The upcoming European design study `Einstein gravitational-wave Telescope' represents the first step towards a substantial, international effort for the design of a third-generation interferometric gravitational wave detector. It is generally believed that third-generation instruments might not be installed into existing infrastructures but will provoke a new search for optimal detector sites. Consequently, the detector design could be subject to fewer constraints than the on-going design of the second generation instruments. In particular, it will be prudent to investigate alternatives to the traditional L-shaped Michelson interferometer. In this article, we review an old proposal to use three Michelson interferometers in a triangular configuration. We use this example of a triple Michelson interferometer to clarify the terminology and will put this idea into the context of more recent research on interferometer technologies. Furthermore the benefits of a triangular detector will be used to motivate this design as a good starting point for a more detailed research effort towards a third-generation gravitational wave detector.
The features of correlated Michelson interferometers are for describing the analysis of Einsteinian spacetime models, and the quantum geometries pertinent with descriptions of GR compatible with particle Physics. Such apparati allow for the spectral decomposition of fractional Planck-scale displacements correlations and fractional Plancktime- interval correlations for kinematical investigations in particle Physics on emerging Minkowski background, and for models which admit GR as a limit after cosmological implementations for Poincaré particles content.
In this paper we demonstrate that a double Michelson interferometer with Fabry-Perot cavities in its arms is able to perform laser- and displacement-noise-free gravitational-wave (GW) detection if certain model assumptions are met. Assuming the input mirrors of a single Michelson/Fabry-Perot interferometer can be rigidly attached to beamsplitter on a central platform one can manipulate with interferometer's response signals in a way to cancel laser noise and displacement noise of all test masses except the cental platform. A pair of symmetrically positioned Michelson/Fabry-Perot interferometer…
Gravitational waves reaching a Michelson interferometer are expected to induce a very small change in the length of its arms causing a phase shift between them, but it is very difficult to observe the extremely small phase shift signals produced. In the present letter we show that the gravitational waves signal could be amplified by orders of magnitude by using very special conditions for a coherent-squeezed Michelson interferometer in which the coherent state enters one port of the interferometer and the squeezed vacuum enters in the other port. We treat the case where without the gravitation…
The possibility of measuring the second order correlation function of the gravitational waves detectors' currents or photonumbers, and the observation of the gravitational signals by using a spectrum analyzer is discussed. The method is based on complicated data processing and is expected to be efficient for coherent periodic gravitational waves. It is suggested as an alternative method to the conventional one which is used now in the gravitational waves observatories.
Electromagnetic methods recently proposed for detecting gravitational waves modify the Michelson phase shift analysis (historically employed for special relativity). We suggest that a frequency modulation analysis is more suited to general relativity. An incident photon in the presence of a very long wavelength gravitational wave will have a finite probability of being returned as a final photon with a frequency shift whose magnitude is equal to the gravitational wave frequency. The effect is due to the non-linear coupling between electromagnetic and gravitational waves. The frequency modulati…
Detecting Free-Mass Common-Mode Motion Induced by Incident Gravitational Waves: Testing General Relativity and Source Direction via Fox-Smith and Michelson Interferometers
We analyze the radiation pressure induced interaction of mirror motion and light fields in Michelson-type interferometers used for the detection of gravitational waves and for fundamental research in table-top quantum optomechanical experiments, focusing on the asymmetric regime with a (slightly) unbalanced beamsplitter and a (small) offset from the dark port. This regime, as it was shown recently, provides new interesting features, in particular a stable optical spring and optical cooling on cavity resonance. We show that generally the nature of optomechanical coupling in Michelson-type inter…
We discuss the theoretical foundations for testing non-linear vacuum electrodynamics with Michelson interferometry. Apart from some non-degeneracy conditions to be imposed, our discussion applies to all non-linear electrodynamical theories of the Plebański class, i.e., to all Lagrangians that depend only on the two Lorentz-invariant scalars quadratic in the field strength. The main idea of the experiment proposed here is to use the fact that, according to non-linear electrodynamics, the phase velocity of light should depend on the strength and on the direction of an electromagnetic background …
Sensitivity of gravitational-wave detectors is limited in the high-frequency band by quantum shot noise and eventually limited by the optical loss in signal recycling cavity. This limit is the main obstacle on the way to detect gravitational waves from the binary neutron star mergers in the current and the future generation detectors, as it does not depend on either the arm length, or the injected squeezing level. In this paper, we come up with the sloshing Sagnac interferometer topology, which can be obtained from the Michelson interferometer by optically connecting the end mirrors into an ad…
We treat the problem of a Michelson interferometer in the field of a plane gravitational wave in the framework of general relativity. The arms of the interferometer are regarded as the world lines of the light beams, whose motion is determined by the Hamilton-Jacobi equation for a massless particle. In the case of a weak monochromatic wave we find that the formula for the delay of a light beam agrees with the result obtained by solving the linearized coupled Einstein-Maxwell equations. We also calculate this delay in the next (quadratic) approximation.
