Parametric instabilities and their control in advanced interferometer gravitational-wave detectors

Observing the optical modes of parametric instability

Parametric instability (PI) is a phenomenon that results from resonant interactions between optical and acoustic modes of a laser cavity. This is problematic in gravitational wave interferometers where the high intracavity power and low mechanical loss mirror suspension systems create an environment where three-mode PI will occur without intervention. We demonstrate a technique for real-time imaging of the amplitude and phase of the optical modes of PI yielding, to the best of the authors' knowledge, the first ever images of this phenomenon which could form part of active control strategies for future detectors.

Stepped beam pipes and helical baffles for scattered light absorption in future gravitational wave detectors

The next generation interferometric gravitational wave detectors require arm lengths measured in tens of kilometers, with each cavity storing megawatts of optical power. The beams are contained in ultrahigh vacuum pipes. Scattered interferometer light in the pipes may reenter the cavities and inject extra noise. The pipes are, therefore, provided with optical baffles necessary to eliminate the scattered light. The design of the vacuum pipes and of the optical baffles is tightly intertwined. We present a thorough discussion that opens the door to the design of an optimized stepped-diameter vacuum pipe system using novel helical baffles. Our analysis suggests that a more efficient pipe design (with special reference to scattered light) may use spiral baffles and sectioned stepped tubes.

Angular instability in high optical power suspended cavities

Advanced gravitational wave detectors use suspended test masses to form optical resonant cavities for enhancing the detector sensitivity. These cavities store hundreds of kilowatts of coherent light and even higher optical power for future detectors. With such high optical power, the radiation pressure effect inside the cavity creates a sufficiently strong coupling between test masses whose dynamics are significantly altered. The dynamics of two independent nearly free masses become a coupled mechanical resonator system. The transfer function of the local control system used for controlling the test masses is modified by the radiation pressure effect. The changes in the transfer function of the local control systems can result in a new type of angular instability which occurs at only 1.3% of the Sidles-Sigg instability threshold power. We report the experimental results on a 74 m suspended cavity with a few kilowatts of circulating power, for which the power to mass ratio is comparable to the current Advanced LIGO. The radiation pressure effect on the test masses behaves like an additional optical feedback with respect to the local angular control, potentially making the mirror control system unstable. When the local angular control system is optimised for maximum stability margin, the instability threshold power increases from 4 kW to 29 kW. The system behaviour is consistent with our simulation, and the power dependent evolution of both the cavity soft and hard mode is observed. We show that this phenomenon is likely to significantly affect the proposed gravitational wave detectors that require very high optical power.

First Demonstration of Electrostatic Damping of Parametric Instability at Advanced LIGO

Interferometric gravitational wave detectors operate with high optical power in their arms in order to achieve high shot-noise limited strain sensitivity. A significant limitation to increasing the optical power is the phenomenon of three-mode parametric instabilities, in which the laser field in the arm cavities is scattered into higher-order optical modes by acoustic modes of the cavity mirrors. The optical modes can further drive the acoustic modes via radiation pressure, potentially producing an exponential buildup. One proposed technique to stabilize parametric instability is active damping of acoustic modes. We report here the first demonstration of damping a parametrically unstable mode using active feedback forces on the cavity mirror. A 15 538 Hz mode that grew exponentially with a time constant of 182 sec was damped using electrostatic actuation, with a resulting decay time constant of 23 sec. An average control force of 0.03 nN was required to maintain the acoustic mode at its minimum amplitude.

Near-self-imaging cavity for three-mode optoacoustic parametric amplifiers using silicon microresonators

Three-mode optoacoustic parametric amplifiers (OAPAs), in which a pair of photon modes are strongly coupled to an acoustic mode, provide a general platform for investigating self-cooling, parametric instability and very sensitive transducers. Their realization requires an optical cavity with tunable transverse modes and a high quality-factor mirror resonator. This paper presents the design of a table-top OAPA based on a near-self-imaging cavity design, using a silicon torsional microresonator. The design achieves a tuning coefficient for the optical mode spacing of 2.46  MHz/mm. This allows tuning of the mode spacing between amplification and self-cooling regimes of the OAPA device. Based on demonstrated resonator parameters (frequencies ∼400  kHz and quality-factors ∼7.5×10(5) we predict that the OAPA can achieve parametric instability with 1.6 μW of input power and mode cooling by a factor of 1.9×10(4) with 30 mW of input power.

First long-term application of squeezed states of light in a gravitational-wave observatory

We report on the first long-term application of squeezed vacuum states of light to improve the shot-noise-limited sensitivity of a gravitational-wave observatory. In particular, squeezed vacuum was applied to the German-British detector GEO 600 during a period of three months from June to August 2011, when GEO 600 was performing an observational run together with the French-Italian Virgo detector. In a second period, the squeezing application continued for about 11 months from November 2011 to October 2012. During this time, squeezed vacuum was applied for 90.2% (205.2 days total) of the time that science-quality data were acquired with GEO 600. A sensitivity increase from squeezed vacuum application was observed broadband above 400 Hz. The time average of gain in sensitivity was 26% (2.0 dB), determined in the frequency band from 3.7 to 4.0 kHz. This corresponds to a factor of 2 increase in the observed volume of the Universe for sources in the kHz region (e.g., supernovae, magnetars). We introduce three new techniques to enable the long-term application of squeezed light, and show that the glitch rate of the detector did not increase from squeezing application. Squeezed vacuum states of light have arrived as a permanent application, capable of increasing the astrophysical reach of gravitational-wave detectors.

