Citation
Yang, Huan (2013) Topics in GravitationalWave Science: Macroscopic Quantum Mechanics and Black Hole Physics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/JMRSDK55. http://resolver.caltech.edu/CaltechTHESIS:05222013233805938
Abstract
The theories of relativity and quantum mechanics, the two most important physics discoveries of the 20th century, not only revolutionized our understanding of the nature of spacetime and the way matter exists and interacts, but also became the building blocks of what we currently know as modern physics. My thesis studies both subjects in great depths  this intersection takes place in gravitationalwave physics.
Gravitational waves are "ripples of spacetime", long predicted by general relativity. Although indirect evidence of gravitational waves has been discovered from observations of binary pulsars, direct detection of these waves is still actively being pursued. An international array of laser interferometer gravitationalwave detectors has been constructed in the past decade, and a first generation of these detectors has taken several years of data without a discovery. At this moment, these detectors are being upgraded into secondgeneration configurations, which will have ten times better sensitivity. Kilogramscale test masses of these detectors, highly isolated from the environment, are probed continuously by photons. The sensitivity of such a quantum measurement can often be limited by the Heisenberg Uncertainty Principle, and during such a measurement, the test masses can be viewed as evolving through a sequence of nearly pure quantum states.
The first part of this thesis (Chapter 2) concerns how to minimize the adverse effect of thermal fluctuations on the sensitivity of advanced gravitational detectors, thereby making them closer to being quantumlimited. My colleagues and I present a detailed analysis of coating thermal noise in advanced gravitationalwave detectors, which is the dominant noise source of Advanced LIGO in the middle of the detection frequency band. We identified the two elastic loss angles, clarified the different components of the coating Brownian noise, and obtained their cross spectral densities.
The second part of this thesis (Chapters 37) concerns formulating experimental concepts and analyzing experimental results that demonstrate the quantum mechanical behavior of macroscopic objects  as well as developing theoretical tools for analyzing quantum measurement processes. In Chapter 3, we study the open quantum dynamics of optomechanical experiments in which a single photon strongly influences the quantum state of a mechanical object. We also explain how to engineer the mechanical oscillator's quantum state by modifying the single photon's wave function.
In Chapters 45, we build theoretical tools for analyzing the socalled "nonMarkovian" quantum measurement processes. Chapter 4 establishes a mathematical formalism that describes the evolution of a quantum system (the plant), which is coupled to a nonMarkovian bath (i.e., one with a memory) while at the same time being under continuous quantum measurement (by the probe field). This aims at providing a general framework for analyzing a large class of nonMarkovian measurement processes. Chapter 5 develops a way of characterizing the nonMarkovianity of a bath (i.e.,whether and to what extent the bath remembers information about the plant) by perturbing the plant and watching for changes in the its subsequent evolution. Chapter 6 reanalyzes a recent measurement of a mechanical oscillator's zeropoint fluctuations, revealing nontrivial correlation between the measurement device's sensing noise and the quantum rackaction noise.
Chapter 7 describes a model in which gravity is classical and matter motions are quantized, elaborating how the quantum motions of matter are affected by the fact that gravity is classical. It offers an experimentally plausible way to test this model (hence the nature of gravity) by measuring the centerofmass motion of a macroscopic object.
The most promising gravitational waves for direct detection are those emitted from highly energetic astrophysical processes, sometimes involving black holes  a type of object predicted by general relativity whose properties depend highly on the strongfield regime of the theory. Although black holes have been inferred to exist at centers of galaxies and in certain socalled Xray binary objects, detecting gravitational waves emitted by systems containing black holes will offer a much more direct way of observing black holes, providing unprecedented details of spacetime geometry in the blackholes' strongfield region.
The third part of this thesis (Chapters 811) studies blackhole physics in connection with gravitationalwave detection.
Chapter 8 applies black hole perturbation theory to model the dynamics of a light compact object orbiting around a massive central Schwarzschild black hole. In this chapter, we present a Hamiltonian formalism in which the lowmass object and the metric perturbations of the background spacetime are jointly evolved. Chapter 9 uses WKB techniques to analyze oscillation modes (quasinormal modes or QNMs) of spinning black holes. We obtain analytical approximations to the spectrum of the weaklydamped QNMs, with relative error O(1/L^2), and connect these frequencies to geometrical features of spherical photon orbits in Kerr spacetime. Chapter 11 focuses mainly on nearextremal Kerr black holes, we discuss a bifurcation in their QNM spectra for certain ranges of (l,m) (the angular quantum numbers) as a/M → 1. With tools prepared in Chapter 9 and 10, in Chapter 11 we obtain an analytical approximate for the scalar Green function in Kerr spacetime.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Quantum Mechanics, Black Hole, Gravitational Wave 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Group:  Institute for Quantum Information and Matter, IQIM 
Thesis Committee: 

Defense Date:  10 May 2013 
NonCaltech Author Email:  huan.yang07 (AT) gmail.com 
Record Number:  CaltechTHESIS:05222013233805938 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:05222013233805938 
DOI:  10.7907/JMRSDK55 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  7744 
Collection:  CaltechTHESIS 
Deposited By:  Huan Yang 
Deposited On:  29 May 2013 20:31 
Last Modified:  26 Apr 2019 18:21 
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