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Topics in Gravitational-Wave Science: Macroscopic Quantum Mechanics and Black Hole Physics Thesis by Huan Yang In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2013 (Submitted May 23, 2013) ii c 2013 Huan Yang All Rights Reserved iii Dedicated to my parents Fuxi Yin and Ganqin Yang iv Acknowledgments There is a Chinese saying that goes, \it takes ten years to sharpen a sword." It took me the continuous effort of many years to become an qualified \sword" (with a Ph.D.), ready for cutting through the fog of unknowns at the frontier of physics. Along my way, studying physics during these years, I have received enormous encouragement and assistance from my family, my friends and my colleagues. I am grateful for the help of all of them, and I shall acknowledge them in chronological order. First I would like to thank my parents Fuxi Yin and Ganqin Yang. They taught me the really important things in life and they showed me how to build my character with integrity, honesty and sheer tenacity. There were times when I was confused and uncertain about my future, but they always told me to follow my heart and they always supported my decisions. My parents greatly helped me to define who I am. I am also thankful to Kip Thorne and Nai-Chang Yeh. I worked with Kip since my sophomore year. He brought me into the field of general relativity, which has become one of my main research interests. He influenced me not only through his scientific wisdom, but also his way of interacting with people and his positive energy. Nai-Chang was my senior thesis advisor. During my time working in her lab, I was truly impressed by her passion and attitude toward doing research. As a female professor, she is also very generous to her students. I would like to thank for all her help in my past studies. I want to give special thanks to my Ph.D thesis advisor Yanbei Chen. As an advisor and as a physicist, he is my favorite type: very considerate to students, always curious about problems in physics and full of ideas. I enjoyed spontaneous discussions with him about many branches of physics, and I learned a lot from him about ways of looking at and solving physics problems. I am also grateful for his encouragement and painstaking effort to teach me how to write scientific articles and give clear presentations . I also want to express my thankfulness to Rana Adhikari, Koji Arai, Jenne Driggers, Jan Harms, Larry Price, David Yeaton-Massey, Nicholas Smith and my colleagues in the TAPIR group: David Nichols, Aaron Zimmerman, Fan Zhang, Bassam Helou, Chad Galley, Jeffrey Kaplan, Anil Zenginoglu, Yasushi Mino, Tanja Hinderer, Jeandrew Brink, Haixing Miao and Roland Haas. I am lucky to have the chance to work with all these brilliant people. We had a lot of fruitful discussions v and many of them have turned into chapters of this thesis. I would like to acknowledge Stefan Danilishin, Thomas Corbitt, Kentaro Somiya, Yiqiu Ma, Farid Khalili and Sergey Vyatchanin and all the other members of the Macroscopic Quantum Mechanics (MQM) discussion group. I also want to thank other colleagues outside Caltech: Howard Wiseman, Scott Hughes, Emanuele Berti, Sam Dolan, Marc Casals, Yi Pan, Steven Detweiler, Steve Carlip, Da-Shin Lee, Bei-lok Hu, Ting Yu, Walter Strunz, Matthew Evans and Ian Vega. I enjoyed and benefitted from stimulating discussions with all of them. I want to thank the two other members of my thesis committee who have not been mentioned before: Christopher Hirata and Christian Ott, for giving me very valuable advice and comments on my thesis research as well as presentation skills. In working on chapters of this thesis, I was supported by the following public funding: NSF Grants PHY-1068881 and PHY-1005655, CAREER Grants PHY-0956189 and PHY-1055103, NASA Grant No.NNX09AF97G, the Sherman Fairchild Foundation and the Brinson Foundation. I am also grateful for the donation from Dr. and Mrs. David and Barbara Groce, whose gift enabled me to finish my Ph.D. degree in physics. Finally, I would like to acknowledge JoAnn Boyd and Shirley Hampton for their assistance on administration matters. vi 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 space-time 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 gravitational-wave physics. Gravitational waves are \ripples of space-time", long predicted by general relativity. Although in- direct 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 gravitational-wave 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 second-generation configurations, which will have ten times better sensitivity. Kilogram-scale test masses of these detectors, highly isolated from the environment, are probed con- tinuously 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 quantum-limited. My colleagues and I present a detailed analysis of coating thermal noise in advanced gravitational-wave 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 3 { 7) 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 4{5, we build theoretical tools for analyzing the so-called \non-Markovian" quantum vii measurement processes. Chapter 4 establishes a mathematical formalism that describes the evolution of a quantum system (the plant), which is coupled to a non-Markovian 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 non-Markovian measurement processes. Chapter 5 develops a way of characterizing the non-Markovianity 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 re-analyzes a recent measurement of a mechanical oscillator's zero-point fluctuations, revealing nontrivial correlation between the measurement device's sensing noise and the quantum rack-action 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 center-of-mass motion of a macroscopic object. The most promising gravitational waves for direct detection are those emitted from highly en- ergetic astrophysical processes, sometimes involving black holes | a type of object predicted by general relativity whose properties depend highly on the strong-field regime of the theory. Although black holes have been inferred to exist at centers of galaxies and in certain so-called X-ray 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 space-time geometry in the black-holes' strong-field region. The third part of this thesis (Chapters 8 { 11) studies black-hole physics in connection with gravitational-wave 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 low-mass object and the metric perturbations of the background spacetime are jointly evolved. Chapter 9 uses WKB techniques to analyze oscillation modes (quasi-normal modes or QNMs) of spinning black holes. We obtain analytical approximations to the spectrum of the weakly-damped QNMs, with relative error O(1=L2), and connect these frequencies to geometrical features of spherical photon orbits in Kerr spacetime. Chapter 11 focuses mainly on near-extremal 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. viii Contents Acknowledgments iv Abstract vi 1 Introduction 1 1.1 Physics of advanced gravitational wave detectors . .1 1.1.1 An overview of laser interferometer gravitational-wave detectors .
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