Laser Interferometric Gravitational Wave Detectors Research Articles

Decihertz Gravitational Waves from Double White Dwarf Merger Remnants

Abstract Close binaries of double white dwarfs (DWDs) inspiral and merge by emitting gravitational waves (GWs). Orbital motion of some of these binaries is expected to be observed at a low-frequency band by space-borne laser interferometric detectors of GWs. The merger remnant may suffer thermonuclear runaway and explode as SNe Ia if they are massive enough. As GW sources, the remnants have so far been scarcely studied. Here we propose a new mechanism of GW emission from DWD merger remnants that may be observed by planned GW detectors in a decihertz frequency band. A remnant is temporarily expected to have a high degree of differential rotation as a consequence of the merger process. It is then unstable to oscillation modes whose azimuthal pattern speed coincides with the stellar rotation. We solve the eigenvalue problem of differentially rotating remnants and identify unstable eigenmodes, which may be categorized to inertial modes. The estimate of characteristic strain of GWs shows that they may be detectable within the distance of the Virgo cluster by planned gravitational wave observatories targeting the decihertz band.

A Broadband Signal Recycling Scheme for Approaching the Quantum Limit from Optical Losses

Quantum noise limits the sensitivity of laser interferometric gravitational-wave detectors. Given the state-of-the-art optics, the optical losses define the lower bound of the best possible quantum-limited detector sensitivity. In this work, we come up with a broadband signal recycling scheme which gives a potential solution to approaching this lower bound by converting the signal recycling cavity to be a broadband signal amplifier using an active optomechanical filter. We will show the difference and advantage of such a scheme compared with the previous white light cavity scheme using the optomechanical filter in [Phys.Rev.Lett.115.211104 (2015)]. The drawback is that the new scheme is more susceptible to the thermal noise of the mechanical oscillator.

Lensed gravitational waves: Scattering and applications

<p indent="0mm">The direct detection of gravitational waves from stellar-mass compact binary merger by ground-based laser interferometer gravitational wave detector LIGO/Virgo has verified the prediction of general relativity and opened a new chapter in gravitational wave astronomy. Up to now, a total of 50 gravitational wave events have been detected and published in GWTC-1 and GWTC-2 catalogue. In the near future, the third-generation ground based gravitational wave detector, such as the Einstein Telescope (ET), will be constructed with sensitivity improved by at least a factor of 10. Tens of thousands of gravitational wave signals are expected to be detected per year in the third-generation detector era. These gravitational wave signals will inevitably overlap with foreground massive celestial bodies (such as black hole, galaxy and galaxy cluster), thus leading to lensed gravitational wave signals which will undoubtedly be another important test of general relativity once detected. Furthermore, strongly lensed gravitational wave signals by galaxy from massive binary black hole could possibly be detected by future space detector, e.g., LISA and DECIGO. Since the wavelengths of gravitational waves are comparable with the size of some lens, the lensed gravitational waves play a unique role in studying the phenomena of wave nature, e.g., interference and diffraction. Lensed gravitational wave-electromagnetic wave system will have a wide range of applications in fundamental physics, cosmology and astrophysics when a series of lensed gravitational wave events and their corresponding electromagnetic counterparts have been detected. The most obvious advantage of lensed gravitational wave-electromagnetic wave system lies in that gravitational wave could provide time delay information with high accuracy, and electromagnetic wave could provide Fermat potential difference with high precision because a relatively complete arc of light could be obtained by electromagnetic wave observations and this is the most important step in measuring the Fermat potential. Thus, by combining the information from both approaches, lensed gravitational wave-electromagnetic wave system could be applied to study the speed of gravitational waves, constrain cosmological parameters, explore the substructure of the dark matter halo and investigate the lens model and so on. In this paper, we will review in detail how to use geodesic equation, lens equation, as well as wave equation to tackle the stationary scattering problem of lensed gravitational waves, and introduce how lensed gravitational wave-electromagnetic wave system could be applied to study the tensor properties, interference and diffraction effects of gravitational wave, as well as its applications in gravitational wave velocity, Hubble constant, cosmic curvature, lens mass, substructure and so on.