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.
An extension of the input-output relation for a conventional Michelson interferometric gravitational-wave detector is carried out to treat an arbitrary coherent state for the injected optical beam. This extension is one of necessary researches toward the clarification of the relation between conventional gravitational-wave detectors and a simple model of a gravitational-wave detector inspired by weak-measurements in [A.~Nishizawa, Phys. Rev. A {\bf 92} (2015), 032123.]. The derived input-output relation describes not only a conventional Michelson-interferometric gravitational-wave detector but…
It is shown in the present Letter that the quantum noise due to high laser intensities in Michelson interferometer for gravitational waves detection can be reduced by sending squeezed vacuum states to the 'dark' port of the interferometer. The experimental details of such physical system have been described in a recent article by Barak and Ben-Aryeh (JOSA-B, 25, 361(2008)). In another very recent article by Voronov and Weyrauch (Phys. Rev.A 81, 053816 (2010)) they have followed our methods for treating the same physical system, and have pointed out an error in the sign of one of our expression…
Low-mass (sub-eV) scalar field dark matter may induce apparent oscillations of fundamental constants, resulting in corresponding oscillations of the size and the index of refraction of solids. Laser interferometers are highly sensitive to changes in the size and index of refraction of the main beamsplitter. Using cross-correlated data of the Fermilab Holometer instrument, which consists of twin co-located 40-m arm length power-recycled interferometers, we investigate the possible existence of scalar field dark matter candidates in the mass range between 1.6$\cdot$10$^{-12}$ eV and 1.0$\cdot$10…
The effect of the angular momentum density of a gravitational source on the times of flight of light rays in an interferometer is analyzed. The calculation is made imagining that the interferometer is at the equator of the gravity source and, as long as possible, the metric, provided it is stationary and axisymmetric, is not approximated. Finally, in order to evaluate the size of the effect in the case of the Earth a weak field approximation is introduced. For laboratory scales and non-geodesic paths the correction turns out to be comparable with the sensitivity expected in gravitational waves…
The network of interferometric gravitational-wave observatories has successfully detected tens of astrophysical signals since 2015. In this paper, we experimentally investigate compact sensors that have the potential to improve the sensitivity of gravitational-wave detectors to intermediate-mass black holes. We use only commercial components, such as sensing heads and lasers, to assemble the setup and demonstrate its subpicometer precision. The setup consists of a pair of Michelson interferferometers that use deep frequency modulation techniques to obtain a linear, relative displacement readou…
We analyze the dynamic optomechanical back-action in signal-recycled Michelson and Michelson-Sagnac interferometers that are operated off dark port. We show that in this case --- and in contrast to the well-studied canonical form of dynamic back-action on dark port --- optical damping in a Michelson-Sagnac interferometer acquires a non-zero value on cavity resonance, and additional stability/instability regions on either side of the resonance, revealing new regimes of cooling/heating of micromechanical oscillators. In a free-mass Michelson interferometer for a certain region of parameters we p…
We describe a setup based on Michelson interferometry for coherent measurements of the backscattered light from a low roughness optical surface under test. Special data processing was developed for the extraction of the useful signal from the various stray contributions to the coherent signal. We achieve coherent detection of light scattered by a mirror down to -130 dB in optical power. We characterize the dependence of the backscattered light with spot position and incidence angle. Results of cross-polarization scattering coherent measurements and preliminary results of dust deposition experi…
