Topics in Gravitational Wave Physics: Quantum Theory for Detector Improvement and High-Precision Modeling of Binary Black Hole Ringdown Waveform

Abstract

This thesis covers topics in gravitational wave physics, including optomechanical measurement theory, novel detection schemes (PT-symmetric interferometer, matter-wave interferometer), and modeling of binary black hole ringdown waveform.

Measurements are accomplished through the interaction between signal and measurement devices. Identifying the nature of couplings is an important step in designing setups for specific applications. In Chapter II, we develop a general framework based on the system Hamiltonian to unambiguously classify optomechanical couplings. We add the new type, “coherent coupling”, where the mechanical oscillation couples several non-degenerate optical modes supported in the cavity. We give examples of different couplings, discuss in detail one particular case of the coherent coupling, and demonstrate its benefits in optomechanical experiments. Our general framework allows the design of optomechanical systems in a methodological way, to precisely exploit the strengths of some particular optomechanical couplings.

Conventional resonant detectors are subject to bandwidth-peak sensitivity tradeoff, which can be traced back to the quantum Cramer-Rao Bound. Chapters III and IV in this thesis are devoted to the study of PT-symmetric amplifier, which is a stable quantum amplification scheme enabled by two-mode non-degenerate parametric amplification. In Chapter III, we study stability and sensitivity improvements for laser-interferometric gravitational-wave detectors and microwave cavity axion detectors, under Hamiltonian formalism adopting single-mode and resolvedsideband approximations. In Chapter IV, we go beyond these approximations and consider realistic parameters in the optomechanical realization of PT-symmetric interferometer for gravitational detection. We show that the main conclusion concerning stability remains intact using Nyquist analysis and a detailed time-domain simulation.

The detection method of gravitational waves is developed with linear quantum measurement theory. In Chapter V, we extend the usage of this theory to another kind of measurement device— matter-wave interferometers, which have been widely discussed as an important platform for many high-precision measurements. This theory allows us to consider fluctuations from both atoms and light and leads to a detailed analysis of back-action (of light back onto the atoms) and its effect on dynamics and measurement noise in atom interferometry. From this analysis, we obtain a Standard Quantum Limit for matter-wave interferometry. We also give a comparison between the LIGO detector and matter-wave interferometer from the perspective of quantum measurement.

In Chapter VI, we switch focus from measurement to gravitational wave sources. Specifically, we study high-frequency gravitational radiation from the ringdown of a binary black hole merger. We study the high-precision modeling on both temporal and spatial features of ringdown wave to propose a more complete test of General Relativity. We show that spin-weighted spheroidal harmonics, rather than spin-weighted spherical harmonics, better represent ringdown angular patterns. We also study the correlation between progenitor binary properties and the excitation of quasinormal modes, including higher-order angular modes, overtones, prograde and retrograde modes. This chapter seeks to provide an analytical strategy and inspire the future development of ringdown tests using data from real gravitational wave events.