A three-dimensional laser interferometer gravitational-wave detector

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 parameters of GW sources, and is capable of constructing null-streams to get rid of the signal-like noise events. A 3-D detector of kilometer scale of such kind would shed new light on the joint search of GW and electromagnetic emission.

Quantum Backaction on kg-Scale Mirrors: Observation of Radiation Pressure Noise in the Advanced Virgo Detector.

The quantum radiation pressure and the quantum shot noise in laser-interferometric gravitational wave detectors constitute a macroscopic manifestation of the Heisenberg inequality. If quantum shot noise can be easily observed, the observation of quantum radiation pressure noise has been elusive, so far, due to the technical noise competing with quantum effects. Here, we discuss the evidence of quantum radiation pressure noise in the Advanced Virgo gravitational wave detector. In our experiment, we inject squeezed vacuum states of light into the interferometer in order to manipulate the quantum backaction on the 42kg mirrors and observe the corresponding quantum noise driven displacement at frequencies between 30 and 70Hz. The experimental data, obtained in various interferometer configurations, is tested against the Advanced Virgo detector quantum noise model which confirmed the measured magnitude of quantum radiation pressure noise.

Designing arm cavities free of parametric instability for gravitational wave detectors

Parametric instability is an intrinsic problem in high power laser interferometer gravitational wave detectors. Optical cavity modes interact with acoustic modes of the test masses, leading to laser power dependent exponential growth of acoustic vibration of the test masses. Future detectors are being planned with designed optical power as high as 5 MW. This increases the requirements for suppressing of parametric instability through various currently available methods. Parametric instabilities could also be alleviated through careful design of the acoustic mode structure and optical mode spacing. Here we study parametric instabilities in future gravitational wave detectors with arm lengths between 6 and 10 km. We show that by careful choice of test mass radii of curvature, dimensions and arm lengths it is possible to design detectors that are free of parametric instability up to 3 MW of intra-cavity power with large enough tolerance on mirror radii of curvature change. We present several case studies and give an example of a design with 6335 m arm cavities and test mass diameter of 52 cm that is parametric instability free. This design is relatively tolerant, staying free of instabilities for a 45 m change in test mass radius of curvature. Maintaining this radius of curvature could easily be done with good design and thermal compensation.

Novel signatures of dark matter in laser-interferometric gravitational-wave detectors

Dark matter may induce apparent temporal variations in the physical "constants", including the electromagnetic fine-structure constant and fermion masses. In particular, a coherently oscillating classical dark-matter field may induce apparent oscillations of physical constants in time, while the passage of macroscopic dark-matter objects (such as topological defects) may induce apparent transient variations in the physical constants. In this paper, we point out several new signatures of the aforementioned types of dark matter that can arise due to the geometric asymmetry created by the beam-splitter in a two-arm laser interferometer. These new signatures include dark-matter-induced time-varying size changes of a freely-suspended beam-splitter and associated time-varying shifts of the main reflecting surface of the beam-splitter that splits and recombines the laser beam, as well as time-varying refractive-index changes in the freely-suspended beam-splitter and time-varying size changes of freely-suspended arm mirrors. We demonstrate that existing ground-based experiments already have sufficient sensitivity to probe extensive regions of unconstrained parameter space in models involving oscillating scalar dark-matter fields and domain walls composed of scalar fields. In the case of oscillating dark-matter fields, Michelson interferometers $-$ in particular, the GEO600 detector $-$ are especially sensitive. The sensitivity of Fabry-Perot-Michelson interferometers, including LIGO, VIRGO and KAGRA, to oscillating dark-matter fields can be significantly increased by making the thicknesses of the freely-suspended Fabry-Perot arm mirrors different in the two arms. We also discuss how small-scale Michelson interferometers, such as the Fermilab holometer, could be used to perform resonant narrowband searches for oscillating dark-matter fields with enhanced sensitivity to dark matter.

Large and extremely low loss: the unique challenges of gravitational wave mirrors.

This paper describes the making of large mirrors for laser interferometer gravitational wave detectors. These optics, working in the near infrared, are among the best optics ever created and played a crucial role in the first direct detection of gravitational waves from black holes or neutron star fusions.

