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

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

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

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

A 1.82 m^2 ring laser gyroscope for nano-rotational motion sensing

We present a fully active-controlled He-Ne ring laser gyroscope, operating in square cavity 1.35 m in side. The apparatus is designed to provide a very low mechanical and thermal drift of the ring cavity geometry and is conceived to be operative in two different orientations of the laser plane, in order to detect rotations around the vertical or the horizontal direction. Since June 2010 the system is active inside the Virgo interferometer central area with the aim of performing high sensitivity measurements of environmental rotational noise. So far, continuous not attempted operation of the gyroscope has been longer than 30 days. The main characteristics of the laser, the active remote-controlled stabilization systems and the data acquisition techniques are presented. An off-line data processing, supported by a simple model of the sensor, is shown to improve the effective long term stability. A rotational sensitivity at the level of ten nanoradiants per squareroot of Hz below 1 Hz, very close to the required specification for the improvement of the Virgo suspension control system, is demonstrated for the configuration where the laser plane is horizontal

New Upper Limit of Terrestrial Equivalence Principle Test for Rotating Extended Bodies

Improved terrestrial experiment to test the equivalence principle for rotating extended bodies is presented, and a new upper limit for the violation of the equivalence principle is obtained at the level of 1.6$10^{\text{-7}}$, which is limited by the friction of the rotating gyroscope. It means the spin-gravity interaction between the extended bodies has not been observed at this level.Comment: 4 page

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

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.

Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency is much smaller than the particle's orbital one. We make neither a priori assumptions about the direction of the wavevector nor on the orbital geometry of the planet. We find that, while the semi-major axis is left unaffected, the eccentricity, the inclination, the longitude of the ascending node, the longitude of pericenter and the mean anomaly undergo non-vanishing long-term changes. They are not secular trends because of the slow modulation introduced by the tidal matrix coefficients and by the orbital elements themselves. They could be useful to indepenedently constrain the ultra-low frequency waves which may have been indirectly detected in the BICEP2 experiment. Our calculation holds, in general, for any gravitationally bound two-body system whose characteristic frequency is much larger than the frequency of the external wave. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.Comment: LaTex2e, 24 pages, no figures, no tables. Changes suggested by the referees include

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