Thermal noise of folding mirrors

Current gravitational wave detectors rely on the use of Michelson interferometers. One crucial limitation of their sensitivity is the thermal noise of their optical components. Thus, for example fluctuational deformations of the mirror surface are probed by a laser beam being reflected from the mirrors at normal incidence. Thermal noise models are well evolved for that case but mainly restricted to single reflections. In this work we present the effect of two consecutive reflections under a non-normal incidence onto mirror thermal noise. This situation is inherent to detectors using a geometrical folding scheme such as GEO\,600. We revise in detail the conventional direct noise analysis scheme to the situation of non-normal incidence allowing for a modified weighting funtion of mirror fluctuations. An application of these results to the GEO\,600 folding mirror for Brownian, thermoelastic and thermorefractive noise yields an increase of displacement noise amplitude by 20\% for most noise processes. The amplitude of thermoelastic substrate noise is increased by a factor 4 due to the modified weighting function. Thus the consideration of the correct weighting scheme can drastically alter the noise predictions and demands special care in any thermal noise design process

Cryogenic and room temperature strength of sapphire jointed by hydroxide-catalysis bonding

Hydroxide-catalysis bonding is a precision technique used for jointing components in opto-mechanical systems and has been implemented in the construction of quasi-monolithic silica suspensions in gravitational wave detectors. Future detectors are likely to operate at cryogenic temperatures which will lead to a change in test mass and suspension material. One candidate material is mono-crystalline sapphire. Here results are presented showing the influence of various bonding solutions on the strength of the hydroxide-catalysis bonds formed between sapphire samples, measured both at room temperature and at 77 K, and it is demonstrated that sodium silicate solution is the most promising in terms of strength, producing bonds with a mean strength of 63 MPa. In addition the results show that the strengths of bonds were undiminished when tested at cryogenic temperatures

Subtraction of test mass angular noise in the LISA Technology Package interferometer

We present recent sensitivity measurements of the LISA Technology Package interferometer with articulated mirrors as test masses, actuated by piezo-electric transducers. The required longitudinal displacement resolution of 9 pm/sqrt[Hz] above 3 mHz has been demonstrated with an angular noise that corresponds to the expected in on-orbit operation. The excess noise contribution of this test mass jitter onto the sensitive displacement readout was completely subtracted by fitting the angular interferometric data streams to the longitudinal displacement measurement. Thus, this cross-coupling constitutes no limitation to the required performance of the LISA Technology Package interferometry.Comment: Applied Physics B - Lasers and Optics (2008

Renormalized perturbation theory for Fermi systems: Fermi surface deformation and superconductivity in the two-dimensional Hubbard model

Divergencies appearing in perturbation expansions of interacting many-body systems can often be removed by expanding around a suitably chosen renormalized (instead of the non-interacting) Hamiltonian. We describe such a renormalized perturbation expansion for interacting Fermi systems, which treats Fermi surface shifts and superconductivity with an arbitrary gap function via additive counterterms. The expansion is formulated explicitly for the Hubbard model to second order in the interaction. Numerical soutions of the self-consistency condition determining the Fermi surface and the gap function are calculated for the two-dimensional case. For the repulsive Hubbard model close to half-filling we find a superconducting state with d-wave symmetry, as expected. For Fermi levels close to the van Hove singularity a Pomeranchuk instability leads to Fermi surfaces with broken square lattice symmetry, whose topology can be closed or open. For the attractive Hubbard model the second order calculation yeilds s-wave superconductivity with a weakly momentum dependent gap, whose size is reduced compared to the mean-field result.Comment: 18 pages incl. 6 figure

Status of the GEO600 gravitational wave detector

The GEO600 laser interferometric gravitational wave detector is approaching the end of its commissioning phase which started in 1995.During a test run in January 2002 the detector was operated for 15 days in a power-recycled michelson configuration. The detector and environmental data which were acquired during this test run were used to test the data analysis code. This paper describes the subsystems of GEO600, the status of the detector by August 2002 and the plans towards the first science run

Generalized Courant-Snyder Theory for Charged-Particle Dynamics in General Focusing Lattices

The Courant-Snyder (CS) theory for one degree of freedom is generalized to the case of coupled transverse dynamics in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D sympletic rotation. The envelope equation, the transfer matrix, and the CS invariant of the original CS theory all have their counterparts, with remarkably similar expressions, in the generalized theory.open7

Modulated differential wavefront sensing: alignment scheme for beams with large higher order mode content

Modulated differential wavefront sensing (MDWS) is an alignment control scheme in the regime of beams with strong higher order transversal modes (HOMs). It is based on the differential wavefront sensing (DWS) technique. MDWS represents a significant upgrade over conventional techniques used in the presence of high HOM content as it allows for higher control bandwidths while eliminating the need of auxiliary alignment modulations, that otherwise cause loss of applied squeezing. The output port of gravitational wave (GW) interferometers (IFO) is one such place where a lot of HOMs are present. These are filtered out by a cavity called the output mode cleaner (OMC), whose alignment gets challenging due to the presence of HOMs. In this paper, we present the first demonstration of the MDWS scheme for aligning the fundamental mode from the IFO to the OMC at the gravitational wave detector-GEO 600

The next detectors for gravitational wave astronomy

This paper focuses on the next detectors for gravitational wave astronomy which will be required after the current ground based detectors have completed their initial observations, and probably achieved the first direct detection of gravitational waves. The next detectors will need to have greater sensitivity, while also enabling the world array of detectors to have improved angular resolution to allow localisation of signal sources. Sect. 1 of this paper begins by reviewing proposals for the next ground based detectors, and presents an analysis of the sensitivity of an 8 km armlength detector, which is proposed as a safe and cost-effective means to attain a 4-fold improvement in sensitivity. The scientific benefits of creating a pair of such detectors in China and Australia is emphasised. Sect. 2 of this paper discusses the high performance suspension systems for test masses that will be an essential component for future detectors, while sect. 3 discusses solutions to the problem of Newtonian noise which arise from fluctuations in gravity gradient forces acting on test masses. Such gravitational perturbations cannot be shielded, and set limits to low frequency sensitivity unless measured and suppressed. Sects. 4 and 5 address critical operational technologies that will be ongoing issues in future detectors. Sect. 4 addresses the design of thermal compensation systems needed in all high optical power interferometers operating at room temperature. Parametric instability control is addressed in sect. 5. Only recently proven to occur in Advanced LIGO, parametric instability phenomenon brings both risks and opportunities for future detectors. The path to future enhancements of detectors will come from quantum measurement technologies. Sect. 6 focuses on the use of optomechanical devices for obtaining enhanced sensitivity, while sect. 7 reviews a range of quantum measurement options

Compact Binary Coalescences in the Band of Ground-based Gravitational-Wave Detectors

As the ground-based gravitational-wave telescopes LIGO, Virgo, and GEO 600 approach the era of first detections, we review the current knowledge of the coalescence rates and the mass and spin distributions of merging neutron-star and black-hole binaries. We emphasize the bi-directional connection between gravitational-wave astronomy and conventional astrophysics. Astrophysical input will make possible informed decisions about optimal detector configurations and search techniques. Meanwhile, rate upper limits, detected merger rates, and the distribution of masses and spins measured by gravitational-wave searches will constrain astrophysical parameters through comparisons with astrophysical models. Future developments necessary to the success of gravitational-wave astronomy are discussed.Comment: Replaced with version accepted by CQG