The techniques of power recycling and signal recycling have proven as key concepts to increase the sensitivity of large-scale gravitational wave detectors by independent resonant enhancement of light power and signal sidebands within the interferometer. Developing the latter concept further, twin signal recycling was proposed as an alternative to conventional detuned signal recycling. Twin signal recycling features the narrow-band sensitivity gain of conventional detuned signal recycling but furthermore facilitates the injection of squeezed states of light, increases the detector sensitivity o…
Measurements are reported of the cross-correlation of spectra of differential position signals from the Fermilab Holometer, a pair of co-located 39 m long, high power Michelson interferometers with flat, broadband frequency response in the MHz range. The instrument obtains sensitivity to high frequency correlated signals far exceeding any previous measurement in a broad frequency band extending beyond the 3.8 MHz inverse light crossing time of the apparatus. The dominant but uncorrelated shot noise is averaged down over $2\times 10^8$ independent spectral measurements with 381 Hz frequency res…
An incoming gravity wave being a stress wave is a surface with intrinsic curvature. When a light beam is parallel transported on this non-Euclidian surface it acquires an excess phase which accumulates with each curcuit. We calculate the separate contributions to excess phase from the wave geometry as well as the dynamic response of mirrors in a Michelson interferometer. Using these results and a combination of analogue and digital signal processing techniques we show how a compact interferometer can be made sensitive to gravity waves of amplitude density $10^{-23}/\sqrt{Hz}$ within a frequenc…
A small fixed-mirror Michelson interferometer has been built in Frascati to experimentally study the alignment method that has been suggested for VIRGO. The experimental results fully confirm the adequacy of the method. The minimum angular misalignment that can be detected in the present set-up is 10 nrad/sqrt{Hz}
We present an overview of quantum noise in gravitational wave interferometers. Gravitational wave detectors are extensively modified variants of a Michelson interferometer and the quantum noise couplings are strongly influenced by the interferometer configuration. We describe recent developments in the treatment of quantum noise in the complex interferometer configurations of present-day and future gravitational-wave detectors. In addition, we explore prospects for the use of squeezed light in future interferometers, including consideration of the effects of losses, and the choice of optimal r…
As a future plan, an advanced gravitational-wave detector will employ an optical configuration of resonant sideband extraction (RSE), achieved with an additional mirror at the signal-detection port of the power-recycled Fabry-Perot Michelson interferometer. To control the complex coupled cavity system, one of the most important design issues is how to extract the longitudinal control signals of the cavities. We developed a new signal-extraction scheme which provides an appropriate sensing matrix. The new method uses two sets of sidebands: one of the sideband components satisfies the critical c…
Two homodyne Michelson interferferometers aboard the LISA Pathfinder spacecraft will measure the the positions of two free-floating test masses, as part of the NASA ST7 mission. The interferometer is required to measure the separation between the test masses with sensitivity of 30 pm/sqrt(Hz) at 10 mHz. The readout scheme is described, error sources are analyzed, and experimental results are presented.
We analyze detector responses of gravitational wave detectors for gravitational waves with arbitrary polarizations predicted in the metric theories of gravity. We present the general formulas for the frequency responses valid in various interferometric arrangements including Michelson, Delay-Line and Fabry-Perot detectors. We analyze the angular and frequency behavior and the sensitivity patterns of the responses for each polarization mode.
We propose a new optical configuration for an interferometric gravitational wave detector based on the speedmeter concept using a sloshing cavity. Speedmeters provide an inherently better quantum-noise limited sensitivity at low frequencies than the currently used Michelson interferometers. We show that a practical sloshing cavity can be added relatively simply to an existing dual-recycled Michelson interferometer such as Advanced LIGO.
