Interferometric Gravitational Wave Research Articles

Vibration-free cryostat for low-noise applications of a pulse tube cryocooler

A new generation of gravitational wave interferometers is under study with the main goal to significantly improve the sensitivity of the detectors presently taking data. Two of the dominant noises which limit the present sensitivity of the interferometers are the thermal noise of the suspended optics and the thermal lensing process. At low temperature it is possible to reduce both these effects. Pulse tube cryocooler technology is a quite promising in this field, but it vibrates and it implies a mechanical link between the cooling element (cold finger) and the thermal load. We developed a vibration-free cryostat equipped with soft mechanical links to attenuate the transmission of cold finger vibration whose amplitude is attenuated by more than two orders of magnitude by means of an active system.

Radiation-pressure cooling and optomechanical instability of a micromirror

Recent table-top optical interferometry experiments and advances in gravitational-wave detectors have demonstrated the capability of optical interferometry to detect displacements with high sensitivity. Operation at higher powers will be crucial for further sensitivity enhancement, but dynamical effects caused by radiation pressure on the interferometer mirrors must be taken into account, and the appearance of optomechanical instabilities may jeopardize the stable operation of the next generation of interferometers. These instabilities are the result of a nonlinear coupling between the motion of the mirrors and the optical field, which modifies the effective dynamics of the mirror. Such 'optical spring' effects have already been demonstrated for the mechanical damping of an electromagnetic waveguide with a moving wall, the resonance frequency of a specially designed flexure oscillator, and the optomechanical instability of a silica microtoroidal resonator. Here we present an experiment where a micromechanical resonator is used as a mirror in a very high-finesse optical cavity, and its displacements are monitored with unprecedented sensitivity. By detuning the laser frequency with respect to the cavity resonance, we have observed a drastic cooling of the microresonator by intracavity radiation pressure, down to an effective temperature of 10 kelvin. For opposite detuning, efficient heating is observed, as well as a radiation-pressure-induced instability of the resonator. Further experimental progress and cryogenic operation may lead to the experimental observation of the quantum ground state of a micromechanical resonator, either by passive or active cooling techniques.

Erratum: Quasiphysical family of gravity-wave templates for precessing binaries of spinning compact objects: Application to double-spin precessing binaries [Phys. Rev. D70, 104003 (2004)

The gravitational waveforms emitted during the adiabatic inspiral of precessing binaries with two spinning compact bodies of comparable masses, evaluated within the post-Newtonian approximation, can be reproduced rather accurately by the waveforms obtained by setting one of the two spins to zero, at least for the purpose of detection by ground-based gravitational-wave interferometers. Here we propose to use this quasi-physical family of single-spin templates to search for the signals emitted by double-spin precessing binaries, and we find that its signal-matching performance is satisfactory for source masses (m1,m2) in [3,15]Msun x [3,15]Msun. For this mass range, using the LIGO-I design sensitivity, we estimate that the number of templates required to yield a minimum match of 0.97 is ~320,000. We discuss also the accuracy to which the single-spin template family can be used to estimate the parameters of the original double-spin precessing binaries.

Application of stochastic resonance in gravitational-wave interferometer

We investigate novel approach, which improves the sensitivity of gravitational wave (GW) interferometer due to stochastic resonance (SR) phenomenon, performing in additional nonlinear cavity (NC). The NC is installed in the output of interferometer before photodetector, so that optical signal emerging interferometer incidents on the NC and passes through it. Under appropriate circumstances a specific transformation of noisy signal inside the NC takes place, which results in the increase of output signal-to-noise ratio (SNR). As a result optical noisy signal of interferometer becomes less noisy after passing through the NC. The improvement of SNR is especially effective in bistable NC for wideband (several hundreds Hz) detection, when chirp GW signal is detected. Then SNR gain reaches amount ~ 10. When detection bandwidth is narrowed, the influence of SR mechanism gradually disappears, and SNR gain tends to 1. SNR gain also tends to 1 when the NC is gradually transformed to linear cavity. Proposed enhancement of SNR due to the SR is not dependent of noise type, which is prevalent in interferometer. Particularly proposed approach is capable to increase signal-to-displacement noise ratio.

Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order

We obtain an efficient description for the dynamics of nonspinning compact binaries moving in inspiralling eccentric orbits to implement the phasing of gravitational waves from such binaries at the 3.5 post-Newtonian (PN) order. Our computation heavily depends on the phasing formalism, presented in [T. Damour, A. Gopakumar, and B. R. Iyer, Phys. Rev. D 70, 064028 (2004)], and the 3PN accurate generalized quasi-Keplerian parametric solution to the conservative dynamics of nonspinning compact binaries moving in eccentric orbits, available in [R.-M. Memmesheimer, A. Gopakumar, and G. Sch\"afer, Phys. Rev. D 70, 104011 (2004)]. The gravitational-wave (GW) polarizations ${h}_{+}$ and ${h}_{\ifmmode\times\else\texttimes\fi{}}$ with 3.5PN accurate phasing should be useful for the earth-based GW interferometers, current and advanced, if they plan to search for gravitational waves from inspiralling eccentric binaries. Our results will be required to do astrophysics with the proposed space-based GW interferometers like LISA, BBO, and DECIGO.

