Laser Interferometric Gravitational Wave Detectors Research Articles

Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors

Long-baseline laser-interferometer gravitational-wave GW detectors are operating at a factor of 10 in amplitude above the standard quantum limit SQL within a broad frequency band in the sense that f f. Such a low-noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the possibility of experimentally probing macroscopic quantum mechanics MQM—quantum mechanical behavior of objects in the realm of everyday experience—using GW detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer’s classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum-state preparation and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses and the performance of the planned Advanced LIGO interferometers in quantum-state preparation.

Suppression of parametric instabilities in future gravitational wave detectors using damping rings

The next generation of laser interferometer gravitational wave detectors requires optical cavities with stored power approaching 1 MW. However, such proposed cavities are subject to parametric instability where carrier power resonantly downconverts to drive a large number of test mass acoustic resonances. Damping rings on the test mass circumference have been proposed as a means of suppressing such instabilities, and in previous work, the affect of such a ring on test mass acoustic modes and thermal noise was analysed. The purpose of this paper is to investigate the general issue of parametric instability suppression with damping rings. We determine the optimal position and geometry of damping rings, so as to obtain sufficient instability suppression with the least thermal noise penalty. It is shown that unilateral stability can be attained with a ring damper alone at the expense of a 20% increase in thermal noise, while if just one optical mode is suppressed, there is only a 5% noise penalty.

Coupling of lateral grating displacement to the output ports of a diffractive Fabry–Perot cavity

Diffraction gratings have been proposed as core elements in future laser-interferometric gravitational-wave detectors. In this paper, we use a steady-state technique to derive coupling of lateral grating displacement to the output ports of a diffractive Fabry-Perot cavity. By introducing a signal to noise ratio (SNR) for each of the three cavity output ports the magnitude of the noise sidebands originating from lateral grating displacement are compared to the magnitude of a potential gravitational wave signal. For the example of a 3km long Fabry-Perot cavity featuring parameters similar to the planned Advanced Virgo instrument, we found that the forward-reflecting grating port offers the highest SNR at low frequencies. Furthermore, for this example suspension requirements for lateral isolation were computed, and a factor of twenty relaxation at a frequency of 10Hz can be gained over the transmitted port by observing the forward-reflected port.

Length Standard: Effects of Air Refractivity and Vacuum for a Laser Interferometer

The current definition of the meter has been based on ‘the speed of light’ since 1983. Length standard measurements are performed using laser interferometers and are generally conducted in air. Specifically, a long length (referred to as “distance”) is measured in air. The accuracy of distance measurements in air is limited by the refractivity of air, which can be determined with an accuracy of only approximately 10-8. For smaller uncertainties, we must measure distances in vacuum. For example, both laser strain meters, which are used for tectonic measurements, and laser interferometer gravitational wave detectors employ long-baseline interferometers in vacuum. Since the sensitivity of gravitational wave detectors become worse by residual gases in vacuum, a pressure of less than 10-5 Pa is required for laser beam paths in the interferometer.

Feedback control of thermal lensing in a high optical power cavity

This paper reports automatic compensation of strong thermal lensing in a suspended 80 m optical cavity with sapphire test mass mirrors. Variation of the transmitted beam spot size is used to obtain an error signal to control the heating power applied to the cylindrical surface of an intracavity compensation plate. The negative thermal lens created in the compensation plate compensates the positive thermal lens in the sapphire test mass, which was caused by the absorption of the high intracavity optical power. The results show that feedback control is feasible to compensate the strong thermal lensing expected to occur in advanced laser interferometric gravitational wave detectors. Compensation allows the cavity resonance to be maintained at the fundamental mode, but the long thermal time constant for thermal lensing control in fused silica could cause difficulties with the control of parametric instabilities.

Quantum noise in differential-type gravitational-wave interferometer and signal recycling

In the sensitivity of laser interferometer gravitational-wave detectors, there exists the standard quantum limit (SQL), derived from Heisenberg's uncertainty relation. The SQL can be overcome using the quantum correlation between shot noise and radiation-pressure noise. One of the methods to overcome SQL, signal recycling, is considered so far only in a recombined-type interferometer such as Advanced-LIGO, LCGT, and GEO600. In this paper, we investigated quantum noise and signal recycling in a differential-type interferometer. We also applied it to a real detector and compared the sensivity with a recombined type.

Space-based gravitational wave detection with LISA

The laser interferometer space antenna will be the first space-based laser interferometric gravitational wave detector. This paper provides a brief introduction to the LISA mission and science goals, highlighting the differences from ground-based detectors. A tutorial of the LISA measurement concept is presented focusing on the LISA interferometry with a summary of laser frequency noise cancellation and clock noise removal schemes.

