Brownian Thermal Noise in Interferometric Gravitational Wave Detectors and Single Photon Optomechanics

The Laser Interferometric Gravitational-Wave Observatory (LIGO) is designed to detect the Gravitational Waves (GW) predicted by Albert Einstein’s general theory of relativity. The advanced LIGO project is ongoing an upgrade to increase the detection sensitivity by more than a factor of 10, which will make the events detection a routine occurrence. In addition to using higher power lasers, heavier test mass, and better isolation systems, several new designs and techniques are proposed in the long-term upgrade, such as modifying the optics configuration to reduce the quantum noise, active noise cancellation of the Newtonian noise, optimizing the coating structure, and employing non-Guassian laser beams etc. In the first part of my thesis (Chapters 2 and 3), I apply statistical mechanics and elastostatics to the LIGO coated mirrors, and study the thermal fluctuations that dominate advanced LIGO’s most sensitive frequency band from 40 Hz to 200 Hz. In particular, in Chapter 2, I study the so-called coating Brownian noise, fluctuations of mirrors coated with multiple layers of dielectrics due to internal friction. Assuming coating materials to be isotropic and homogeneous, I calculate the cross spectra of Brownian fluctuations in the bulk and shear strains of the coating layers, as well as fluctuations in the height of the coating-substrate interface. The additional phase shifting and back-scattering caused by photo elastic effects are also considered for the first time. In Chapter 3, I study whether it is realistic to adopt higher-order Laguerre-Gauss modes in LIGO, in order to mitigate the effect of mirror thermal noise. We investigate the effect on the detector’s contrast defect caused by the mode degeneracy. With both analytical calculation and numerical simulation, we show that with this approach, the detector’s susceptibility to mirror figure errors is reduced greatly compared to using the nondegenerate modes, therefore making it unacceptable for LIGO requirements. For the future GW detectors, with much lower noises and higher sensitivity, this might be used to investigate the quantum behaviors of macroscopic mechanical objects. In recent years the linear optomechanical systems with cavity modes coupling to a mechanical oscillator have been studied extensively. In the second part of my thesis (Chapter 4), I study the interaction between a single photon and a high-finesse cavity with a movable mirror, in the so-called strong coupling regime, where v the recoil of the photon can cause significant change in the momentum of the mirror. The results are applied to analyze the case with a Fabry-Perot cavity. We also present that with engineering the photon wave function, it is possible to prepare the oscillator into an arbitrary quantum state.