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.

Grain growth in protoplanetary disks

The majority of young, low-mass stars are surrounded by optically thick accretion disks. These circumstellar disks provide large reservoirs of gas and dust that will eventually be transformed into planetary systems. Theory and observations suggest that the earliest stage toward planet formation in a protoplanetary disk is the growth of particles, from sub-micron-sized grains to centimeter- sized pebbles. Theory indicates that small interstellar grains are well coupled into the gas and are incorporated to the disk during the proto-stellar collapse. These dust particles settle toward the disk mid-plane and simultaneously grow through collisional coagulation in a very short timescale. Observationally, grain growth can be inferred by measuring the spectral energy distribution at long wavelengths, which traces the continuum dust emission spectrum and hence the dust opacity. Several observational studies have indicated that the dust component in protoplanetary disks has evolved as compared to interstellar medium dust particles, suggesting at least 4 orders of magnitude in particle- size growth. However, the limited angular resolution and poor sensitivity of previous observations has not allowed for further exploration of this astrophysical process.

As part of my thesis, I embarked in an observational program to search for evidence of radial variations in the dust properties across a protoplanetary disk, which may be indicative of grain growth. By making use of high angular resolution observations obtained with CARMA, VLA, and SMA, I searched for radial variations in the dust opacity inside protoplanetary disks. These observations span more than an order of magnitude in wavelength (from sub-millimeter to centimeter wavelengths) and attain spatial resolutions down to 20 AU. I characterized the radial distribution of the circumstellar material and constrained radial variations of the dust opacity spectral index, which may originate from particle growth in these circumstellar disks. Furthermore, I compared these observational constraints with simple physical models of grain evolution that include collisional coagulation, fragmentation, and the interaction of these grains with the gaseous disk (the radial drift problem). For the parameters explored, these observational constraints are in agreement with a population of grains limited in size by radial drift. Finally, I also discuss future endeavors with forthcoming ALMA observations.

The deuteron-deuteron reaction and the stopping cross section of D_2O ice below 600 kev

The energy loss of protons and deuterons in D_2O ice has been measured over the energy range, E_p 18 - 541 kev. The double focusing magnetic spectrometer was used to measure the energy of the particles after they had traversed a known thickness of the ice target. One method of measurement is used to determine relative values of the stopping cross section as a function of energy; another method measures absolute values. The results are in very good agreement with the values calculated from Bethe’s semi-empirical formula. Possible sources of error are considered and the accuracy of the measurements is estimated to be ± 4%.

The D(dp)H^3 cross section has been measured by two methods. For E_D = 200 - 500 kev the spectrometer was used to obtain the momentum spectrum of the protons and tritons. From the yield and stopping cross section the reaction cross section at 90° has been obtained.

For E_D = 35 – 550 kev the proton yield from a thick target was differentiated to obtain the cross section. Both thin and thick target methods were used to measure the yield at each of ten angles. The angular distribution is expressed in terms of a Legendre polynomial expansion. The various sources of experimental error are considered in detail, and the probable error of the cross section measurements is estimated to be ± 5%.

Variable-angle electron spectroscopic studies of various polyatomic molecular systems

The complementary techniques of low-energy, variable-angle electron-impact spectroscopy and ultraviolet variable-angle photoelectron spectroscopy have been used to study the electronic spectroscopy and structure of several series of molecules. Electron-impact studies were performed at incident beam energies between 25 eV and 100 eV and at scattering angles ranging from 0° to 90°. The energy-loss regions from 0 eV to greater than 15 eV were studied. Photoelectron spectroscopic studies were conducted using a HeI radiation source and spectra were measured at scattering angles from 45° to 90°. The molecules studied were chosen because of their spectroscopic, chemical, and structural interest. The operation of a new electron-impact spectrometer with multiple-mode target source capability is described. This spectrometer has been used to investigate the spin-forbidden transitions in a number of molecular systems.