Increasing future gravitational-wave detectors’ sensitivity by means of amplitude filter cavities and quantum entanglement

The future laser interferometric gravitational-wave detectors' sensitivity can be improved using squeezed light. In particular, recently a scheme which uses the optical field with frequency-dependent squeeze factor, prepared by means of a relatively short ({approx}30 m) amplitude filter cavity, was proposed [Thomas Corbitt, Nergis Mavalvala, and Stan Whitcomb, Phys. Rev. D 70, 022002 (2004).]. Here we consider an improved version of this scheme, which allows one to further reduce the quantum noise by exploiting the quantum entanglement between the optical fields at the filter cavity two ports.

Observation of enhanced optical spring damping in a macroscopic mechanical resonator and application for parametric instability control in advanced gravitational-wave detectors

We show that optical spring damping in an optomechanical resonator can be enhanced by injecting a phase delay in the laser frequency-locking servo to rotate the real and imaginary components of the optical spring constant. This enhances damping at the expense of optical rigidity. We demonstrate enhanced parametric damping which reduces the $Q$ factor of a 0.1-kg-scale resonator from $1.3\ifmmode\times\else\texttimes\fi{}{10}^{5}$ to $6.5\ifmmode\times\else\texttimes\fi{}{10}^{3}$. By using this technique adequate optical spring damping can be obtained to damp parametric instability predicted for advanced laser interferometer gravitational-wave detectors.

Measurement and simulation of laser power noise in GEO 600

This paper describes measurements and simulations related to power fluctuations of the laser light in the GEO 600 laser-interferometric gravitational wave detector. Measurements of the relative fluctuations of the light power at three different ports of the main interferometer are presented. In addition, measurements and simulations of the coupling transfer functions from power fluctuations at the input laser to these ports are shown. The transfer function from the input laser to the output port of the interferometer is found to be non-trivial. Despite this, the numerical simulation produces an excellent match to it and gives insight to the mechanisms leading to the complicated shape. Furthermore, the coupling transfer functions of power fluctuations to the main (heterodyne) detector outputs are measured and simulated. These are used to evaluate the level with which laser power fluctuations contribute to the overall noise level of the instrument.

Generation of a stable low-frequency squeezed vacuum field with periodically poled KTiOPO_4 at 1064 nm

We report the generation of a stable continuous-wave low-frequency squeezed vacuum field with a squeezing level of 7.4+/-0.1 dB at 1064 nm, the wavelength at which laser-interferometric gravitational wave (GW) detectors operate, using periodically poled KTiOPO4 (PPKTP) in a subthreshold optical parametric oscillator. The squeezing was observed in a broad band of frequencies above 700 Hz where the sensitivity of the currently operational GW detectors is limited by shot noise. PPKTP has the advantages of higher nonlinearity, smaller pump-induced seed absorption, and wider temperature tuning range than alternative nonlinear materials such as MgO-doped or periodically poled LiNbO3, and is, therefore, an excellent material for generation of squeezed vacuum fields for application to laser interferometers for GW detection.

Phase and alignment noise in grating interferometers

Diffraction gratings have been proposed as core optical elements in future laser interferometric gravitational-wave detectors. In this paper, we derive equations for the coupling between alignment noise and phase noise at diffraction gratings. In comparison to a standard reflective component (mirror or beam splitter) the diffractive nature of the gratings causes an additional coupling of geometry changes into alignment and phase noise. Expressions for the change in angle and optical path length of each outgoing beam are provided as functions of a translation or rotation of the incoming beam with respect to the grating. The analysis is based entirely on the grating equation and the geometry of the set-up. We further analyse exemplary optical set-ups which have been proposed for the use in future gravitational-wave detectors. We find that the use of diffraction gratings yields a strong coupling of alignment noise into phase noise. By comparing the results with the specifications of current detectors, we show that this additional noise coupling results in new, challenging requirements for the suspension and isolation systems for optical components.

Optical modulation techniques for length sensing and control of optical cavities

We present a discussion of the use of amplitude modulation techniques with regard to the length sensing and control of optical cavities for laser interferometric gravitational-wave detectors. Traditional radio-frequency amplitude modulation techniques automatically include phase modulation as a product of the modulation process, which can contaminate the signal after demodulation. In particular, with many length-sensing and control schemes the detected signals are demodulated in quadrature, which, in the case of a traditional amplitude modulation scheme, will result in offsets due to the additional phase modulation. We demonstrate this effect using a simple optical cavity configuration and show that minor adjustments to the modulator system can be used to compensate for the extra modulation components and provide additional flexibility.