Theoretical analysis of mechanical displacement measurement using a multiple cavity mode transducer

We present an optomechanical displacement transducer that relies on three cavity modes parametrically coupled to a mechanical oscillator and whose frequency spacing matches the mechanical resonance frequency. The additional resonances allow reaching the standard quantum limit at a substantially lower input power (compared to the case of a single cavity mode), as both sensitivity and quantum backaction are enhanced. Furthermore, it is shown that in the case of multiple cavity modes, coupling between the modes is induced via reservoir interaction, e.g., enabling quantum backaction noise cancellation. Experimental implementation of the schemes is discussed in both the optical and microwave domain.

Three-mode optoacoustic parametric amplifier: a tool for macroscopic quantum experiments

We introduce the three-mode optoacoustic parametric amplifier (OAPA), a close analog of the optical parametric amplifier, for macroscopic quantum mechanics experiments. The radiation pressure reaction of light on the reflective surface of an acoustic resonator provides a nonlinearity similar to the Kerr effect in the optical parametric amplifier. The OAPA can be tuned to operate in a positive gain regime where acoustic signals are amplified or in a negative gain regime where acoustic modes are cooled. Compared with conventional optoacoustic devices, (i) the OAPA incorporates two transverse cavity modes such that the carrier and sideband fields simultaneously resonate, and (ii) it is less susceptible to the laser phase and amplitude noise. These two features significantly ease the experimental requirements for cooling of acoustic modes to their quantum-ground state and creating entangled pairs of phonons and photons.

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.

Cooling of a Gram-Scale Cantilever Flexure to 70 mK with a Servo-Modified Optical Spring

A series of recent articles have presented results demonstrating optical cooling of macroscopic objects, highlighting the importance of this phenomenon for investigations of macroscopic quantum mechanics and its implications for thermal noise in gravitational wave detectors. In this Letter, we present a measurement of the off-resonance suspension thermal noise of a 1 g oscillator, and we show that it can be cooled to just 70 mK. The cooling is achieved by using a servo to impose a phase delay between oscillator motion and optical force. A model is developed to show how optical rigidity and optical cooling can be interchangeable using this technique.

Numerical calculations of diffraction losses in advanced interferometric gravitational wave detectors

Knowledge of the diffraction losses in higher-order modes of large optical cavities is essential for predicting three-mode parametric photon-phonon scattering, which can lead to mechanical instabilities in long-baseline gravitational wave detectors. We explore different numerical methods in order to determine the diffraction losses of the higher-order optical modes. Diffraction losses not only affect the power buildup inside the cavity but also influence the shape and frequency of the mode, which ultimately affect the parametric instability gain. Results depend on both the optical mode shape (order) and the mirror diameter. We also present a physical interpretation of these results.

Chaotically spiking canards in an excitable system with 2D inertial fast manifolds

We introduce a new class of excitable systems with two-dimensional fast dynamics that includes inertia. A novel transition from excitability to relaxation oscillations is discovered where the usual Hopf bifurcation is followed by a cascade of period doubled and chaotic small excitable attractors and, as they grow, by a new type of canard explosion where a small chaotic background erratically but deterministically triggers excitable spikes. This scenario is also found in a model for a nonlinear Fabry-Perot cavity with one pendular mirror.

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.

Compensation of strong thermal lensing in high-optical-power cavities

In an experiment to simulate the conditions in high optical power advanced gravitational wave detectors, we show for the first time that the time evolution of strong thermal lenses follows the predicted infinite sum of exponentials (approximated by a double exponential), and that such lenses can be compensated using an intracavity compensation plate heated on its cylindrical surface. We show that high finesse approximately 1400 can be achieved in cavities with internal compensation plates, and that mode matching can be maintained. The experiment achieves a wave front distortion similar to that expected for the input test mass substrate in the Advanced Laser Interferometer Gravitational Wave Observatory, and shows that thermal compensation schemes are viable. It is also shown that the measurements allow a direct measurement of substrate optical absorption in the test mass and the compensation plate.

Rayleigh scattering, absorption, and birefringence of large-size bulk single-crystal sapphire

While the thermomechanical properties of sapphire make it an excellent candidate of test mass for advanced laser interferometers, its optical quality is not well understood or well controlled. We have studied the results from high-resolution measurements of scattering, absorption, and birefringence in test-mass samples to better understand issues of quality. Samples show large-scale scattering structures clearly linked to the crystal-growth process. Samples characterized by the presence of point defects have significantly lower scattering (except at the point defects). In general on a large scale, high scattering also correlates with higher absorption and higher average birefringence inhomogeneity. However, on a smaller scale there is not a clear point-to-point correlation between scattering and absorption. Often a large-scale scattering structure is spatially displaced by tens of millimeters from a similar absorption structure, indicating that quite separate microscopic mechanisms give rise to scattering and absorption. The spatial displacements indicate that absorption centers and scattering centers are laid down during crystal growth at different distances from the solid-liquid interface. We suggest that absorption may be linked to F centers, while scattering may be linked to impurities such as iron.