Thesis (Ph.D.)--Lehigh University, 2007.

Thesis (Ph.D.)--Brown University, 2006. / (UMI)AAI3227970. Adviser: Georgios Daskalopoulos. Source: Dissertation Abstracts International, Volume: 67-08, Section: B, page: 4466.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008. / Source: Dissertation Abstracts International, Volume: 69-11, Section: B, page: 6887. Adviser: Alfred Huebler. Includes bibliographical references (leaves 73-76) Available on microfilm from Pro Quest Information and Learning.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. / Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 3869. Adviser: Paul Kwiat. Includes bibliographical references (leaves 123-127) Available on microfilm from Pro Quest Information and Learning.

Scattering problem is one of the most fundamental problems in physics, spanning almost all areas of physics. In this dissertation, we focus on scattering theory in two types of systems: two dimensional electron scattering in the presence of a random potential and light scattering by metallic nanoparticles. The first scattering problem we study is electron branched flow. In this system, electrons are confined to move in two dimensions while a smoothly changing weak random potential deflects their trajectories, resulting in the so-called branched flow. A semiclassical theory based on ray tracing was developed to explain all the observed features of branched flow. However, this semiclassical theory was challenged by the result of a more recent experiment, which claims to have uncovered "unexpected features of branched flow". We show how these features can actually be explained by the semiclassical theory. Besides electron scattering, we also investigate light scattering by metallic nanoparticles. In this case, we study the multiple scattering effect in the plasmon dimer system and show that one can use these metallic nanoparticles to put the incoming electromagnetic fields into different shapes by solving an inverse scattering problem.

Diagonal unitary operators are commonly found in many quantum algorithms. They find application as analytical potential operators for quantum simulation, as well as for complex oracles used in quantum searches. However, in order to implement a quantum algorithm on a given quantum device, each operator must be decomposed into a sequence of fault-tolerant, device-level instructions. In general, to implement an $n$-qubit diagonal unitary {\em exactly} on a quantum computer generally requires $2^{n+1}-3$ one- and two-qubit gates. However, for most practical implementations of diagonal unitaries, some degree of approximation will be necessary if the circuit is to be efficient. In this thesis we develop two complementary methods for the approximate synthesis of quantum circuits for diagonal unitaries. We show how to apply these techniques to real-space quantum simulation and show how efficient high fidelity quantum simulations can be implemented with low-depth quantum circuits. / Engineering and Applied Sciences - Applied Physics

The current frontier of our understanding of the physical universe is dominated by quantum phenomena. Uncovering the prospects and limitations of acquiring and processing information using quantum effects is an outstanding challenge in physical science. This thesis presents an analysis of several new model systems and applications for quantum information processing and metrology. First, we analyze quantum optomechanical systems exhibiting quantum phenomena in both optical and mechanical degrees of freedom. We investigate the strength of non-classical correlations in a model system of two optical and one mechanical mode. We propose and analyze experimental protocols that exploit these correlations for quantum computation. We then turn our attention to atom-cavity systems involving strong coupling of atoms with optical photons, and investigate the possibility of using them to store information robustly and as relay nodes. We present a scheme for a robust two-qubit quantum gate with inherent error-detection capabilities. We consider several remote entanglement protocols employing this robust gate, and we use these systems to study the performance of the gate in practical applications. Finally, we present a new protocol for running multiple, remote atomic clocks in quantum unison. We show that by creating a cascade of independent Greenberger-Horne-Zeilinger states distributed across the network, the scheme asymptotically reaches the Heisenberg limit, the fundamental limit of measurement accuracy. We propose an experimental realization of such a network consisting of neutral atom clocks, and analyze the practical performance of such a system. / Physics

The first half of this thesis introduces the time-dependent W.K.B. approximation of quantum mechanics from basic principles in classical and quantum mechanics. After discussing the van Vleck-Morette-Gutzwiller propagator, the real-trajectory time-dependent W.K.B. approximation of a coherent state is introduced. This is also called the off-center ''thawed'' Gaussian approximation and has a closed-form solution consisting of a Gaussian with time-dependent position and momentum, dispersion, and position-momentum correlation. This result is then extended to third order in the classical action of guiding real trajectories - a parabolization in phase space, and equivalently, a uniformization over two saddle points - allowing for the novel treatment of non-linearity in its underlying classical dynamics. The result is another simple closed-form solution, but this time made up of Airy functions and their derivatives multiplied by an exponential. Unlike the lower-order treatment, which stopped at linearization of phase space, this expression is able to capture global as well as local non-linear dynamics at finite Planck's constant. We then proceed to discuss another uniformization of the semiclassical primitive propagator: the Heller-Herman-Kluk-Kay (H.H.K.K.) propagator. The H.H.K.K. involves an integral over all of phase space which can be trimmed down to only a one-dimensional integral, regardless of the dimensions of the system, by appealing to similar guiding manifold techniques discussed in the previous section. This is the basis for the directed H.H.K.K. propagator which we investigate. Though many possibilities for speeding up the semiclassical evaluation of H.H.K.K. been examined over the years, few have focused on using the actual dynamics of underlying trajectories to simplify its computation. Our findings offer encouraging evidence about the promise of this direction. The second half of this thesis is concerned with describing the Raman spectrum of graphene within the Born-Oppenheimer approximation using the Kramers-Heisenberg-Dirac (K.H.D.) formalism. The electronic and vibrational properties of graphene are introduced, along with simple tight-binding methods of calculating them. With these tools, K.H.D. is then applied to explain the origin of the unique and few prominent peaks in graphene's Raman spectrum. Here, the dominant effect of graphene's linear Dirac cone in its electronic dispersion is easily seen. The latter leads to novel electron-light-phonon ''sliding transitions'' that explain the brightness of the overtone 2D peak. Finally, some more minor results on the subject of the asymptotic zeros of orthogonal polynomials are presented. / Chemical Physics

We describe some aspects of classical gauge theory from the perspective of connections on vector bundles. We begin by examining classical electromagnetism, and use it to motivate the development of gauge theory on vector bundles. If G is a Lie group, we review some of the theory of vector G-bundles, their associated principal G-bundles, and the related theory of connections. We then discuss the idea of gauge transformations on principal and vector G-bundles, and view electromagnetism as an example of an abelian gauge theory. We briefly review the action principle in order to describe non-abelian gauge theories such as the Yang-Mills equation. Finally, we present the main results from an article by John Baez entitled "Higher Yang-Mills Theory" where he attempts to abstract Yang-Mills theory using some concepts from category theory.

We study light hadron phenomenology using Lattice QCD. We focus on the calculations of the light pseudoscalar quantities: masses, decay constants and B-parameters; in particular the calculation of the Kaon B-parameter, BK, which when combined with experimental results yields a constraint of the unitarity triangle apex. We describe a calculation with 2+1 dynamical flavours of Domain Wall Fermions on two lattice volumes, with a lattice spacing a = 0:1 fm. The Iwasaki gauge action was used with coupling beta = 2:13 and the extent of the fifth dimension was Ls = 16. Following a brief review of continuum QCD and Lattice QCD we describe the Domain Wall formalism and the lattice methods used to calculate physical quantities. We present results from the two simulations and make comparisons with next-to-leading order chiral perturbation theory. We study the region of validity of chiral perturbation theory and calculate the associated low energy constants. We find these to agree with phenomenological estimates and other lattice calculations. We calculate the physical decay constants and find them to be in relatively good agreement with experimental values. We present a renormalised value for BK which includes systematic error estimates.