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

The noise in gravitational-wave detectors and other classical-force measurements is not influenced by test-mass quantization

It is shown that photon shot noise and radiation-pressure back-action noise are the sole forms of quantum noise in interferometric gravitational wave detectors that operate near or below the standard quantum limit, if one filters the interferometer output appropriately. No additional noise arises from the test masses' initial quantum state or from reduction of the test-mass state due to measurement of the interferometer output or from the uncertainty principle associated with the test-mass state. Two features of interferometers are central to these conclusions: (i) The interferometer output (the photon number flux N(t) entering the final photodetector) commutes with itself at different times in the Heisenberg Picture, [N(t), N(t')] = 0, and thus can be regarded as classical. (ii) This number flux is linear in the test-mass initial position and momentum operators x_o and p_o, and those operators influence the measured photon flux N(t) in manners that can easily be removed by filtering -- e.g., in most interferometers, by discarding data near the test masses' 1 Hz swinging freqency. The test-mass operators x_o and p_o contained in the unfiltered output N(t) make a nonzero contribution to the commutator [N(t), N(t')]. That contribution is cancelled by a nonzero commutation of the photon shot noise and radiation-pressure noise, which also are contained in N(t). This cancellation of commutators is responsible for the fact that it is possible to derive an interferometer's standard quantum limit from test-mass considerations, and independently from photon-noise considerations. These conclusions are true for a far wider class of measurements than just gravitational-wave interferometers. To elucidate them, this paper presents a series of idealized thought experiments that are free from the complexities of real measuring systems.Comment: Submitted to Physical Review D; Revtex, no figures, prints to 14 pages. Second Revision 1 December 2002: minor rewording for clarity, especially in Sec. II.B.3; new footnote 3 and passages before Eq. (2.35) and at end of Sec. III.B.

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

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

An analysis of a QND speed-meter interferometer

In the quest to develop viable designs for third-generation optical interferometric gravitational-wave detectors (e.g. LIGO-III and EURO), one strategy is to monitor the relative momentum or speed of the test-mass mirrors, rather than monitoring their relative position. This paper describes and analyzes the most straightforward design for a {\it speed meter interferometer} that accomplishes this -- a design (due to Braginsky, Gorodetsky, Khalili and Thorne) that is analogous to a microwave-cavity speed meter conceived by Braginsky and Khalili. A mathematical mapping between the microwave speed meter and the optical interferometric speed meter is developed and is used to show (in accord with the speed being a Quantum Nondemolition [QND] observable) that {\it in principle} the interferometric speed meter can beat the gravitational-wave standard quantum limit (SQL) by an arbitrarily large amount, over an arbitrarily wide range of frequencies, and can do so without the use of squeezed vacuum or any auxiliary filter cavities at the interferometer's input or output. However, {\it in practice}, to reach or beat the SQL, this specific speed meter requires exorbitantly high input light power. The physical reason for this is explored, along with other issues such as constraints on performance due to optical dissipation. This analysis forms a foundation for ongoing attempts to develop a more practical variant of an interferometric speed meter and to combine the speed meter concept with other ideas to yield a promising LIGO-III/EURO interferometer design that entails low laser power.Comment: 12 pages, 5 figures; corrected formula and some values describing power requirement

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

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

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

Sensitivity limitations in optical speed meter topology of gravitational-wave antennae

The possible design of QND gravitational-wave detector based on speed meter principle is considered with respect to optical losses. The detailed analysis of speed meter interferometer is performed and the ultimate sensitivity that can be achieved is calculated. It is shown that unlike the position meter signal-recycling can hardly be implemented in speed meter topology to replace the arm cavities as it is done in signal-recycled detectors, such as GEO 600. It is also shown that speed meter can beat the Standard Quantum Limit (SQL) by the factor of $\sim 3$ in relatively wide frequency band, and by the factor of $\sim 10$ in narrow band. For wide band detection speed meter requires quite reasonable amount of circulating power $\sim 1$ MW. The advantage of the considered scheme is that it can be implemented with minimal changes in the current optical layout of LIGO interferometer.Comment: 20 pages, 12 figure

QND measurements for future gravitational-wave detectors

Second-generation interferometric gravitational-wave detectors will be operating at the Standard Quantum Limit, a sensitivity limitation set by the trade off between measurement accuracy and quantum back action, which is governed by the Heisenberg Uncertainty Principle. We review several schemes that allows the quantum noise of interferometers to surpass the Standard Quantum Limit significantly over a broad frequency band. Such schemes may be an important component of the design of third-generation detectors.Comment: 22 pages, 6 figures, 1 table; In version 2, more tutorial information on quantum noise in GW interferometer and several new items into Reference list were adde