Fundamental relations between measurement, radiation, and decoherence in gravitational wave laser interferometer detectors

As laser interferometer gravitational wave (GW) detectors become quantum noise dominated, understanding the fundamental limit on measurement sensitivity imposed by quantum uncertainty is crucial to guide the search for further noise reduction. Recent efforts have included applying ideas from quantum information theory to GW detection -- specifically the quantum Cramer Rao bound, which is a minimum bound on error in parameter estimation using a quantum state and is determined by the state's quantum Fisher information (QFI) with respect to the parameter. Identifying the QFI requires knowing the interaction between the quantum measurement device and the signal, which was rigorously derived for GW interferometer detectors in [Phys. Rev. D 98, 124006]. In this paper, we calculate the QFI and fundamental quantum limit (FQL) for GW detection, and furthermore derive explicit reciprocity relations involving the QFI which summarize information exchange between the detector and a surrounding weak quantum GW field. Specifically, we show that the GW power radiation by the detector's quantum fluctuations are proportional to the QFI, and therefore inversely proportional to its FQL. Similarly, the detector's decoherence rate in a white noise GW bath can be explicitly related to the QFI/FQL. These relations are fundamental and appear generalizable to a broader class of quantum measurement systems.

Advanced quantum techniques for future gravitational-wave detectors

Quantum fluctuation of light limits the sensitivity of advanced laser interferometric gravitational-wave detectors. It is one of the principal obstacles on the way towards the next-generation gravitational-wave observatories. The envisioned significant improvement of the detector sensitivity requires using quantum non-demolition measurement and back-action evasion techniques, which allow us to circumvent the sensitivity limit imposed by the Heisenberg uncertainty principle. In our previous review article (Danilishin and Khalili in Living Rev Relativ 15:5, 2012), we laid down the basic principles of quantum measurement theory and provided the framework for analysing the quantum noise of interferometers. The scope of this paper is to review novel techniques for quantum noise suppression proposed in the recent years and put them in the same framework. Our delineation of interferometry schemes and topologies is intended as an aid in the process of selecting the design for the next-generation gravitational-wave observatories.

Quantum Limit for Laser Interferometric Gravitational-Wave Detectors from Optical Dissipation

We derive a quantum limit to the sensitivity of laser interferometric gravitational-wave detectors from optical-loss-induced dissipation, analogous to the sensitivity limit from the mechanical dissipation. It applies universally to different interferometer configurations, and cannot be surpassed unless the optical property is improved. This result provides an answer to the long-standing question of how far we can push the detector sensitivity given the state-of-the-art optics.

SOGRO — Terrestrial full-tensor detector for mid-frequency gravitational waves

Laser interferometer gravitational-wave (GW) detectors are observing signals from merging black hole and neutron star binaries with a frequency window from 10[Formula: see text]Hz to several kHz. Future space-based laser interferometers will open a new window of 0.1[Formula: see text]mHz to 0.1[Formula: see text]Hz. In this paper, we discuss the possibility of constructing a terrestrial GW detector named Superconducting Omni-directional Gravitational Radiation Observatory (SOGRO), which can fill the missing frequency window, 0.1 to 10[Formula: see text]Hz, with astronomically interesting sensitivity. SOGRO measures all five tensor components of the spacetime metric, which results in uniform sensitivity for all-sky directions and enables identification of the source direction and wave polarization with a single detector. Seismic and Newtonian gravity noise pose the greatest challenges for constructing ground-based detectors below 10[Formula: see text]Hz. SOGRO utilizes enhanced mechanical and electrical stabilities of materials at cryogenic temperatures to reject common-mode seismic noise to a very high degree. Further, its full-tensor characteristic gives an advantage in the rejection of the Newtonian noise over conventional detectors.

