Polarized deep inelastic scattering experiments play a vital role in the exploration of the spin structure of the proton. The polarized proton-proton collider at RHIC provides direct access to the gluon spin distribution through longitudinal double spin asymmetry measurements of inclusive jets, pions, and dijets. This thesis presents the measurement of the dijet double differential cross-section in proton-proton collisions at center of mass energies of √s = 500 GeV. The data represent an integrated luminosity of 8.7 pb-1 recorded by the STAR detector during the 2009 RHIC run. A comprehensive jet analysis was performed to determine the ideal jet algorithm and jet parameters used in √s = 500 GeV collisions at the STAR detector. The cross-section is measured as a function of the dijet invariant mass (30 ≤ Mij ≤ 152 GeV) in the mid rapidity region with a maximum rapidity range of |ymax| ≤ 0.8. This result shows agreement with theoretical next-to-leading order pQCD calculations, motivating the use of dijet asymmetries at STAR to further constrain the shape of Δg(x).

An energy functional is formulated for mass calculations of nuclei across the nuclear chart with major-shell occupations as the relevant degrees of freedom. The functional is based on Hohenberg-Kohn theory. Motivation for its form comes from both phenomenology and relevant microscopic systems, such as the three-level Lipkin Model. A global fit of the 17-parameter functional to nuclear masses yields a root- mean-square deviation of χ[chi] = 1.31 MeV, on the order of other mass models. The construction of the energy functional includes the development of a systematic method for selecting and testing possible functional terms. Nuclear radii are computed within a model that employs the resulting occupation numbers.

abstract: In the traditional setting of quantum mechanics, the Hamiltonian operator does not depend on time. While some Schrödinger equations with time-dependent Hamiltonians have been solved, explicitly solvable cases are typically scarce. This thesis is a collection of papers in which this first author along with Suslov, Suazo, and Lopez, has worked on solving a series of Schrödinger equations with a time-dependent quadratic Hamiltonian that has applications in problems of quantum electrodynamics, lasers, quantum devices such as quantum dots, and external varying fields. In particular the author discusses a new completely integrable case of the time-dependent Schrödinger equation in R^n with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. The author also considers several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schrödinger equation with variable quadratic Hamiltonians. The Green functions are explicitly found in terms of elementary functions and the corresponding gauge transformations are discussed. The factorization technique is applied to the case of a shifted harmonic oscillator. The time-evolution of the expectation values of the energy related operators is determined for two models of the quantum damped oscillators under consideration. The classical equations of motion for the damped oscillations are derived for the corresponding expectation values of the position operator. Finally, the author constructs integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application. / Dissertation/Thesis / Ph.D. Applied Mathematics for the Life and Social Sciences 2011

abstract: The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle. / Dissertation/Thesis / Ph.D. Mathematics 2011

Interacting Fermi gases are one of the chief paradigms of condensed matter physics. They have been studied since the beginning of the development of quantum mechanics, but continue to produce surprises today. Recent experimental developments in the field of ultracold atomic gases, as well as conventional solid state materials, have produced new and exotic forms of Fermi gases, the theoretical understanding of which is still in its infancy. This Thesis aims to provide updated tools and additional insights into some of these systems, through the application of both numerical and analytical techniques. The first Part of this Thesis is concerned with the development of improved numerical tools for the study of interacting Fermi gases. These tools take the form of accurate model potentials for the dipolar and contact interactions, as found in various ultracold atomic gas experiments, and a new form of Jastrow correlation factor that interpolates between the radial symmetry of the inter-electron Coulomb potential at short inter-particle distances, and the symmetry of the numerical simulation cell at large separation. These methods are designed primarily for use in quantum Monte Carlo numerical calculations, and provide high accuracy along with considerable acceleration of simulations. The second Part shifts focus to an analytical analysis of spin-imbalanced Fermi gases with an attractive contact interaction. The spin-imbalanced Fermi gas is shown to be unstable to the formation of multi-particle instabilities, generalisations of a Cooper pair containing more than two fermions, and then a theory of superconductivity is built from these instabilities. This multi-particle superconductivity is shown to be energetically favourable over conventional superconducting phases in spin-imbalanced Fermi gases, and its unusual experimental consequences are discussed.

Neste trabalho apresentamos uma investigação sobre o ensino de física quântica na formação inicial de professores. Essa pesquisa foi desenvolvida junto a uma disciplina da sétima etapa do curso de Licenciatura em Física da Universidade Federal do Rio Grande do Sul, durante o segundo semestre de 2007, através de uma atividade de ensino centrada na exploração de um software que simula o interferômetro de Mach-Zehnder. Inspirados nos trabalhos de Müller e Wiesner (2002) e Pessoa Jr. (2005), utilizamos o conceito de dualidade onda-partícula como o eixo central das discussões em sala de aula. O objetivo desse estudo consiste em analisar as tensões nos enunciados de estudantes, à luz do referencial sociocultural, e avaliar em que medida os enunciados dos estudantes se articulam à internalização de conceitos de física quântica no uso de instrumentos semióticos. Os resultados mostraram que as ações mediadas pelo uso do interferômetro virtual de Mach-Zehnder, como ferramenta cultural, auxiliaram os processos de compreensão, por parte dos alunos, viabilizando a negociação de significados em sala de aula que são aceitos e compartilhados pela comunidade científica. / In this paper, we present a research of quantum physics teaching in the context of a teachers preparation course. This investigation has been developed in a seventh level discipline of a Bachelor Degree Course in Physics Education, in the Federal University of Rio Grande do Sul, during the second semester of 2006, through a didatical activity based on the use of a computer program that simulate the Mach-Zehnder interferometer. Ispired by Müller and Wiesner (2002) and Pessoa Jr. (2005), we used the concept of wave-particle duality as the central espect of discussions in the classroom. The aim of the present study was to analyze the student’s utterences, in the light of sociocultural theories, and to investigate how the speech of the studants articulates it self to the internalization of quantum physics concepts, in the use of semiotics instruments. The results showed that the actions mediated by the use of virtual Mach-Zehnder interferometer, as a cultural tool, supported the comprehendig process in studants, feasing the negotiation of meanings that are accepted and shared in scientific community.

