Topics in gravitational-wave science : macroscopic quantum mechanics and black hole physics

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 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 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 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 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 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 energetic 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/L^2), 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.

High fidelity probe and mitigation of mirror thermal fluctuations

Thermal noise arising from mechanical loss in high reflective dielectric coatings is a significant source of noise in precision optical measurements. In particular, Advanced LIGO, a large scale interferometer aiming to observed gravitational wave, is expected to be limited by coating thermal noise in the most sensitive region around 30–300 Hz. Various theoretical calculations for predicting coating Brownian noise have been proposed. However, due to the relatively limited knowledge of the coating material properties, an accurate approximation of the noise cannot be achieved. A testbed that can directly observed coating thermal noise close to Advanced LIGO band will serve as an indispensable tool to verify the calculations, study material properties of the coating, and estimate the detector’s performance.

This dissertation reports a setup that has sensitivity to observe wide band (10Hz to 1kHz) thermal noise from fused silica/tantala coating at room temperature from fixed-spacer Fabry–Perot cavities. Important fundamental noises and technical noises associated with the setup are discussed. The coating loss obtained from the measurement agrees with results reported in the literature. The setup serves as a testbed to study thermal noise in high reflective mirrors from different materials. One example is a heterostructure of Al_xGa_1−xAs (AlGaAs). An optimized design to minimize thermo–optic noise in the coating is proposed and discussed in this work.

Magnetic alignment of high-aspect ratio microwires into vertical arrays

Fundamental studies of magnetic alignment of highly anisotropic mesostructures can enable the clean-room-free fabrication of flexible, array-based solar and electronic devices, in which preferential orientation of nano- or microwire-type objects is desired. In this study, ensembles of 100 micron long Si microwires with ferromagnetic Ni and Co coatings are oriented vertically in the presence of magnetic fields. The degree of vertical alignment and threshold field strength depend on geometric factors, such as microwire length and ferromagnetic coating thickness, as well as interfacial interactions, which are modulated by varying solvent and substrate surface chemistry. Microwire ensembles with vertical alignment over 97% within 10 degrees of normal, as measured by X-ray diffraction, are achieved over square cm scale areas and set into flexible polymer films. A force balance model has been developed as a predictive tool for magnetic alignment, incorporating magnetic torque and empirically derived surface adhesion parameters. As supported by these calculations, microwires are shown to detach from the surface and align vertically in the presence of magnetic fields on the order of 100 gauss. Microwires aligned in this manner are set into a polydimethylsiloxane film where they retain their vertical alignment after the field has been removed and can subsequently be used as a flexible solar absorber layer. Finally, these microwires arrays can be protected for use in electrochemical cells by the conformal deposition of a graphene layer.

Effect of Microstructural Interfaces on the Mechanical Response of Crystalline Metallic Materials

Advances in nano-scale mechanical testing have brought about progress in the understanding of physical phenomena in materials and a measure of control in the fabrication of novel materials. In contrast to bulk materials that display size-invariant mechanical properties, sub-micron metallic samples show a critical dependence on sample size. The strength of nano-scale single crystalline metals is well-described by a power-law function, σαD^-n, where D is a critical sample size and n is a experimentally-fit positive exponent. This relationship is attributed to source-driven plasticity and demonstrates a strengthening as the decreasing sample size begins to limit the size and number of dislocation sources. A full understanding of this size-dependence is complicated by the presence of microstructural features such as interfaces that can compete with the dominant dislocation-based deformation mechanisms. In this thesis, the effects of microstructural features such as grain boundaries and anisotropic crystallinity on nano-scale metals are investigated through uniaxial compression testing. We find that nano-sized Cu covered by a hard coating displays a Bauschinger effect and the emergence of this behavior can be explained through a simple dislocation-based analytic model. Al nano-pillars containing a single vertically-oriented coincident site lattice grain boundary are found to show similar deformation to single-crystalline nano-pillars with slip traces passing through the grain boundary. With increasing tilt angle of the grain boundary from the pillar axis, we observe a transition from dislocation-dominated deformation to grain boundary sliding. Crystallites are observed to shear along the grain boundary and molecular dynamics simulations reveal a mechanism of atomic migration that accommodates boundary sliding. We conclude with an analysis of the effects of inherent crystal anisotropy and alloying on the mechanical behavior of the Mg alloy, AZ31. Through comparison to pure Mg, we show that the size effect dominates the strength of samples below 10 μm, that differences in the size effect between hexagonal slip systems is due to the inherent crystal anisotropy, suggesting that the fundamental mechanism of the size effect in these slip systems is the same.