The electron-impact spectroscopy of the six chloro-substituted ethylenes has been studied over the energy-loss region from 0-15 eV. Spin-forbidden excitations corresponding to the π → π*, N → T transition have been observed at excitation energies ranging from 4.13 eV in vinyl chloride to 3.54 eV in tetrachloroethylene. Symmetry-forbidden transitions of the type π → np have been oberved in trans-dichloroethyene and tetrachlor oethylene. In addition, transitions to many states lying above the first ionization potential were observed for the first time. Many of these bands have been assigned to Rydberg series converging to higher ionization potentials. The trends observed in the measured transition energies for the π → π*, N → T, and N → V as well as the π → 3s excitation are discussed and compared to those observed in the methyl- and fluoro- substituted ethylenes.

The electron energy-loss spectra of the group VIb transition metal hexacarbonyls have been studied in the 0 eV to 15 eV region. The differential cross sections were obtained for several features in the 3-7 eV energy-loss region. The symmetry-forbidden nature of the ¹A_1g → ¹A_1g, 2t_2g(π) → 3t_2g(π*) transition in these compounds was confirmed by the high-energy, low-angle behavior of their relative intensities. Several low lying transitions have been assigned to ligand field transitions on the basis of the energy and angular behavior of the differential cross sections for these transitions. No transitions which could clearly be assigned to singlet → triplet excitations involving metal orbitals were located. A number of states lying above the first ionization potential have been observed for the first time. A number of features in the 6-14 eV energy-loss region of the spectra of these compounds correspond quite well to those observed in free CO.

A number of exploratory studies have been performed. The π → π*, N → T, singlet → triplet excitation has been located in vinyl bromide at 4.05 eV. We have also observed this transition at approximately 3.8 eV in a cis-/trans- mixture of the 1,2-dibromoethylenes. The low-angle spectrum of iron pentacarbonyl was measured over the energy-loss region extending from 2-12 eV. A number of transitions of 8 eV or greater excitation energy were observed for the first time. Cyclopropane was also studied at both high and low angles but no clear evidence for any spin- forbidden transitions was found. The electron-impact spectrum of the methyl radical resulting from the pyrolysis of tetramethyl tin was obtained at 100 eV incident energy and at 0° scattering angle. Transitions observed at 5.70 eV and 8.30 eV agree well with the previous optical results. In addition, a number of bands were observed in the 8-14 eV region which are most likely due to Rydberg transitions converging to the higher ionization potentials of this molecule. This is the first reported electron-impact spectrum of a polyatomic free radical.

Variable-angle photoelectron spectroscopic studies were performed on a series of three-membered-ring heterocyclic compounds. These compounds are of great interest due to their highly unusual structure. Photoelectron angular distributions using HeI radiation have been measured for the first time for ethylene oxide and ethyleneimine. The measured anisotropy parameters, β, along with those measured for cyclopropane were used to confirm the orbital correlations and photoelectron band assignments. No high values of β similar to those expected for alkene π orbitals were observed for the Walsh or Forster-Coulson-Moffit type orbitals.

Studies in nuclear reactor dynamics : I. The accuracy of point kinetics. II. The effect of delayed neutrons on the spectrum of the group-diffusion operator

This thesis is a theoretical work on the space-time dynamic behavior of a nuclear reactor without feedback. Diffusion theory with G-energy groups is used.

In the first part the accuracy of the point kinetics (lumped-parameter description) model is examined. The fundamental approximation of this model is the splitting of the neutron density into a product of a known function of space and an unknown function of time; then the properties of the system can be averaged in space through the use of appropriate weighting functions; as a result a set of ordinary differential equations is obtained for the description of time behavior. It is clear that changes of the shape of the neutron-density distribution due to space-dependent perturbations are neglected. This results to an error in the eigenvalues and it is to this error that bounds are derived. This is done by using the method of weighted residuals to reduce the original eigenvalue problem to that of a real asymmetric matrix. Then Gershgorin-type theorems .are used to find discs in the complex plane in which the eigenvalues are contained. The radii of the discs depend on the perturbation in a simple manner.

In the second part the effect of delayed neutrons on the eigenvalues of the group-diffusion operator is examined. The delayed neutrons cause a shifting of the prompt-neutron eigenvalue s and the appearance of the delayed eigenvalues. Using a simple perturbation method this shifting is calculated and the delayed eigenvalues are predicted with good accuracy.