Carrier mode selective working point and side band imbalance in LIGO I

In gravitational wave interferometers, the input laser beam is phase modulated to generate radio-frequency side bands that are used to lock the cavities. The mechanism is the following: the frequency of the side bands and the carrier is chosen in such a way that their response to small changes of the longitudinal degrees of freedom is different. This difference is therefore monitored and it serves as an error signal for controlling the optical cavity lengths, as they are linearly related to the set of observed phases between carrier and side bands. Among the others, one longitudinal degree of freedom is optimally sensitive to the space-time distortions propagating through the cosmos, as predicted by the general theory of relativity. The observation of the astrophysical signal relies on the measurement of that specific degree of freedom. The entire problem is more complex when the transverse degrees of freedom are taken into account, because the relative phase between the fields also depends on their overlap. In order to establish an unambiguous relation between length changes and phase measurements, there must be one circulating optical mode and the only difference between carrier and side bands must be their amplitude. We will show that the variability of the transverse degrees of freedom and their different actions on carrier and side band fields puts a severe limit on this assumption. Unless the system is made of perfect and perfectly matched optical cavities, it is never governed by one unique coherent state and any adjustment of the optical lengths results from a compromise between the lengths that are optimal for the carrier field and the side band ones. Such a compromise alters the correspondence between error signals and cavity lengths, calculated in the one-dimensional treatment. We assess the strength of this effect and relate it to the sensitivity of the instrument (which relies on the reconstruction of that correspondence) in realistic circumstances.

Frequency-dependent squeeze-amplitude attenuation and squeeze-angle rotation by electromagnetically induced transparency for gravitational-wave interferometers

We study the effects of frequency-dependent squeeze-amplitude attenuation and squeeze-angle rotation by electromagnetically induced transparency (EIT) on gravitational-wave (GW) interferometers. We propose the use of low-pass, bandpass, and high-pass EIT filters, an S-shaped EIT filter, and an intracavity EIT filter to generate frequency-dependent squeezing for injection into the antisymmetric port of GW interferometers. We find that the EIT filters have several advantages over the previous filter designs with regard to optical losses, compactness, and the tunability of the filter linewidth.

Squeezed-field injection for gravitational wave interferometers

In a recent table-top experiment, we demonstrated the compatibility of three advanced interferometer techniques for gravitational wave detection, namely power-recycling, detuned signal recycling and squeezed-field injection. The interferometer's signal-to-noise ratio was improved by up to 2.8 dB beyond the coherent state's shot-noise. This value was mainly limited by optical losses on the squeezed field. We present a detailed analysis of the optical losses in our experiment and provide an estimation of the possible nonclassical performance of a future squeezed-field enhanced GEO 600 detector.

The CLIO project

The CLIO project including a 100 m baseline cryogenic gravitational wave laser interferometer and a 100 m baseline geophysical strain meter was conducted in the Kamioka mine in Japan to investigate the technical feasibility of the large-scale cryogenic gravitational wave telescope (LCGT), which is planned to be constructed in the same Kamioka mine with 30 times longer baseline than CLIO, and to demonstrate the collaborative operation between these instruments about long-term continuous operation and gravitational wave signal veto analysis. About the cryogenic gravitational wave interferometer, the whole vacuum system and four cryostats, which house and cool sapphire mirrors, were constructed, and the required vacuum level of 10−6 mbar and the temperature of 8 K at the inner radiation shield in the cryostat were achieved. About the geophysical strain meter, the obtained geophysical strain in the Kamioka mine was successfully simulated with a finite element model with a good agreement with less than 5% error. The strain meter also verified a permanent ground step change of micrometre order due to some earthquakes. We present the recent progress about the CLIO project.

Beating quantum limits in an optomechanical sensor by cavity detuning

We study the quantum limits in an optomechanical sensor based on a detuned high-finesse cavity with a movable mirror. We show that the radiation pressure exerted on the mirror by the light in the detuned cavity induces a modification of the mirror dynamics and makes the mirror motion sensitive to the signal. This leads to an amplification of the signal by the mirror dynamics, and to an improvement of the sensor sensitivity beyond the standard quantum limit, up to an ultimate quantum limit only related to the mechanical dissipation of the mirror. This improvement is somewhat similar to the one predicted in detuned signal-recycled gravitational-wave interferometers, and makes a high-finesse cavity a model system to test these quantum effects.

Veto analysis for gravitational wave burst signals in TAMA300 data using an ALF filter

Data taken by interferometers for gravitational waves include noises caused by instabilities of the interferometers. Veto analyses to remove false events caused by detectors are then necessary to detect real gravitational waves or to obtain a lower upper limit. In this paper, a veto analysis with an environmental monitor channel was implemented. We calculate the trigger rate of TAMA300 data and demonstrate the veto analysis using an alternative linear fit (ALF) filter. A threshold for the environmental monitor channel signals is set to be at 1% of the false dismissal rate. The result shows a 1/10–1/1000 reduction of trigger event rates.

