Self-attraction effect and correction on three absolute gravimeters

The perturbations of the gravitational field due to the mass distribution of an absolute gravimeter have been studied. The so called Self Attraction Effect (SAE) is crucial for the measurement accuracy, especially for the International Comparisons, and for the uncertainty budget evaluation. Three instruments have been analysed: MPG-2, FG5-238 and IMPG-02. The SAE has been calculated using a numerical method based on FEM simulation. The observed effect has been treated as an additional vertical gravity gradient. The correction (SAC) to be applied to the computed g value has been associated with the specific height level, where the measurement result is typically reported. The magnitude of the obtained corrections is of order 1E-8 m/s2.Comment: 14 pages, 8 figures, submitted to Metrologi

Correction due to finite speed of light in absolute gravimeters

Correction due to finite speed of light is among the most inconsistent ones in absolute gravimetry. Formulas reported by different authors yield corrections scattered up to 8 $\mu$Gal with no obvious reasons. The problem, though noted before, has never been studied, and nowadays the correction is rather postulated than rigorously proven. In this paper we make an attempt to revise the subject. Like other authors, we use physical models based on signal delays and the Doppler effect, however, in implementing the models we additionally introduce two scales of time associated with moving and resting reflectors, derive a set of rules to switch between the scales, and establish the equivalence of trajectory distortions as obtained from either time delay or distance progression. The obtained results enabled us to produce accurate correction formulas for different types of instruments, and to explain the differences in the results obtained by other authors. We found that the correction derived from the Doppler effect is accountable only for $\frac23$ of the total correction due to finite speed of light, if no signal delays are considered. Another major source of inconsistency was found in the tacit use of simplified trajectory models

A nonlinear detection algorithm for periodic signals in gravitational wave detectors

We present an algorithm for the detection of periodic sources of gravitational waves with interferometric detectors that is based on a special symmetry of the problem: the contributions to the phase modulation of the signal from the earth rotation are exactly equal and opposite at any two instants of time separated by half a sidereal day; the corresponding is true for the contributions from the earth orbital motion for half a sidereal year, assuming a circular orbit. The addition of phases through multiplications of the shifted time series gives a demodulated signal; specific attention is given to the reduction of noise mixing resulting from these multiplications. We discuss the statistics of this algorithm for all-sky searches (which include a parameterization of the source spin-down), in particular its optimal sensitivity as a function of required computational power. Two specific examples of all-sky searches (broad-band and narrow-band) are explored numerically, and their performances are compared with the stack-slide technique (P. R. Brady, T. Creighton, Phys. Rev. D, 61, 082001).Comment: 9 pages, 3 figures, to appear in Phys. Rev.

Comparison between two mobile absolute gravimeters: optical versus atomic interferometers

We report a comparison between two absolute gravimeters: the LNE-SYRTE cold atoms gravimeter and FG5#220 of Leibniz Universit\"at of Hannover. They rely on different principles of operation: atomic and optical interferometry. Both are movable which enabled them to participated to the last International Comparison of Absolute Gravimeters (ICAG'09) at BIPM. Immediately after, their bilateral comparison took place in the LNE watt balance laboratory and showed an agreement of 4.3 +/- 6.4 {\mu}Gal

Perturbations of the local gravity field due to mass distribution on precise measuring instruments: a numerical method applied to a cold atom gravimeter

We present a numerical method, based on a FEM simulation, for the determination of the gravitational field generated by massive objects, whatever geometry and space mass density they have. The method was applied for the determination of the self gravity effect of an absolute cold atom gravimeter which aims at a relative uncertainty of 10-9. The deduced bias, calculated with a perturbative treatment, is finally presented. The perturbation reaches (1.3 \pm 0.1) \times 10-9 of the Earth's gravitational field.Comment: 12 pages, 7 figure