Currently operating gravitational-wave interferometers are Michelson interferometers with effective arm length L ~ 4x10e5 m. While the interferometer remains in lock, data at the fsr sideband frequency encode information on slow phase changes in the f ~ 10e-5 Hz range, with a fringe sensitivity ~ 10e-10. Preliminary LIGO data presented in 2009 show no Lorentz violating signal at the second harmonic of the Earth's sidereal frequency. This sets a limit on a possible change in refractine index, dn/n < 2x10e-22, an improvement of more than three orders of magnitude over existing limits.
We calculate the quantum noise limited displacement sensitivity of a Michelson-Fabry-Perot (MFP) with detuned cavities, followed by phase-sensitive homodyne detection. We show that the standard quantum limit can be surpassed even with resonant cavities and without any signal-recycling mirror nor additional cavities. Indeed, thanks to the homodyne detection, the output field quadrature can be chosen in such a way to cancel the effect of input amplitude fluctuations, i.e., eliminating the force noise. With detuned cavities, the modified opto-mechanical susceptivity allows to reach unlimited sens…
LIGO, the Laser Interferometer Gravitational-wave Observatory, has been designed and constructed to measure gravitational wave strain via differential arm length. The LIGO 4-km Michelson arms with Fabry-Perot cavities have auxiliary length control servos for suppressing Michelson motion of the beam-splitter and arm cavity input mirrors, which degrades interferometer sensitivity. We demonstrate how a post-facto pipeline (AMPS) improves a data sample from LIGO Science Run 6 with feedforward subtraction. Dividing data into 1024-second windows, we numerically fit filter functions representing the …
The French-Italian interferometric gravitational wave detector VIRGO is currently being commissioned. Its principal instrument is a Michelson interferometer with 3 km long optical cavities in the arms and a power-recycling mirror. This paper gives an overview of the present status of the system. We report on the presently attained sensitivity and the system's performance during the recent commissioning runs. After a sequence of intermediate stages, the interferometer is now being used in the so-called recombined configuration. The input laser beam is spatially filtered by a 144 m long input mo…
The possibility of using squeezed states and balanced homodyne detection of gravitational waves is discussed. It is shown that the quantum noise due to high laser intensities in Michelson interferometer for gravitational waves detection can be reduced by sending squeezed vacuum states to the 'dark' port of the interferometer. The present analysis describes photon statistics measurements effects related to quadrature balanced homodyne detection showing the advantage of using this scheme for detecting gravitational waves.
Broadband suppression of quantum noise below the Standard Quantum Limit (SQL) becomes a top-priority problem for the future generation of large-scale terrestrial detectors of gravitational waves, as the interferometers of the Advanced LIGO project, predesigned to be quantum-noise-limited in the almost entire detection band, are phased in. To this end, among various proposed methods of quantum noise suppression or signal amplification, the most elaborate approach implies a so-called *xylophone* configuration of two Michelson interferometers, each optimised for its own frequency band, with a com…
Several relatively small-scale experimental setups aimed on prototyping of future laser gravitational-wave detectors and testing of new methods of quantum measurements with macroscopic mechanical objects, are under development now. In these devices, not devoted directly to the gravitational-wave detection, Mach-Zehnder interferometer with pass-through Fabry-Perot cavities in the arms can be used instead of the standard Michelson/Fabry-Perot one. The advantage of this topology is that it does not contain high-reflectivity end mirrors with multilayer coatings, which Brownian noise could constitu…
Detection of gravitational waves (GW) opened new windows on fundamental physics and it would be natural to search how the role of extra dimensional effects can be traced to gravitational wave physics. In this article, we consider a toy model of five dimensional pure gravity theory compactified on a circle. The resulting four dimensional theory is a scalar-Maxwell theory which is minimally coupled with gravity. By finding the equations of motion for scalar, electric and magnetic fields , we would be able to find exact wave solutions of coupled equations which are zero mode solutions. We also pe…
The second generation of large scale interferometric gravitational wave detectors will be limited by quantum noise over a wide frequency range in their detection band. Further sensitivity improvements for future upgrades or new detectors beyond the second generation motivate the development of measurement schemes to mitigate the impact of quantum noise in these instruments. Two strands of development are being pursued to reach this goal, focusing both on modifications of the well-established Michelson detector configuration and development of different detector topologies. In this paper, we pr…
