Observing binary inspiral in gravitational radiation: One interferometer

We investigate the sensitivity of individual LIGO/VIRGO-like interferometers and the precision with which they can determine the characteristics of an inspiralling binary system. Since the two interferometers of the LIGO detector share nearly the same orientation, their joint sensitivity is similar to that of a single, more sensitive interferometer. We express our results for a single interferometer of both initial and advanced LIGO design, and also for the LIGO detector in the limit that its two interferometers share exactly the same orientation. We approximate the evolution of a binary system as driven exclusively by leading order quadrupole gravitational radiation. To assess the sensitivity, we calculate the rate at which sources are expected to be observed, the range to which they are observable, and the precision with which characteristic quantities describing the observed binary system can be determined. Assuming a conservative rate density for coalescing neutron star binary systems we expect that the advanced LIGO detector will observe approximately 69~yr${}^{-1}$ with an amplitude SNR greater than 8. Of these, approximately 7~yr${}^{-1}$ will be from binaries at distances greater than 950~Mpc. We explore the sensitivity of these results to a tunable parameter in the interferometer design (the recycling frequency). The optimum choice of the parameter is dependent on the goal of the observations, e.g., maximizing the rate of detections or maximizing the precision of measurement. We determine the optimum parameter values for these two cases.Comment: 40 pages (plus 7 figures), LaTeX/REVTEX3.0, NU-GR-

Squeezed Light for the Interferometric Detection of High Frequency Gravitational Waves

The quantum noise of the light field is a fundamental noise source in interferometric gravitational wave detectors. Injected squeezed light is capable of reducing the quantum noise contribution to the detector noise floor to values that surpass the so-called Standard-Quantum-Limit (SQL). In particular, squeezed light is useful for the detection of gravitational waves at high frequencies where interferometers are typically shot-noise limited, although the SQL might not be beaten in this case. We theoretically analyze the quantum noise of the signal-recycled laser interferometric gravitational-wave detector GEO600 with additional input and output optics, namely frequency-dependent squeezing of the vacuum state of light entering the dark port and frequency-dependent homodyne detection. We focus on the frequency range between 1 kHz and 10 kHz, where, although signal recycled, the detector is still shot-noise limited. It is found that the GEO600 detector with present design parameters will benefit from frequency dependent squeezed light. Assuming a squeezing strength of -6 dB in quantum noise variance, the interferometer will become thermal noise limited up to 4 kHz without further reduction of bandwidth. At higher frequencies the linear noise spectral density of GEO600 will still be dominated by shot-noise and improved by a factor of 10^{6dB/20dB}~2 according to the squeezing strength assumed. The interferometer might reach a strain sensitivity of 6x10^{-23} above 1 kHz (tunable) with a bandwidth of around 350 Hz. We propose a scheme to implement the desired frequency dependent squeezing by introducing an additional optical component to GEO600s signal-recycling cavity.Comment: Presentation at AMALDI Conference 2003 in Pis

Sagnac Interferometer as a Speed-Meter-Type, Quantum-Nondemolition Gravitational-Wave Detector

According to quantum measurement theory, "speed meters" -- devices that measure the momentum, or speed, of free test masses -- are immune to the standard quantum limit (SQL). It is shown that a Sagnac-interferometer gravitational-wave detector is a speed meter and therefore in principle it can beat the SQL by large amounts over a wide band of frequencies. It is shown, further, that, when one ignores optical losses, a signal-recycled Sagnac interferometer with Fabry-Perot arm cavities has precisely the same performance, for the same circulating light power, as the Michelson speed-meter interferometer recently invented and studied by P. Purdue and the author. The influence of optical losses is not studied, but it is plausible that they be fairly unimportant for the Sagnac, as for other speed meters. With squeezed vacuum (squeeze factor $e^{-2R} = 0.1$) injected into its dark port, the recycled Sagnac can beat the SQL by a factor $\sqrt{10} \simeq 3$ over the frequency band 10 {\rm Hz} \alt f \alt 150 {\rm Hz} using the same circulating power $I_c\sim 820$ kW as is used by the (quantum limited) second-generation Advanced LIGO interferometers -- if other noise sources are made sufficiently small. It is concluded that the Sagnac optical configuration, with signal recycling and squeezed-vacuum injection, is an attractive candidate for third-generation interferometric gravitational-wave detectors (LIGO-III and EURO).Comment: 12 pages, 6 figure

