Suspension thermal noise and Opto-mechanics in gram-scale flexures

Abstract

Recent direct detections of gravitational waves by the Advanced Laser Interferometry Gravitational wave Observatory (LIGO) have opened a new field of astronomy. Upgrades to improve the sensitivity of detectors around the world promise a future of rich astronomical observations, which will both expand our knowledge of the universe and complement discoveries from electromagnetic astronomy. The detectable displacement signals caused by gravitational waves are extremely small and easily masked by noise. Suspension thermal noise is one of them. It couples into the detectors through the isolation systems that suspend and isolate the test mass mirrors, placing a fundamental limit on the displacement sensitivity of interferometric gravitational wave detectors. One way to mitigate this noise source is by careful selection and thorough characterisation of the materials used in these suspension and isolation systems. We used a Fabry-Perot cavity with one mirror mounted on a gram-scale flexure to study suspension thermal noise and opto-mechanical response of the system. The behaviour of this macroscopic system could then be used to evaluate the responses of a kilogram-scale opto-mechanical system, such as gravitational wave detectors. Thermal noise is governed by the Fluctuation-Dissipation Theorem, which links mechanical loss to the displacement caused by the thermal energy in each mode. In this thesis, a simple model using this theorem was developed to predict the thermal-noise-induced displacement of the flexures. We present the frequency distribution of thermal noise for flexures made of aluminium, niobium and silicon. Silicon in particular is a promising material for suspension systems in future gravitational wave detectors. These measurements are in the audio-frequency band between 10Hz and 10kHz and span up to an order of magnitude above and below the fundamental flexure resonances. Our analysis indicates that, for aluminium and niobium, structural noise dominates the displacement fluctuation spectra at low frequencies, whereas thermoelastic noise dominates at higher frequencies. The silicon flexure, as a result of careful design, shows a displacement spectrum dominated by structural damping both below and above the fundamental resonance. Results from a second niobium flexure provide evidence for qualitative changes in the displacement spectrum caused by surface damage in addition to a reduction of the mechanical quality factor. The measurement results show good agreement when compared to the simple model. Lastly, we show experimental results of a statically and dynamically stable opto- mechanical cavity. The system is driven by a single optical field without external feedback control. The cavity exhibits stiffening due to radiation-pressure force, as well as an optically induced damping which cannot be due to radiation pressure. The optical damping is measured to be four orders of magnitude larger than the mechanical damping of the flexure. The cavity is shown to self-lock under the combined influence of these effects.