Generation of non-Gaussian flat laser beams

The use of non-Gaussian flat laser beams is currently under study to reduce the thermoelastic noise in the advanced gravitational wave interferometers. In this work we present a system based on two deformable mirrors to transform a Gaussian beam in a non-Gaussian flat beam. We use an approximated representation of flat beam based on the usual Hermite-Gaussian modes which is particularly useful when the flat beam is generated by using deformable mirrors. This system can be used either for flat beams generation or for beam matching in the mexican-hat mirrors Fabry–Perot cavities proposed for next generation of gravitational wave interferometers.

Comparison of parametric instabilities for different test mass materials in advanced gravitational wave interferometers

Following the recognition that parametric instabilities can significantly compromise the performance of advanced laser interferometer gravitational wave detectors, we compare the performance of three different test mass configurations: all fused silica test masses, all sapphire test masses and fused silica inboard test masses with sapphire end test masses. We show that the configuration with sapphire end test masses offers the opportunity for thermal tuning on a time scale comparable to the ring up time of oscillatory instabilities. This approach may enable significant reduction of parametric gain.

Cryogenic Q-factor measurement of optical substrates for optimization of gravitational wavedetectors

Future generations of gravitational wave interferometers are likely to be operated atcryogenic temperatures because one of the sensitivity limiting factors of the presentgeneration is the thermal noise of end mirrors and beam splitters that occurs in the opticalsubstrates as well as in the dielectric coatings. A possible method for minimizing thermalnoise is cooling to cryogenic temperatures, maximizing the mechanical quality factorQ, and maximizing the eigenfrequencies of the substrate. We present experimental details ofa new cryogenic apparatus that is suitable for the measurement of the temperature-dependentQ-factor of reflective, transmissive as well as nano-structured grating optics down to 5 K. Inparticular, the SQUID-based and the optical interferometric approaches to themeasurement of the amplitude of vibrating test bodies are compared and the method ofring-down recording is described.

Vibration Free Cryostat for cooling suspended mirrors

A new generation of gravitational wave interferometers is under study with the main goal to improve the sensitivity of the present detectors which are taking data now. Two of the dominant noises which limit the actual sensitivity of the interferometers are the thermal noise of the suspended optics and the thermal lensing process. At low temperature it is possible to reduce both the effects. However, lowering the temperature of the test masses without injecting vibration noise from the cooling system is a technological challenge. We present the first results on a new active system to dampen the vibrations from a pulse tube refrigerator coupled to a suspended mirror.

Squeezed-state source using radiation-pressure-induced rigidity

We propose an experiment to extract ponderomotive squeezing from an interferometer with high circulating power and low mass mirrors. In this interferometer, optical resonances of the arm cavities are detuned from the laser frequency, creating a mechanical rigidity that dramatically suppresses displacement noises. After taking into account imperfection of optical elements, laser noise, and other technical noise consistent with existing laser and optical technologies and typical laboratory environments, we expect the output light from the interferometer to have measurable squeezing of $5\phantom{\rule{0.3em}{0ex}}\mathrm{dB}$, with a frequency-independent squeeze angle for frequencies below $1\phantom{\rule{0.3em}{0ex}}\mathrm{kHz}$. This squeeze source is well suited for injection into a gravitational-wave interferometer, leading to improved sensitivity from reduction in the quantum noise. Furthermore, this design provides an experimental test of quantum-limited radiation pressure effects, which have not previously been tested.

Photothermal fluctuations as a fundamental limit to low-frequency squeezing in a degenerate optical parametric oscillator

We study the effect of photothermal fluctuations on squeezed states of light through the photo-refractive effect and thermal expansion in a degenerate optical parametric oscillator (OPO). We also discuss the effect of the photothermal noise in various cases and how to minimize its undesirable consequences. We find that the photothermal noise in the OPO introduces a significant amount of noise on phase squeezed beams, making them less than ideal for low-frequency applications such as gravitational wave (GW) interferometers, whereas amplitude squeezed beams are relatively immune to the photothermal noise and may represent the best choice for application in GW interferometers.

An off-axis Hartmann sensor for the measurement of absorption-induced wavefront distortion in advanced gravitational wave interferometers

We describe a novel off-axis Hartmann wavefront sensor, developed for the measurement of wavefront distortions induced in the mirrors (test masses) of advanced gravitational wave interferometers by residual absorption of the circulating laser power.

Status of Virgo

The gravitational wave interferometer Virgo is presently in its commissioning phase. The status of the detector will be presented, focusing attention on the results obtained during this last year of commissioning activity, running the interferometer in the recombined configuration (a Michelson interferometer with Fabry–Perot cavities in both the arms) and finally recycling the light beam into the interferometer.

Mathematical framework for simulation of quantum fields in complex interferometers using the two-photon formalism

We present a mathematical framework for simulation of optical fields in complex gravitational-wave interferometers. The simulation framework uses the two-photon formalism for optical fields and includes radiation pressure effects, an important addition required for simulating signal and noise fields in next-generation interferometers with high circulating power. We present a comparison of results from the simulation with analytical calculation and show that accurate agreement is achieved.