Analyses of planetary atmospheres across the spectrum : from Titan to exoplanets

Planetary atmospheres exist in a seemingly endless variety of physical and chemical environments. There are an equally diverse number of methods by which we can study and characterize atmospheric composition. In order to better understand the fundamental chemistry and physical processes underlying all planetary atmospheres, my research of the past four years has focused on two distinct topics. First, I focused on the data analysis and spectral retrieval of observations obtained by the Ultraviolet Imaging Spectrograph (UVIS) instrument onboard the Cassini spacecraft while in orbit around Saturn. These observations consisted of stellar occultation measurements of Titan's upper atmosphere, probing the chemical composition in the region 300 to 1500 km above Titan's surface. I examined the relative abundances of Titan's two most prevalent chemical species, nitrogen and methane. I also focused on the aerosols that are formed through chemistry involving these two major species, and determined the vertical profiles of aerosol particles as a function of time and latitude. Moving beyond our own solar system, my second topic of investigation involved analysis of infra-red light curves from the Spitzer space telescope, obtained as it measured the light from stars hosting planets of their own. I focused on both transit and eclipse modeling during Spitzer data reduction and analysis. In my initial work, I utilized the data to search for transits of planets a few Earth masses in size. In more recent research, I analyzed secondary eclipses of three exoplanets and constrained the range of possible temperatures and compositions of their atmospheres.

The complex angular momentum theory of the production of three particles in collisions of two strongly interacting particles at high energy

The problem of the continuation to complex values of the angular momentum of the partial wave amplitude is examined for the simplest production process, that of two particles → three particles. The presence of so-called "anomalous singularities" complicates the procedure followed relative to that used for quasi two-body scattering amplitudes. The anomalous singularities are shown to lead to exchange degenerate amplitudes with possible poles in much the same way as "normal" singularities lead to the usual signatured amplitudes. The resulting exchange-degenerate trajectories would also be expected to occur in two-body amplitudes.

The representation of the production amplitude in terms of the singularities of the partial wave amplitude is then developed and applied to the high energy region, with attention being paid to the emergence of "double Regge" terms. Certain new results are obtained for the behavior of the amplitude at zero momentum transfer, and some predictions of polarization and minima in momentum transfer distributions are made. A calculation of the polarization of the ρ^o meson in the reaction π ^- p → π ^- ρ^op at high energy with small momentum transfer to the proton is compared with data taken at 25 Gev by W. D. Walker and collaborators. The result is favorable, although limited by the statistics of the available data.

A theory of strong and weak scintillations with applications to astrophysics

The propagation of waves in an extended, irregular medium is studied under the "quasi-optics" and the "Markov random process" approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of the moment equations with different transverse coordinates and different wavenumbers is then obtained from the characteristic functional. The derivation does not require Gaussian statistics of the random medium and the result can be applied to the time-dependent problem. We then solve the moment equations for the phase correlation function, angular broadening, temporal pulse smearing, intensity correlation function, and the probability distribution of the random waves. The necessary and sufficient conditions for strong scintillation are also given.

We also consider the problem of diffraction of waves by a random, phase-changing screen. The intensity correlation function is solved in the whole Fresnel diffraction region and the temporal pulse broadening function is derived rigorously from the wave equation.

The method of smooth perturbations is applied to interplanetary scintillations. We formulate and calculate the effects of the solar-wind velocity fluctuations on the observed intensity power spectrum and on the ratio of the observed "pattern" velocity and the true velocity of the solar wind in the three-dimensional spherical model. The r.m.s. solar-wind velocity fluctuations are found to be ~200 km/sec in the region about 20 solar radii from the Sun.

We then interpret the observed interstellar scintillation data using the theories derived under the Markov approximation, which are also valid for the strong scintillation. We find that the Kolmogorov power-law spectrum with an outer scale of 10 to 100 pc fits the scintillation data and that the ambient averaged electron density in the interstellar medium is about 0.025 cm^-3. It is also found that there exists a region of strong electron density fluctuation with thickness ~10 pc and mean electron density ~7 cm^-3 between the PSR 0833-45 pulsar and the earth.