裂缝光纤传感的工程应用

光纤传感的灵敏性及工程"存活率"是其工程实用化的两个关键技术参量,对光纤-混凝土结构两种常用裂缝光纤传感光信号对裂缝宽度的灵敏性与存活率进行了实验研究,对光纤涂覆层对灵敏性影响的大小和机理进行了分析,并制作了灵敏性与存活率均较高的光纤试验样本,与裂缝成45°夹角时,相比于等直径的普通二次涂覆粗光纤(10/125/900μm),样本的灵敏性提高近65%,而存活率亦高出约15%。研究结果可为裂缝光纤传感的优化设计和工程应用提供了基本参照。

Estudo da influência do teor de segmentos hidrofílicos na síntese de poliuretanos dispersos em água

Considerações ambientais têm aumentado a pesquisa e o desenvolvimento de sistemas poliméricos aquosos para diversos tipos de aplicações, principalmente como revestimentos. Nesta dissertação, foram sintetizadas formulações não-poluentes à base de poliuretanos dispersos em água (PUDs), com 40% de teor de sólidos, na ausência de solventes orgânicos. Os monômeros empregados foram copolímeros em bloco à base de poli(glicol etilênico) e poli(glicol propilênico) (EG-b-PG), com teor de 25% de segmento hidrofílico EG, poli (glicol propilênico) (PPG), ácido dimetilolpropiônico (DMPA), diisocianato de isoforona (IPDI) e hidrazina (HYD), como extensor de cadeia. Foram variadas as razões entre o número de equivalente-grama de grupamentos isocianato e hidroxila (NCO/OH) e a proporção em equivalente-grama de PPG e dos copolímeros em bloco (EG-b-PG). Foi observado que a incorporação de altas quantidades de copolímero dificultou a síntese dos poliuretanos dispersos em água, levando à formação de géis. O tamanho médio de partícula e a viscosidade das dispersões foram determinados. Os filmes vazados a partir dessas dispersões foram avaliados quanto à capacidade de absorção de água, resistência mecânica, termogravimetria (TG), e caracterizados por espectroscopia na região do infravermelho (FTIR). As dispersões poliuretânicas produzidas se mostraram satisfatórias quando aplicadas como revestimento para madeira, metais e vidro

Metaconcrete: Engineered aggregates for enhanced dynamic performance

This work presents the development and investigation of a new type of concrete for the attenuation of waves induced by dynamic excitation. Recent progress in the field of metamaterials science has led to a range of novel composites which display unusual properties when interacting with electromagnetic, acoustic, and elastic waves. A new structural metamaterial with enhanced properties for dynamic loading applications is presented, which is named metaconcrete. In this new composite material the standard stone and gravel aggregates of regular concrete are replaced with spherical engineered inclusions. Each metaconcrete aggregate has a layered structure, consisting of a heavy core and a thin compliant outer coating. This structure allows for resonance at or near the eigenfrequencies of the inclusions, and the aggregates can be tuned so that resonant oscillations will be activated by particular frequencies of an applied dynamic loading. The activation of resonance within the aggregates causes the overall system to exhibit negative effective mass, which leads to attenuation of the applied wave motion. To investigate the behavior of metaconcrete slabs under a variety of different loading conditions a finite element slab model containing a periodic array of aggregates is utilized. The frequency dependent nature of metaconcrete is investigated by considering the transmission of wave energy through a slab, which indicates the presence of large attenuation bands near the resonant frequencies of the aggregates. Applying a blast wave loading to both an elastic slab and a slab model that incorporates the fracture characteristics of the mortar matrix reveals that a significant portion of the supplied energy can be absorbed by aggregates which are activated by the chosen blast wave profile. The transfer of energy from the mortar matrix to the metaconcrete aggregates leads to a significant reduction in the maximum longitudinal stress, greatly improving the ability of the material to resist damage induced by a propagating shock wave. The various analyses presented in this work provide the theoretical and numerical background necessary for the informed design and development of metaconcrete aggregates for dynamic loading applications, such as blast shielding, impact protection, and seismic mitigation.