Quantum noise in differential-type gravitational-wave interferometer and signal recycling

There exists the standard quantum limit (SQL), derived from Heisenberg's uncertainty relation, in the sensitivity of laser interferometer gravitational-wave (GW) detectors. However, in the context of a full quantum-mechanical approach, SQL can be overcome using the correlation of shot noise and radiation-pressure noise. So far, signal recycling, which is one of the methods to overcome SQL, is considered only in a recombined-type interferometer such as Advanced LIGO, LCGT, and GEO600. In this paper, we investigated quantum noise and the possibility of signal recycling in a differential-type interferometer. As a result, we found that signal recycling is possible and creates at most three dips in the sensitivity curve of the detector due to two coupled resonators. The additional third dip makes it possible to decrease quantum noise at low frequencies, keeping the moderate sensitivity at high frequencies. Then, taking advantage of the third dip and comparing the sensitivity of a differential-type interferometer with that of a next-generation Japanese GW interferometer, LCGT, we found that signal-to-noise ratio (SNR) of inspiral binary is improved by a factor of {approx_equal}1.43 for neutron star binary, {approx_equal}2.28 for 50M{sub {center_dot}} black hole binary, and {approx_equal}2.94 for 100M{sub {center_dot}} black hole binary. We also found that powermore » recycling to increase laser power is possible in our signal-recycling configuration of a detector.« less

Quantum-noise power spectrum of fields with discrete classical components

We present an algorithmic approach to calculate the quantum-noise spectral density of photocurrents generated by optical fields with arbitrary discrete classical spectrum in coherent or squeezed states. The measurement scheme may include an arbitrary number of demodulations of the photocurrent. Thereby, our method is applicable to the general heterodyne detection scheme which is implemented in many experiments. For some of these experiments, e.g. in laser-interferometric gravitational-wave detectors, a reliable prediction of the quantum noise of fields in coherent and squeezed states plays a decisive role in the design phase and detector characterization. Still, our investigation is limited in two ways. First, we only consider coherent and squeezed states of the field and second, we demand that the photocurrent depends linearly on the field's vacuum amplitudes which means that at least one of the classical components is comparatively strong.

Utility investigation of artificial time delay in displacement-noise-free interferometers

Laser interferometer gravitational wave detectors are usually limited by displacement noise in their lower frequency band. Recently, theoretical proposals have been put forward to construct schemes of interferometry that are insusceptible to displacement noise as well as classical laser noise. These so-called displacement-noise-free interferometry (DFI) schemes take advantage of the difference between gravitational waves and displacement noise in their effects on light propagation. However, since this difference diminishes in lower frequencies (i.e., $\ensuremath{\Omega}<c/{\mathcal{L}}_{D}$, with ${\mathcal{L}}_{D}$ the size of the detector), shot-noise-limited sensitivity of DFI schemes deteriorates dramatically in these frequencies---exactly the regime in which they are supposed to be superior, thereby limiting their applicability. In this paper, we explore the obvious possibility of increasing the effective size of the detector in the time domain, by introducing artificial time delays (${\mathcal{T}}_{D}\ensuremath{\gg}{\mathcal{L}}_{D}/c$) into the interferometry scheme, with the hope of improving low-frequency sensitivity. We found that sensitivity can only be improved by schemes in which fluctuations in the artificial time delays are not canceled.

GEO600: building a gravitational wave observatory

An international network of laser-interferometric gravitational wave detectors is nearing the end of the main commissioning phase and will soon enter into an extended observational period, collecting data for a duration of order one year. This article outlines the construction, design and commissioning of the GEO 600 gravitational wave observatory. GEO 600 is a laserinterferometric gravitational wave detector which has 600 m long arms and uses advanced optical and suspension techniques to achieve a sensitivity comparable to the longer base-line detectors currently operating in the U.S.A and Europe.

A new apparatus for mechanical Q-factor measurements between 5 and 300 K

Today’s laser interferometric gravitational wave detectors are sensitivity limited by thermal noise of the optical components within the detection band of about 0.1–1 kHz. Cooling down these parts to cryogenic temperatures is a promising technique to increase the sensitivity of the gravitational wave detectors by at least one to two orders of magnitudes. Cooling substantially increases the material Q-factor contributing to reduced thermal noise. This article describes a new cryogenic apparatus which allows the measurement of the mechanical Q-factor – as a measure of internal losses – in a temperature range from 5 K up to 300 K. The requirements for cryogenic Q-factor measurements and their realization are shown. The measuring technique as well as the key parameters are discussed. Exemplary, measurements on crystalline quartz and silicon (1 0 0) are given to characterize the setup.

Improvement in the shot noise of a laser interferometer gravitational wave detector by means of an output mode-cleaner

The sensitivity of a gravitational wave detector based on a laser interferometer is limited by photon shot noise for signals with frequencies above a few hundred hertz. The amplitude of this noise depends on the interferometer fringe contrast. By means of a complete simulation, we show that using a short optical cavity placed at the interferometer output port, the contrast can be significantly improved and the optimal sensitivity recovered. Such an output mode-cleaner has been realized and tested. The adopted design and the results of the tests are presented.

Sub-standard-quantum-limit sensitivity via optical rigidity in the advanced LIGO interferometer with optical losses

The ``optical springs'' regime of the signal-recycled configuration of laser interferometric gravitational-wave detectors is analyzed taking in account optical losses in the interferometer arm cavities. This regime allows to obtain sensitivity better than the Standard Quantum Limits both for a free test mass and for a conventional harmonic oscillator. The optical losses restrict the gain in sensitivity and achievable signal-to-noise ratio. Nevertheless, for parameters values planned for the Advanced LIGO gravitational-wave detector, this restriction is insignificant.