Quantum interactions between a laser interferometer and gravitational waves

LIGO's detection of gravitational waves marks a first step in measurable effects of general relativity on quantum matter. In their current operation, laser interferometer gravitational-wave detectors are already quantum limited at high frequencies, and planned upgrades aim to decrease the noise floor to the quantum level over a wider bandwidth. This raises the interesting idea of what a gravitational-wave detector---or, more generally, an optomechanical system---may reveal about gravity beyond detecting gravitational waves from highly energetic astrophysical events, such as its quantum versus classical nature. In this paper we develop a quantum treatment of gravitational waves and their interactions with the detector. We show that the treatment recovers known equations of motion in the classical limit for gravity, and we apply our formulation to study the system dynamics, with a particular focus on the implications of gravity quantization. Our framework can also be extended to study alternate theories of gravity and the ways in which their features manifest themselves in a quantum optomechanical system.

Silicon nitride and silica quarter-wave stacks for low-thermal-noise mirror coatings

This study investigates a multilayer high reflector with new coating materials for next-generation laser interferometer gravitational wave detectors operated at cryogenic temperatures. We use the plasma-enhanced chemical vapor deposition method to deposit amorphous silicon nitride and silica quarter-wave high-reflector stacks and studied the properties pertinent to the coating thermal noise. Room- and cryogenic-temperature mechanical loss angles of the silicon nitride and silica quarter-wave bilayers are measured using the cantilever ring-down method. We show, for the first time, that the bulk and shear loss angles of the coatings can be obtained from the cantilever ring-down measurement, and we use the bulk and shear losses to calculate the coating thermal noise of silicon nitride and silica high-reflector coatings. The mechanical loss angle of the silicon nitride and silica bilayer is dispersive with a linear weakly positive frequency dependence, and, hence, the coating thermal noise of the high reflectors show a weakly positive frequency dependence in addition to the normal $1/\sqrt{f}$ dependence. The coating thermal noise of the silicon nitride and silica high-reflector stack is compared to the lower limit of the coating thermal noise of the end test mirrors of ET-LF, KAGRA, LIGO Voyager, and the directly measured coating thermal noise of the current coatings of Advanced LIGO. The optical absorption of the silicon nitride and silica high reflector at 1550 nm is 45.9 ppm. Using a multimaterial system composed of seven pairs of ion-beam-sputter deposited $\mathrm{Ti}:{\mathrm{Ta}}_{2}{\mathrm{O}}_{5}$ and silica and nine pairs of silicon nitride and silica on a silicon substrate, the optical absorption can be reduced to 2 ppm, which meets the specification of LIGO Voyager.

Fundamental Quantum Limits of Multicarrier Optomechanical Sensors.

Optomechanical sensors involving multiple optical carriers can experience mechanically mediated interactions causing multimode correlations across the optical fields. One instance is laser-interferometric gravitational wave detectors which introduce multiple carrier frequencies for classical sensing and control purposes. An outstanding question is whether such multicarrier optomechanical sensors outperform their single-carrier counterpart in terms of quantum-limited sensitivity. We show that the best precision is achieved by a single-carrier instance of the sensor. For the current LIGO detection system this precision is already reachable.

Matrix heater in the gravitational wave observatory GEO 600.

Large scale laser interferometric gravitational wave detectors (GWDs), such as GEO 600 require high quality optics to reach their design sensitivity. The inevitable surface imperfections, inhomogeneities, and light-absorption induced thermal lensing in the optics, can convert laser light from the fundamental mode to unwanted higher order modes, and pose challenges to the operation and sensitivity of the GWDs. Here we demonstrate the practical implementation of a thermal projection system which reduces those unwanted effects via targeted spatial heating of the optics. The thermal projector consists of 108 individually addressable heating elements which are imaged onto the beam splitter of GEO 600. We describe the optimization of the spatial heating profile and present the obtained results.

Fundamentals of the orbit and response for TianQin

TianQin is a space-based laser interferometric gravitational wave detector aimed at detecting gravitational waves at low frequencies (0.1 mHz–1 Hz). It is formed by three identical drag-free spacecrafts in an equilateral triangular constellation orbiting around the Earth. The distance between each pair of spacecrafts is approximately . The spacecrafts are interconnected by infrared laser beams forming up to three Michelson-type interferometers. The detailed mission design and the study of science objectives for the TianQin project depend crucially on the orbit and the response of the detector. In this paper, we provide the analytic expressions for the coordinates of the orbit for each spacecraft in the heliocentric-ecliptic coordinate system to the leading orders. This enables a sufficiently accurate study of science objectives and data analysis, and serves as a first step to further orbit design and optimization. We calculate the response of a single Michelson detector to plane gravitational waves in arbitrary waveform which is valid in the full range of the sensitive frequencies. It is then used to generate the more realistic sensitivity curve of TianQin. We apply this model on a reference white-dwarf binary as a proof of principle.