Electrocatalytic reduction of dioxygen at chemically modified electrodes

The kinetics of the reduction of O₂ by Ru(NH₃)₆⁺² as catalyzed by cobalt(II) tetrakis(4-N-methylpyridyl)porphyrin are described both in homogeneous solution and when the reactants are confined to Nafion coatings on graphite electrodes. The catalytic mechanism is determined and the factors that can control the total reduction currents at Nafion-coated electrodes are specified. A kinetic zone diagram for analyzing the behavior of catalyst-mediator-substrate systems at polymer coated electrodes is presented and utilized in identifying the current-limiting processes. Good agreement is demonstrated between calculated and measured reduction currents at rotating disk electrodes. The experimental conditions that will yield the optimum performance of coated electrodes are discussed, and a relationship is derived for the optimal coating thickness.

The relation between the reduction potentials of adsorbed and unadsorbed cobalt(III) tetrakis(4-N-methylpyridyl)porphyrin and those where it catalyzes the electroreduction of dioxygen is described. There is an unusually large change in the formal potential of the Co(III) couple upon the adsorption of the porphyrin on the graphite electrode surface. The mechanism in which the (inevitably) adsorbed porphyrin catalyzes the reduction of O₂ is in accord with a general mechanistic scheme proposed for most monomeric cobalt porphyrins.

Four new dimeric metalloporphyrins (prepared in the laboratory of Professor C. K. Chang) have the two porphyrin rings linked by an anthracene bridge attached to meso positions. The electrocatalytic behavior of the diporphyrins towards the reduction of O₂ at graphite electrodes has been examined for the following combination of metal centers: Co-Cu, Co-Fe, Fe-Fe, Fe-H₂. The Co-Cu diporphyrin catalyzes the reduction of O₂ to H₂O₂ but no further. The other three catalysts all exhibit mixed reduction pathways leading to both H₂O₂ and H₂O. However, the pathways that lead to H₂O do not involve H₂O₂ as an intermediate. A possible mechanistic scheme is offered to account for the observed behavior.

High-efficiency reflective diffraction gratings in fused silica as (de)multiplexers at 1.55 mu m for dense wavelength division multiplexing application

We describe high-efficiency, high-dispersion reflection gratings fabricated in bulk fused Silica illuminated by incident lights in the C + L bands as (de)multiplexers for dense wavelength division multiplexing (DWDM) application. Based on the phenomenon of total internal reflection, gratings with optimized profile parameters exhibit diffraction efficiencies of more than 90% under TM- and TE-polarized incident lights for 101-nm spectral bandwidths (1520-1620 nm) and can reach an efficiency of greater than 97% for both polarizations at a wavelength of 1550 nm. Without loss of metal absorption, without coating of dielectric film layers, and independent of tooth shape, this new kind of grating should be of great interest for DWDM application. (C) 2005 Optical Society of America.

单长周期光栅迈克耳孙干涉仪特性研究

单长周期光栅迈克耳孙（Michelson）干涉仪是由尾纤端面蒸镀高反膜的单根长周期光纤光栅构成。入射光经长周期光栅后，部分被耦合到包层中传输。经过包层和纤芯传输的光信号经尾纤端面反射后，重新耦合回到长周期光栅中，在光栅区域形成干涉。通过理论计算分析了各种因素对其光谱响应的影响。从实验上得到了干涉光谱的谐振峰波长位移与光纤段温度变化成良好的线性关系，测得其温度系数为31．3pm／℃。表明这种结构可用于高温传感或作为波分复用滤波器。

Cryogenic Silicon Optical Reference Cavities

Thermodynamical fluctuations in temperature and position exist in every physical system, and show up as a fundamental noise limit whenever we choose to measure some quantity in a laboratory environment. Thermodynamical fluctuations in the position of the atoms in the dielectric coatings on the mirrors for optical cavities at the forefront of precision metrology (e.g., LIGO, the cavities which probe atomic transitions to define the second) are a current limiting noise source for these experiments, and anything which involves locking a laser to an optical cavity. These thermodynamic noise sources scale physical geometry of experiment, material properties (such as mechanical loss in our dielectric coatings), and temperature. The temperature scaling provides a natural motivation to move to lower temperatures, with a potential huge benefit for redesigning a room temperature experiment which is limited by thermal noise for cryogenic operation.