Searching for periodic sources with LIGO

We investigate the computational requirements for all-sky, all-frequency searches for gravitational waves from spinning neutron stars, using archived data from interferometric gravitational wave detectors such as LIGO. These sources are expected to be weak, so the optimal strategy involves coherent accumulaton of signal-to-noise using Fourier transforms of long stretches of data (months to years). Earth-motion-induced Doppler shifts, and intrinsic pulsar spindown, will reduce the narrow-band signal-to-noise by spreading power across many frequency bins; therefore, it is necessary to correct for these effects before performing the Fourier transform. The corrections can be implemented by a parametrized model, in which one does a search over a discrete set of parameter values. We define a metric on this parameter space, which can be used to determine the optimal spacing between points in a search; the metric is used to compute the number of independent parameter-space points Np that must be searched, as a function of observation time T. The number Np(T) depends on the maximum gravitational wave frequency and the minimum spindown age tau=f/(df/dt) that the search can detect. The signal-to-noise ratio required, in order to have 99% confidence of a detection, also depends on Np(T). We find that for an all-sky, all-frequency search lasting T=10^7 s, this detection threshhold is at a level of 4 to 5 times h(3/yr), where h(3/yr) is the corresponding 99% confidence threshhold if one knows in advance the pulsar position and spin period.Comment: 18 pages, LaTeX, 12 PostScript figures included using psfig. Submitted to Phys. Rev.

Noise reduction in gravitational wave interferometers using feedback

We show that the quantum locking scheme recently proposed by Courty {\it et al.} [Phys. Rev. Lett. {\bf 90}, 083601 (2003)] for the reduction of back action noise is able to significantly improve the sensitivity of the next generation of gravitational wave interferometers.Comment: 12 pages, 2 figures, in print in the Special Issue of J. Opt. B on Fluctuations and Noise in Photonics and Quantum Optic

Searching for periodic sources with LIGO. II: Hierarchical searches

The detection of quasi-periodic sources of gravitational waves requires the accumulation of signal-to-noise over long observation times. If not removed, Earth-motion induced Doppler modulations, and intrinsic variations of the gravitational-wave frequency make the signals impossible to detect. These effects can be corrected (removed) using a parameterized model for the frequency evolution. We compute the number of independent corrections $N_p(\Delta T,N)$ required for incoherent search strategies which use stacked power spectra---a demodulated time series is divided into $N$ segments of length $\Delta T$, each segment is FFTed, the power is computed, and the $N$ spectra are summed up. We estimate that the sensitivity of an all-sky search that uses incoherent stacks is a factor of 2--4 better than would be achieved using coherent Fourier transforms; incoherent methods are computationally efficient at exploring large parameter spaces. A two-stage hierarchical search which yields another 20--60% improvement in sensitivity in all-sky searches for old (>= 1000 yr) slow (= 40 yr) fast (<= 1000 Hz) pulsars. Assuming 10^{12} flops of effective computing power for data analysis, enhanced LIGO interferometers should be sensitive to: (i) Galactic core pulsars with gravitational ellipticities of \epsilon\agt5\times 10^{-6} at 200 Hz, (ii) Gravitational waves emitted by the unstable r-modes of newborn neutron stars out to distances of ~8 Mpc, and (iii) neutron stars in LMXB's with x-ray fluxes which exceed $2 \times 10^{-8} erg/(cm^2 s)$. Moreover, gravitational waves from the neutron star in Sco X-1 should be detectable is the interferometer is operated in a signal-recycled, narrow-band configuration.Comment: 22 Pages, 13 Figure

Quantum noise in laser-interferometer gravitational-wave detectors with a heterodyne readout scheme

We analyze and discuss the quantum noise in signal-recycled laser interferometer gravitational-wave detectors, such as Advanced LIGO, using a heterodyne readout scheme and taking into account the optomechanical dynamics. Contrary to homodyne detection, a heterodyne readout scheme can simultaneously measure more than one quadrature of the output field, providing an additional way of optimizing the interferometer sensitivity, but at the price of additional noise. Our analysis provides the framework needed to evaluate whether a homodyne or heterodyne readout scheme is more optimal for second generation interferometers from an astrophysical point of view. As a more theoretical outcome of our analysis, we show that as a consequence of the Heisenberg uncertainty principle the heterodyne scheme cannot convert conventional interferometers into (broadband) quantum non-demolition interferometers.Comment: 16 pages, 8 figure

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