein's equations. We will then explore how these formalisms have been used in constructing initial data for spacetimes containing black holes and neutron stars. In the topics discussed, emphasis is placed on those issues that are important for obtaining astrophysically realistic initial data for compact binary coalescence.