Analysis of Parametric Oscillatory Instability in Power Recycled LIGO Interferometer

We present the analysis of a nonlinear effect of parametric oscillatory instability in power recycled LIGO interferometer with the Fabry-Perot (FP) cavities in the arms. The basis for this effect is the excitation of the additional (Stokes) optical mode and the mirror elastic mode, when the optical energy stored in the main FP cavity main mode exceeds the certain threshold and the frequencies are related so that sum of frequencies of Stokes and elastic modes are approximately equal to frequencyof main mode. The presence of anti-Stokes modes (with frequency approximately equal to sum of frequencies of main and elastic modes) can depress parametric instability. However, it is very likely that the anti-Stokes modes will not compensate the parametric instability completely.Comment: 9 pages, 2 figures. submitted to Physics Letters

Stroboscopic Variation Measurement

A new procedure of the linear position measurement which allows to obtain sensitivity better than the Standard Quantum Limit and close to the Energetic Quantum Limit is proposed and analyzed in details. Proposed method is based on the principles of stroboscopic quantum measurement and variation quantum measurement and allows to avoid main disadvantages of both these procedures. This method can be considered as a good candidate for use as a local position meter in the ``intracavity'' topologies of the laser gravitational-wave antennae.Comment: 13 pages, 2 figures drawn in TeX and 2 figures in postscript, misprint correcte

The "optical lever" intracavity readout scheme for gravitational-wave antennae

An improved version of the ``optical bar'' intracavity readout scheme for gravitational-wave antennae is considered. We propose to call this scheme ``optical lever'' because it can provide significant gain in the signal displacement of the local mirror similar to the gain which can be obtained using ordinary mechanical lever with unequal arms. In this scheme displacement of the local mirror can be close to the signal displacement of the end mirrors of hypothetical gravitational-wave antenna with arm lengths equal to the half-wavelength of the gravitational wave.Comment: 10 pages, 3 figure

Quantum limits and symphotonic states in free-mass gravitational-wave antennae

Quantum mechanics sets severe limits on the sensitivity and required circulating energy in traditional free-mass gravitational-wave antennas. One possible way to avoid these restrictions is the use of intracavity QND measurements. We analyze a new QND observable, which possesses a number of features that make it a promising candidate for such measurements and propose a practical scheme for the realization of this measurement. In combination with an advanced coordinate meter, this scheme makes it possible to lower substantially the requirements on the circulating power.Comment: 21 pages, 2 figure

Corner reflectors and Quantum-Non-Demolition Measurements in gravitational wave antennae

We propose Fabry-Perot cavity with corner reflectors instead of spherical mirrors to reduce the contribution of thermoelastic noise in the coating which is relatively large for spherical mirrors and which prevents the sensitivity better than Standard Quantum Limit (SQL) from being achieved in laser gravitational wave antenna. We demonstrate that thermo-refractive noise in corner reflector (CR) is substantially smaller than SQL. We show that the distortion of main mode of cavity with CR caused by tilt and displacement of one reflector is smaller than for cavity with spherical mirrors. We also consider the distortion caused by small nonperpendicularity of corner facets and by optical inhomogeneity of fused silica which is proposed as a material for corner reflectors.Comment: 12 pages, LaTex, 7 figure

Frequency-dependent rigidity in large-scale interferometric gravitational-wave detectors

Electromagnetic rigidity which exists in large-scale optical resonators if pumping frequency is detuned from the eigenfrequency of resonator have sophisticated spectral dependence which allows to obtain sensitivity better than the Standard Quantum Limits both for the free test mass and the harmonic oscillator.Comment: 11 pages, 6 figures, corrected typo

Measurements of the optical mirror coating properties

The results of measurement of optical mirror coating are presented. These results indicate that Standard Quantum Limit of sensitivity can be reached in the second stage of LIGO project if it is limited by thermoelastic noise in the coating only.Comment: 5 page

Thermodynamical fluctuations in optical mirror coatings

Thermodynamical fluctuations of temperature in mirrors may produce surface fluctuations not only through thermal expansion in mirror body but also through thermal expansion in mirror coating. We analyze the last "surface" effect which can be larger than the first "volume" one due to larger thermal expansion coefficient of coating material and smaller effective volume. In particular, these fluctuations may be important in laser interferometric gravitational antennae.Comment: 12 pages, LaTex, 3 figure

Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae

Thermodynamical fluctuations of temperature in mirrors of gravitational wave antennae are transformed through thermal expansion coefficient into additional noise. This source of noise, which may also be interpreted as fluctuations due to thermoelastic damping, may not be neglected and leads to the necessity to reexamine the choice of materials for the mirrors. Additional source of noise are fluctuations of the mirrors' surfaces caused by optical power absorbed in dielectrical reflective layers.Comment: 20 pages, 2 figure

Dynamos with weakly convecting outer layers: implications for core-mantle boundary interaction

Convection in the Earth's core is driven much harder at the bottom than the top. This is partly because the adiabatic gradient steepens towards the top, partly because the spherical geometry means the area involved increases towards the top, and partly because compositional convection is driven by light material released at the lower boundary and remixed uniformly throughout the outer core, providing a volumetric sink of buoyancy. We have therefore investigated dynamo action of thermal convection in a Boussinesq fluid contained within a rotating spherical shell driven by a combination of bottom and internal heating or cooling. We first apply a homogeneous temperature on the outer boundary in order to explore the effects of heat sinks on dynamo action; we then impose an inhomogeneous temperature proportional to a single spherical harmonic Y2² in order to explore core-mantle interactions. With homogeneous boundary conditions and moderate Rayleigh numbers, a heat sink reduces the generated magnetic field appreciably; the magnetic Reynolds number remains high because the dominant toroidal component of flow is not reduced significantly. The dipolar structure of the field becomes more pronounced as found by other authors. Increasing the Rayleigh number yields a regime in which convection inside the tangent cylinder is strongly affected by the magnetic field. With inhomogeneous boundary conditions, a heat sink promotes boundary effects and locking of the magnetic field to boundary anomalies. We show that boundary locking is inhibited by advection of heat in the outer regions. With uniform heating, the boundary effects are only significant at low Rayleigh numbers, when dynamo action is only possible for artificially low magnetic diffusivity. With heat sinks, the boundary effects remain significant at higher Rayleigh numbers provided the convection remains weak or the fluid is stably stratified at the top. Dynamo action is driven by vigorous convection at depth while boundary thermal anomalies dominate in the upper regions. This is a likely regime for the Earth's core