We study the thermal-noise spectrum of multi-loop pendulum suspensions for test masses in interferometric gravitational-wave detectors. The dependence of the thermal noise on suspension parameters and on properties of the wire material is discussed for the situation in which the losses are dominated by the internal friction in the pendulum wires.
We describe a torsion pendulum with a large mass-quadrupole moment and a resonant frequency of 2.8 mHz, whose angle is measured using a modified Michelson interferometer. The system achieved noise levels of $\sim200\ \text{prad}/\sqrt{\text{Hz}}$ between 0.2-30 Hz and $\sim10\ \text{prad}/\sqrt{\text{Hz}}$ above 100 Hz. Such a system can be applied to a broad range of fields from the study of rotational seismic motion and elastogravity signals to gravitational wave observation and tests of gravity.
Low mass suspension systems with high-Q pendulum stages are used to enable quantum radiation pressure noise limited experiments. Utilising multiple pendulum stages with vertical blade springs and materials with high quality factors provides attenuation of seismic and thermal noise, however damping of these high-Q pendulum systems in multiple degrees of freedom is essential for practical implementation. Viscous damping such as eddy-current damping can be employed but introduces displacement noise from force noise due to thermal fluctuations in the damping system. In this paper we demonstrate a …
Current terrestrial gravitational-wave detectors operate at frequencies above 10 Hz. There is strong astrophysical motivation to construct low-frequency gravitational-wave detectors capable of observing 10 mHz - 10Hz signals. While space-based detectors provide one means of achieving this end, one may also consider terretrial detectors. However, there are numerous technological challenges. In particular, it is difficult to isolate test masses so that they are both seismically isolated and freely falling under the influence of gravity at millihertz frequencies. We investigate the challenges of …
Thermal noise from the suspension fibres used in the mirror pendulums in current gravitational wave detectors is a critical noise source. Future detectors will require improved suspension performance with the specific ability to suspend much heavier masses to reduce radiation pressure noise, whilst retaining good thermal noise performance. In this letter, we propose and experimentally demonstrate a design for a large-scale fused silica suspension, demonstrating its suitability for holding an increased mass of 160 kg. We demonstrate the concepts for improving thermal noise via longer suspension…
Spring-antispring systems have been investigated as possible low-frequency seismic isolation in high-precision optical experiments. These systems provide the possibility to tune the fundamental resonance frequency to, in principle, arbitrarily low values, and at the same time maintain a compact design of the isolation system. It was argued though that thermal noise in spring-antispring systems would not be as small as one may naively expect from lowering the fundamental resonance frequency. In this paper, we present a detailed calculation of the suspension thermal noise for a specific spring-a…
The test mass suspensions of cryogenic gravitational-wave detectors such as the KAGRA project are tasked with extracting the heat deposited on the optics. Thus these suspensions have a non-uniform temperature, requiring the calculation of thermal noise in non-equilibrium conditions. While it is not possible to describe the whole suspension system with one temperature, the local temperature anywhere in the system is still well defined. We therefore generalize the application of the fluctuation-dissipation theorem to mechanical systems, pioneered by Saulson and Levin, to non-equilibrium conditio…
In interferometric cryogenic gravitational wave detectors, there are plans to cool mirrors and their suspension systems (payloads) in order to reduce thermal noise, that is, one of the fundamental noise sources. Because of the large payload masses (several hundred kg in total) and their thermal isolation, a cooling time of several months is required. Our calculation shows that a high-emissivity coating (e.g. a diamond-like carbon (DLC) coating) can reduce the cooling time effectively by enhancing radiation heat transfer. Here, we have experimentally verified the effect of the DLC coating on th…
It has been reported that treating music wire (high carbon steel wire) by cooling to cryogenic temperatures can enhance its mechanical properties with particular reference to those properties important for musical performance. We use such wire for suspending many of the optics in Advanced LIGO, the upgrade to LIGO - the Laser Interferometric Gravitational-Wave Observatory. Two properties that particularly interest us are mechanical loss and breaking strength. A decrease in mechanical loss would directly reduce the thermal noise associated with the suspension, thus enhancing the noise performan…
KAGRA is a 3-km cryogenic interferometric gravitational wave telescope located at an underground site in Japan. In order to achieve its target sensitivity, the relative positions of the mirrors of the interferometer must be finely adjusted with attached actuators. We have developed a model to simulate the length control loops of the KAGRA interferometer with realistic suspension responses and various noises for mirror actuation. Using our model, we have designed the actuation parameters to have sufficient force range to acquire lock as well as to control all the length degrees of freedom witho…
Cryogenic cooling of the test masses of interferometric gravitational wave detectors is a promising way to reduce thermal noise. However, cryogenic cooling limits the incident power to the test masses, which limits the freedom of shaping the quantum noise. Cryogenic cooling also requires short and thick suspension fibers to extract heat, which could result in the worsening of thermal noise. Therefore, careful tuning of multiple parameters is necessary in designing the sensitivity of cryogenic gravitational wave detectors. Here, we propose the use of particle swarm optimization to optimize the …