We design, build, and characterize a pair of linear Fabry-Perot cavities to explore limitations to ultra low noise laser stabilization experiments at cryogenic temperatures. We use silicon as the primary material for the cavity and mirrors, due to a zero crossing in its linear coefficient of thermal expansion (CTE) at 123 K, and other desirable material properties. We use silica tantala coatings, which are currently the best for making high finesse low noise cavities at room temperature. The material properties of these coating materials (which set the thermal noise levels) are relatively unknown at cryogenic temperatures, which motivates us to study them at these temperatures. We were not able to measure any thermal noise source with our experiment due to excess noise. In this work we analyze the design and performance of the cavities, and recommend a design shift from mid length cavities to short cavities in order to facilitate a direct measurement of cryogenic coating noise.

In addition, we measure the cavities (frequency dependent) photo-thermal response. This can help characterize thermooptic noise in the coatings, which is poorly understood at cryogenic temperatures. We also explore the feasibility of using the cavity to do macroscopic quantum optomechanics such as ground state cooling.

掺铒磷酸盐玻璃离子交换波导表面保护的研究

对离子交换波导制备过程中掺铒磷酸盐玻璃表面的侵蚀问题进行了研究，分析了产生侵蚀的原因，提出镀K9玻璃薄膜的方法，对掺铒磷酸盐玻璃表面进行保护．采用光学显微镜和原子力显微镜对波导表面特性进行了表征。同时对平板波导的光学特性进行了测试．研究表明K9玻璃薄膜不仅能够对掺铒磷酸盐玻璃起到保护作用，同时允许交换离子透过进入磷酸盐玻璃形成波导层．

K9玻璃薄膜对离子交换磷酸盐玻璃波导表面保护的优化研究

采用镀K9玻璃薄膜方法来解决离子交换掺铒磷酸盐玻璃波导表面的侵蚀问题,对K9玻璃薄膜的厚度进行了优化研究。测量分析了样品的荧光光谱和荧光寿命,采用光学显微镜和棱镜耦合技术对不同K9玻璃薄膜厚度下制备波导的表面形貌和导光特性进行了表征和测试。结果表明,与掺铒磷酸盐玻璃原材料相比,镀K9玻璃薄膜后荧光光谱保持不变,荧光寿命稍有下降(约0.2 ms);K9玻璃薄膜的厚度在60~80 nm的范围内保护效果最佳。为下一步制备掺铒有源玻璃光波导器件奠定了良好的实验基础。

钛宝石强激光负载的有机硅复合凝胶增透膜研究

以硅酸四乙酯(TEOS)和甲基三乙氧基硅烷(MTEOS)为前驱材料，用溶胶-凝胶(sol-gel)方法在钛宝石表面制备得到均匀性良好且具有高激光损伤阈值的有机硅复合凝胶增透膜。膜层在钛宝石激光器输出波段(750～850nm)的增透效果显著，其平均透过率超过98．6％；激光破坏阈值为2．2J／cm^2(800nm，300ps)；膜层表面均匀性达到激光波面的要求，在皮秒、飞秒超短脉冲高功率激光领域具有应用价值。溶胶的性能测试结果表明，溶胶粘度和成膜折射率均随溶液中CH3SiO1.5溶胶体含量的增加而增大，而膜

溶胶-凝胶多孔二氧化硅减反膜稳定性研究

多孔SiO2膜层经热处理后，具有很高的激光破坏阈值，但是结构中有许多Si-OH亲水基团，导致光学透过率受环境相对湿度的影响很大。实验目的是改善膜层内部结构，使膜层结构中的亲水基团转变为疏水基团。提高膜层的疏水性，增强膜层的透过率稳定性。系统地研究了膜层透过率随时间变化的规律，在氨气和六甲基二硅氮烷(HMDS)混合气氛下热处理膜层，处理后生成Si-O-Si(CH2)3非极性疏水基团，使膜层的疏水性大大提高，因而膜层的透过率稳定性有大幅度提高。稳定性的提高延长了膜层的寿命。处理后膜层的表面粗糙度良好，均方根表