Laser-interferometer gravitational-wave optical-spring detectors

Using a quantum mechanical approach, we show that in a gravitational-wave interferometer composed of arm cavities and a signal recycling cavity, e.g., the LIGO-II configuration, the radiation-pressure force acting on the mirrors not only disturbs the motion of the free masses randomly due to quantum fluctuations, but also and more fundamentally, makes them respond to forces as though they were connected to an (optical) spring with a specific rigidity. This oscillatory response gives rise to a much richer dynamics than previously known, which enhances the possibilities for reshaping the LIGO-II's noise curves. However, the optical-mechanical system is dynamically unstable and an appropriate control system must be introduced to quench the instability.Comment: 7 pages, 3 figures; to appear in the Proceedings of 4th Edoardo Amaldi Conference on Gravitational Waves, Perth, Australia, 8-13 July 200

Experimental demonstration of a squeezing enhanced power recycled Michelson interferometer for gravitational wave detection

Interferometric gravitational wave detectors are expected to be limited by shot noise at some frequencies. We experimentally demonstrate that a power recycled Michelson with squeezed light injected into the dark port can overcome this limit. An improvement in the signal-to-noise ratio of 2.3dB is measured and locked stably for long periods of time. The configuration, control and signal readout of our experiment are compatible with current gravitational wave detector designs. We consider the application of our system to long baseline interferometer designs such as LIGO.Comment: 4 pages 4 figure

Simulating a dual-recycled gravitational wave interferometer with realistically imperfect optics

We simulate the performance of a gravitational wave interferometer in the Dual Recycling (DR) configuration, as will be used for systems like Advanced-LIGO. Our grid-based simulation program models complex interferometric detectors with realistic optical deformations (e.g., fine-scale mirror surface roughness). Broadband and Tuned DR are modeled here; the results are also applied qualitatively to Resonant Sideband Extraction (RSE). Several beneficial properties anticipated for DR detectors are investigated: signal response tuning and narrowbanding, power loss reduction, and the reclamation of lost power as useful light for signal detection. It is shown that these benefits would be limited by large scattering losses in large (multi-kilometer) systems. Furthermore, losses may be resonantly enhanced (particularly for RSE), if the interferometer's modal resonance conditions are not well chosen. We therefore make two principal recommendations for DR/RSE interferometers: the DR/RSE cavity must be modally nondegenerate; and fabricated mirror surfaces and coatings must be as smooth as is practically feasible.Comment: 50 pages, 11 figure

Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors

It has long been thought that the sensitivity of laser interferometric gravitational-wave detectors is limited by the free-mass standard quantum limit, unless radical redesigns of the interferometers or modifications of their input/output optics are introduced. Within a fully quantum-mechanical approach we show that in a second-generation interferometer composed of arm cavities and a signal recycling cavity, e.g., the LIGO-II configuration, (i) quantum shot noise and quantum radiation-pressure-fluctuation noise are dynamically correlated, (ii) the noise curve exhibits two resonant dips, (iii) the Standard Quantum Limit can be beaten by a factor of 2, over a frequency range \Delta f/f \sim 1, but at the price of increasing noise at lower frequencies.Comment: 35 pages, 9 figures; few misprints corrected and some references adde

Gravitational Radiation from Rotational Instabilities in Compact Stellar Cores with Stiff Equations of State

We carry out 3-D numerical simulations of the dynamical instability in rapidly rotating stars initially modeled as polytropes with n = 1.5, 1.0, and 0.5. The calculations are done with a SPH code using Newtonian gravity, and the gravitational radiation is calculated in the quadrupole limit. All models develop the global m=2 bar mode, with mass and angular momentum being shed from the ends of the bar in two trailing spiral arms. The models then undergo successive episodes of core recontraction and spiral arm ejection, with the number of these episodes increasing as n decreases: this results in longer-lived gravitational wave signals for stiffer models. This instability may operate in a stellar core that has expended its nuclear fuel and is prevented from further collapse due to centrifugal forces. The actual values of the gravitational radiation amplitudes and frequencies depend sensitively on the radius of the star R_{eq} at which the instability develops.Comment: 39 pages, uses Latex 2.09. To be published in the Dec. 15, 1996 issue of Physical Review D. 21 figures (bitmapped). Originals available in compressed Postscript format at ftp://zonker.drexel.edu/papers/bars

Squeezed light in a frontal-phase-modulated signal-recycled interferometer

The application of squeezed Light to a frontal-phase-modulated signal-recycled interferometer is considered. We present a simple model to understand the required spectrum of squeezing so as to make the interferometer more sensitive. In particular we analyze the broad-and narrow-band cases for signal recycling and fmd that the sensitivity of the detector can be enhanced provided an appropriate input squeezed spectrum is used. We also discuss the effect of using squeezed light on the bandwidth of the detector