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.

Wave interactions in periodic structures and periodic dielectric waveguides

This work is concerned with a general analysis of wave interactions in periodic structures and particularly periodic thin film dielectric waveguides.

The electromagnetic wave propagation in an asymmetric dielectric waveguide with a periodically perturbed surface is analyzed in terms of a Floquet mode solution. First order approximate analytical expressions for the space harmonics are obtained. The solution is used to analyze various applications: (1) phase matched second harmonic generation in periodically perturbed optical waveguides; (2) grating couplers and thin film filters; (3) Bragg reflection devices; (4) the calculation of the traveling wave interaction impedance for solid state and vacuum tube optical traveling wave amplifiers which utilize periodic dielectric waveguides. Some of these applications are of interest in the field of integrated optics.

A special emphasis is put on the analysis of traveling wave interaction between electrons and electromagnetic waves in various operation regimes. Interactions with a finite temperature electron beam at the collision-dominated, collisionless, and quantum regimes are analyzed in detail assuming a one-dimensional model and longitudinal coupling.

The analysis is used to examine the possibility of solid state traveling wave devices (amplifiers, modulators), and some monolithic structures of these devices are suggested, designed to operate at the submillimeter-far infrared frequency regime. The estimates of attainable traveling wave interaction gain are quite low (on the order of a few inverse centimeters). However, the possibility of attaining net gain with different materials, structures and operation condition is not ruled out.

The developed model is used to discuss the possibility and the theoretical limitations of high frequency (optical) operation of vacuum electron beam tube; and the relation to other electron-electromagnetic wave interaction effects (Smith-Purcell and Cerenkov radiation and the free electron laser) are pointed out. Finally, the case where the periodic structure is the natural crystal lattice is briefly discussed. The longitudinal component of optical space harmonics in the crystal is calculated and found to be of the order of magnitude of the macroscopic wave, and some comments are made on the possibility of coherent bremsstrahlung and distributed feedback lasers in single crystals.

Effect of PbCl2 addition on structure, OH- content, and upconversion luminescence in Yb3+/Er3+-codoped germanate glasses

Yb3+/ Er3+-codoped oxychloride germanate glasses have been synthesized by a conventional melting and quenching method. Structural properties were obtained based on Raman-spectra investigation, indicating that PbCl2 plays an important role in the formation of the glass network and has an important influence on the phonon density and the maximum phonon energy. The Judd - Ofelt intensity parameters and quantum efficiencies were calculated based on the Judd - Ofelt theory and lifetime measurements. The enhanced upconversion luminescence intensity of Er3+ with increasing PbCl2 content could not be explained only by the maximum phonon-energy change of the host glasses. For the first time, the effect of PbCl2 addition on phonon density, OH- content, and upconversion luminescence in oxychloride glasses has been discussed and evaluated. The results show that the effect of phonon density and OH- content on upconversion luminescence in oxychloride glasses is much stronger than that of the decrease of the maximum phonon energy. The possible upconversion luminescence mechanisms have also been estimated and are discussed.

Experimental analysis of SCM-based transmission over 500 m of FDDI-grade multimode fiber with enhancement from electronic equalization

Experimental analysis is applied for the first time to identify optimal launch conditions and carrier frequencies for SCM transmission over worst-case MMF. Potential for performance enhancement using electronic equalization is demonstrated for the first time. © 2006 Optical Society of America.

Er3+-doped glass-polymer composite thin films fabricated using combinatorial pulsed laser deposition

Siloxane Polymer exhibits low loss in the 800-1500 nm range which varies between 0.01 and 0.66 dB cm1. It is for such low loss the material is one of the most promising candidates in the application of engineering passive and active optical devices [1, 2]. However, current polymer fabrication techniques do not provide a methodology which allows high structurally solubility of Er3+ ions in siloxane matrix. To address this problem, Yang et al.[3] demonstrated a channel waveguide amplifier with Nd 3+-complex doped polymer, whilst Wong and co-workers[4] employed Yb3+ and Er3+ co-doped polymer hosts for increasing the gain. In some recent research we demonstrated pulsed laser deposition of Er-doped tellurite glass thin films on siloxane polymer coated silica substrates[5]. Here an alternative methodology for multilayer polymer-glass composite thin films using Er3+ - Yb3+ co-doped phosphate modified tellurite (PT) glass and siloxane polymer is proposed by adopting combinatorial pulsed laser deposition (PLD). © 2011 IEEE.

Low power all-optical switch in a passive InGaAsP multiple quantum well waveguide

We demonstrate the use of resonant bandfilling nonlinearity in an InGaAsP/InGaAsP Multiple Quantum Well (MQW) waveguide due to photogenerated carriers to obtain switching at pulse powers, which can readily be obtained from an erbium amplified diode laser source. In order to produce gating a polarisation rotation gate was used, which relies on an asymmetry in the nonlinear refraction on the principle axes of the waveguide.

10-Gbits/s all-optical 3R regeneration and format conversion using a gain-switched DFB laser

A strain-compensated multiple quantum well device is used as a DFB laser, this has been optimized for low jitter gain switched operation at 10 GHz. The signal is transmitted down 80 km of standard fiber then amplified, filtered and polarization controlled before being injected into a DFB laser. The purpose of this regeneration process is to gain switch the DFB with the extracted clock signal in order to retime the converted signal. This process also simultaneously converts the input NRZ format to an output RZ data to format and results in a signal whose optical power and extinction ratio are considerably improved by the regeneration process.

Single-photon detection using a quantum dot field effect transistor

A novel device for detection of single photons based on a GaAs/AlGaAs modulation doped field effect transistor (MODFET) which does not rely on avalanche processes is proposed. The optimal channel electron densities and quantum dot parameters for detection of single photons are discussed.