Optical performance of large-area crystalline coatings.

Given their excellent optical and mechanical properties, substrate-transferred crystalline coatings are an exciting alternative to amorphous multilayers for applications in precision interferometry. The high mechanical quality factor of these single-crystal interference coatings reduces the limiting thermal noise in precision optical instruments such as reference cavities for narrow-linewidth laser systems and interferometric gravitational wave detectors. In this manuscript, we explore the optical performance of GaAs/AlGaAs crystalline coatings transferred to 50.8-mm (2-inch) diameter fused silica and sapphire substrates. We present results for the transmission, scattering, absorption, and surface quality of these prototype samples including the defect density and micro-roughness. These novel coatings exhibit optical performance on par with state-of-the-art dielectric structures, encouraging further work focused on the fabrication of larger optics using this technique.

Silicon nitride films fabricated by a plasma-enhanced chemical vapor deposition method for coatings of the laser interferometer gravitational wave detector

Silicon is a potential substrate material for the large-areal-size mirrors of the next-generation laser interferometer gravitational wave detector operated in cryogenics. Silicon nitride thin films uniformly deposited by a chemical vapor deposition method on large-size silicon wafers is a common practice in the silicon integrated circuit industry. We used plasma-enhanced chemical vapor deposition to deposit silicon nitride films on silicon and studied the physical properties of the films that are pertinent to application of mirror coatings for laser interferometer gravitational wave detectors. We measured and analyzed the structure, optical properties, stress, Young's modulus, and mechanical loss of the films, at both room and cryogenic temperatures. Optical extinction coefficients of the films were in the ${10}^{\ensuremath{-}5}$ range at 1550-nm wavelength. Room-temperature mechanical loss of the films varied in the range from low ${10}^{\ensuremath{-}4}$ to low ${10}^{\ensuremath{-}5}$ within the frequency range of interest. The existence of a cryogenic mechanical loss peak depended on the composition of the films. We measured the bond concentrations of $\mathrm{N}─\mathrm{H}$, $\mathrm{Si}─\mathrm{H}$, $\mathrm{Si}─\mathrm{N}$, and $\mathrm{Si}─\mathrm{Si}$ bonds in the films and analyzed the correlations between bond concentrations and cryogenic mechanical losses. We proposed three possible two-level systems associated with the $\mathrm{N}─\mathrm{H}$, $\mathrm{Si}─\mathrm{H}$, and $\mathrm{Si}─\mathrm{N}$ bonds in the film. We inferred that the dominant source of the cryogenic mechanical loss for the silicon nitride films is the two-level system of exchanging position between a ${\mathrm{H}}^{+}$ and electron lone pair associated with the $\mathrm{N}─\mathrm{H}$ bond. Under our deposition conditions, superior properties in terms of high refractive index with a large adjustable range, low optical absorption, and low mechanical loss were achieved for films with lower nitrogen content and lower $\mathrm{N}─\mathrm{H}$ bond concentration. Possible pairing of the silicon nitride films with other materials in the quarter-wave stack is discussed.

Quantum estimation of parameters of classical spacetimes

We describe a quantum limit to measurement of classical spacetimes. Specifically, we formulate a quantum Cramér-Rao lower bound for estimating the single parameter in any one-parameter family of spacetime metrics. We employ the locally covariant formulation of quantum field theory in curved spacetime, which allows for a manifestly background-independent derivation. The result is an uncertainty relation that applies to all globally hyperbolic spacetimes. Among other examples, we apply our method to detection of gravitational waves with the electromagnetic field as a probe, as in laser-interferometric gravitational-wave detectors. Other applications are discussed, from terrestrial gravimetry to cosmology.