Mass measurements of some proton-rich nuclei

The Q values and 0^o cross sections of (He³, n) reactions forming seven proton-rich nuclei have been measured with accuracies varying from 6 to 18 keV. The Q values (in keV) are: Si²⁶ (85), S³⁰ (-573), Ar³⁴ (-759), Ti⁴² (-2865), Cr⁴⁸ (5550), Ni⁵⁶ (4513) and Zn⁶⁰ (818). At least one excited state was found for all but Ti⁴². The first four nuclei complete isotopic spin triplets; the results obtained agree well with charge-symmetry predictions. The last three, all multiples of the α particle, are important in the α and e-process theories of nucleo-synthesis in stars. The energy available for β decay of these three was found by magnetic spectrometer measurements of the (He³, p) Q values of reactions leading to V⁴⁸, Co⁵⁶, and Cu⁶⁰. Many excited states were seen: V⁴⁸ (3), Co⁵⁶ (15), Cu⁶⁰ (23). The first two states of S³⁰ are probably 0⁺ and 2⁺ from (He³, n) angular distribution measurements. Two NaI γ-ray measurements are described: the decay of Ar³⁴ (measured ^Ƭ1/2 = 1.2 ± 0.3s) and the prompt γ-ray spectrum from Fe⁵⁴(He³, nγ)Ni⁵⁶. Possible collective structure in Ni⁵⁶ and Ca⁴⁰, both doubly magic, is discussed.

The (He³, n) neutron energy and yield measurements utilized neutron-induced nuclear reactions in a silicon semiconductor detector. Cross sections for the most important detection processes, Si²⁸ (n, α) Mg²⁵ and Si²⁸ (n, p) Al²⁸, are presented for reactions leading to the first four states of both residual nuclei for neutron energies from 7.3 to 16.4 MeV. Resolution and pulse-height anomalies associated with recoil Mg²⁵ and Al²⁸ ions are discussed. The 0^o cross section for Be⁹ (α, n) C¹², used to provide calibration neutrons, has been measured with a stilbene spectrometer for n_o (5.0 ≤ E_α ≤ 12 MeV), n₁ (4.3 ≤ E_α ≤ 12.0 MeV) and n₂ (6.0 ≤ E_α ≤ 10.1 MeV). Resonances seen in the n_o yield may correspond to nine new levels in C¹³.

High-energy scattering processes with cuts in the angular momentum plane

The experimental consequence of Regge cuts in the angular momentum plane are investigated. The principle tool in the study is the set of diagrams originally proposed by Amati, Fubini, and Stanghellini. Mandelstam has shown that the AFS cuts are actually cancelled on the physical sheet, but they may provide a useful guide to the properties of the real cuts. Inclusion of cuts modifies the simple Regge pole predictions for high-energy scattering data. As an example, an attempt is made to fit high energy elastic scattering data for pp, ṗp, π^±p, and K^±p, by replacing the Igi pole by terms representing the effect of a Regge cut. The data seem to be compatible with either a cut or the Igi pole.

Photonic and Device Design Principles for Ultrahigh-Efficiency (>50%), Spectrum-Splitting Photovoltaics