The photon motion in a Michelson interferometer is re-analyzed in both geometrical optics and wave optics. The classical paths of the photons in the background of gravitational wave are derived from Fermat principle, which is the same as the null geodesics in general relativity. The deformed Maxwell equations and the wave equations of electric fields in the background of gravitational wave are presented in flat-space approximation. Both methods show that the response of an interferometer depends on the frequency of a gravitational wave, however it is almost independent of the frequency of the …
We propose a new implementation of a quantum speed meter QND measurement scheme. It employs two independent optical readouts of the interferometer test masses, featuring strongly different values of the bandwidths $γ_{1,2}$ and of the optical circulating power $I_{1,2}$, with the special relationship of $I_1/I_2=γ_1/γ_2$. The outputs of these two position meters have to be combined by an additional beamsplitter. In this scheme, signals at the common and the differential outputs of the interferometer setup are proportional to the position and the velocity of the test masses, respectively. The i…
Several km-scale gravitational-wave detectors have been constructed world wide. These instruments combine a number of advanced technologies to push the limits of precision length measurement. The core devices are laser interferometers of a new kind; developed from the classical Michelson topology these interferometers integrate additional optical elements, which significantly change the properties of the optical system. Much of the design and analysis of these laser interferometers can be performed using well-known classical optical techniques; however, the complex optical layouts provide a ne…
The gravitational wave (GW) has opened a new window to the universe beyond the electromagnetic spectrum. Since 2015, dozens of GW events have been caught by the ground-based GW detectors through laser interferometry. However, all the ground-based detectors are L-shaped Michelson interferometers, with very limited directional response to GW. Here we propose a three-dimensional (3-D) laser interferometer detector in the shape of a regular triangular pyramid, which has more spherically symmetric antenna pattern. Moreover, the new configuration corresponds to much stronger constraints on parameter…
Current limits on violation of local Lorentz invariance in the photon sector are derived mainly from experiments that search for a spatial anisotropy in the speed of light. The presently operating gravitational wave detectors are Michelson interferometers with long effective arms, 4e5 m, and sensitive to a fringe shift 2e-9. Therefore they can be used to test for a difference in the speed of light in the two arms, as modulated bi-annualy by the orientation of the Earth's velocity with respect to the direction of motion of the local system. A limit can be set on the Robertson-Mansouri-Sexl para…
The response of Michelson interferometers to weak plane gravitational waves is computed at one order of accuracy beyond the eikonal equation. The modulation of the electromagnetic field amplitude and polarisation are taken into account by solving the transport equations of geometrical optics with boundary conditions adapted to laser interferometry. Considering both DC and balanced homodyne readout schemes, explicit formulae for the interferometer output signals are derived. These signals comprise perturbations of the optical path length, frequency and amplitude, and are shown to be insensitive…
The recent discovery of gravitational waves (GW) by LIGO has impressively launched the novel field of gravitational astronomy and it allowed us to glimpse at exciting objects we could so far only speculate about. Further sensitivity improvements at the low frequency end of the detection band of future GW observatories rely on quantum non-demolition (QND) methods to suppress fundamental quantum fluctuations of the light fields used to readout the GW signal. Here we invent a novel concept of how to turn a conventional Michelson interferometer into a QND speed meter interferometer with coherently…
Inelastic back-scattering of stray light is a long-standing and fundamental problem in high-sensitivity interferometric measurements and a potential limitation for advanced gravitational-wave detectors. The emerging parasitic interferences cannot be distinguished from a scientific signal via conventional single readout. In this work, we propose the subtraction of inelastic back-scatter signals by employing dual homodyne detection on the output light, and demonstrate it for a table-top Michelson interferometer. The additional readout contains solely parasitic signals and is used to model the sc…