The sun has the potential to power the Earth's total energy needs, but electricity from solar power still constitutes an extremely small fraction of our power generation because of its high cost relative to traditional energy sources. Therefore, the cost of solar must be reduced to realize a more sustainable future. This can be achieved by significantly increasing the efficiency of modules that convert solar radiation to electricity. In this thesis, we consider several strategies to improve the device and photonic design of solar modules to achieve record, ultrahigh (> 50%) solar module efficiencies. First, we investigate the potential of a new passivation treatment, trioctylphosphine sulfide, to increase the performance of small GaAs solar cells for cheaper and more durable modules. We show that small cells (mm2), which currently have a significant efficiency decrease (~ 5%) compared to larger cells (cm2) because small cells have a higher fraction of recombination-active surface from the sidewalls, can achieve significantly higher efficiencies with effective passivation of the sidewalls. We experimentally validate the passivation qualities of treatment by trioctylphosphine sulfide (TOP:S) through four independent studies and show that this facile treatment can enable efficient small devices. Then, we discuss our efforts toward the design and prototyping of a spectrum-splitting module that employs optical elements to divide the incident spectrum into different color bands, which allows for higher efficiencies than traditional methods. We present a design, the polyhedral specular reflector, that has the potential for > 50% module efficiencies even with realistic losses from combined optics, cell, and electrical models. Prototyping efforts of one of these designs using glass concentrators yields an optical module whose combined spectrum-splitting and concentration should correspond to a record module efficiency of 42%. Finally, we consider how the manipulation of radiatively emitted photons from subcells in multijunction architectures can be used to achieve even higher efficiencies than previously thought, inspiring both optimization of incident and radiatively emitted photons for future high efficiency designs. In this thesis work, we explore novel device and photonic designs that represent a significant departure from current solar cell manufacturing techniques and ultimately show the potential for much higher solar cell efficiencies.

Photoproduction of charged pion pairs from hydrogen at energies up to 1500 MeV

Charged pion pair photoproduction has been investigated up to a gamma energy of 1500 MeV, using the Caltech 12-inch heavy liquid bubble chamber with a small diameter, high intensity photon beam passing through a central beam tube gaseous hydrogen target surrounded by the sensitive Freon. Scanning, analysis, and data reduction techniques have been developed to deal with the problems of two-vie stereo, hidden event origins, absence of magnetic field, and the range-energy and multiple scattering relationships that occur in the heavy materials. Roughly 5700 pictures have been scanned and analyzed, yielding 754 acceptable events. Cross section and parameter distributions are generally consistent with the results of previous experiments. A statistically insignificant “bump” was observed in the dipion mass spectrum in the region of 500 MeV, the disputed σ meson mass. This region was investigated as carefully as the limited statistics would allow; dipion angular distributions are consistent with isotropy, and there is indication that some of the events in this region might come from decay of an intermediate N*₁₁ (1425) into a proton and dipion.

Photographic materials on pp. 18, 20, 22, and 24 are essential and will not reproduce clearly on Xerox copies. Photographic copies should be ordered.

Beta and gamma vibrational bands in deformed nuclei

Energies and relative intensities of gamma transitions in ¹⁵²Sm, ¹⁵²Gd, ¹⁵⁴Gd, ¹⁶⁶Er, and ²³²U following radioactive decay have been measured with a Ge(Li) spectrometer. A peak fitting program has been developed to determine gamma ray energies and relative intensities with precision sufficient to give a meaningful test of nuclear models. Several previously unobserved gamma rays were placed in the nuclear level schemes. Particular attention has been paid to transitions from the beta and gamma vibrational bands, since the gamma ray branching ratios are sensitive tests of configuration mixing in the nuclear levels. As the reduced branching ratios depend on the multipolarity of the gamma transitions, experiments were performed to measure multipole mixing ratios for transitions from the gamma vibrational band. In ¹⁵⁴Gd, angular correlation experiments showed that transitions from the gamma band to the ground state band were predominantly electric quadrupole, in agreement with the rotational model. In ²³²U, the internal conversion spectrum has been studied with a Si(Li) spectrometer constructed for electron spectroscopy. The strength of electric monopole transitions and the multipolarity of some gamma transitions have been determined from the measured relative electron intensities.

The results of the experiments have been compared with the rotational model and several microscopic models. Relative B(E2) strengths for transitions from the gamma band in ²³²U and ¹⁶⁶Er are in good agreement with a single parameter band mixing model, with values of z₂= 0.025(10) and 0.046(2), respectively. Neither the beta nor the gamma band transition strengths in ¹⁵²Sm and ¹⁵⁴Gd can be accounted for by a single parameter theory, nor can agreement be found by considering the large mixing found between the beta and gamma bands. The relative B(E2) strength for transitions from the gamma band to the beta band in ²³²U is found to be five times greater than the strength to the ground state band, indicating collective transitions with strength approximately 15 single particle units.