Quantum correlations play a fundamental role in quantum information science. The variety of their manifestations has become increasingly apparent following the development of novel light sources, protocols and photodetectors. One broad classification identifies two instances of non-classical correlations: particle and mode entanglement. These categories mirror two coexisting descriptions of quantum systems in terms of discrete and continuous variables of the electromagnetic field. The past decades have generated a number of promising results based on schemes which encompass elements from both frameworks, rather than viewing the two descriptions as mutually exclusive. In this context, it is possible to conceive and realise experiments where either the quantum resource or the detection system is 'hybrid'. Optical weak-field homodyne detectors bring together phase sensitivity and photon counting; as such, they represent a detection scheme which works across continuous and discrete variables of the radiation field. In this thesis we present a two-mode weak-field homodyne detection layout with added photon-number resolution and apply it to the study of a split single-photon state and a squeezed vacuum state. As a first test of the capabilities of this system, we investigate the reconstruction of relevant features of a given quantum resource - such as its photon statistics - with our detection scheme. Further, we experimentally demonstrate the observation of an instance of non-classical optical coherence which combines the continuous- and discrete-variable descriptions explicitly. The ability to probe phenomena at the interface of wave and particle regimes opens the way to novel, improved schemes for quantum information processing. From a more fundamental perspective, such hybrid approaches may shed light on the very roots of quantum enhancement.

xv, 215 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / In this dissertation, several new methods for the measurement and control of transverse photonic degrees of freedom are developed. We demonstrate a mode sorter for two-dimensional (2-D) parity of transverse spatial states of light based on an out-of-plane Sagnac interferometer. The first experimental 2-D parity sorting measurements of Hermite-Gauss transverse spatial modes are presented. Due to the inherent phase stability of this type of interferometer, it provides a promising tool for the manipulation of higher order transverse spatial modes for the purposes of quantum information processing. We propose two such applications: the production of both spatial-mode entangled Bell states and heralded single photons, tailored to cover the entire Poincaré sphere of first-order transverse modes. In addition to the aforementioned transverse spatial manipulation based on free-space parity sorting, we introduce several more such techniques involving photons propagating in optical fibers. We show that when a photon propagates in a cylindrically symmetric waveguide, its spin angular momentum and its orbital angular momentum (OAM) interact. This spin-orbit interaction (SOI) leads to the prediction of several novel rotational effects: the spatial or time evolution of the photonic polarization vector is controlled by its OAM quantum number or, conversely, its spatial wave function is controlled by its spin. We demonstrate how these phenomena can be used to reversibly transfer entanglement between the spin and OAM degrees of freedom of two-particle states. In order to provide a deeper insight into the cause of the SOI for photons, we also investigate an analogous interaction for electrons in a cylindrical waveguide and find that each of the SOI effects mentioned above remain manifest for the electron case. We show that the SOI dynamics are quantitatively described by a single expression applying to both electrons and photons and explain their common origin in terms of a universal geometric phase associated with the interplay between either particle's spin and OAM. This implies that these SOI-based effects occur for any particle with spin and thereby exist independently of whether or not the particle has mass, charge, or magnetic moment. / Committee in charge: Daniel Steck, Chairperson, Physics; Michael Raymer, Member, Physics; Jens Noeckel, Member, Physics; Steven van Enk, Member, Physics; Andrew Marcus, Outside Member, Chemistry

xvi, 176 p. : ill. (some col.) / The research presented in this dissertation aims to contribute to the field of atom optics via the implementation and demonstration of an all-optical one-way barrier for 87 Rb atoms--a novel tool for controlling atomic motion. This barrier--a type of atomic turnstile--transmits atoms traveling in one direction but hinders their passage in the other direction. We create the barrier with two laser beams, generating its unidirectional behavior by exploiting the two hyperfine ground states of 87 Rb. In particular, we judiciously choose the frequency of one beam to present a potential well to atoms in one ground state (the transmitting state) and a potential barrier to atoms in the other state (the reflecting state). The second beam optically pumps the atoms from the transmitting state to the reflecting state. A significant component of the experimental work presented here involves generating ultra-cold rubidium atoms for demonstrating the one-way barrier. To this end, we have designed and constructed a sophisticated 87 Rb cooling and trapping apparatus. This apparatus comprises an extensive ultra-high vacuum system, four home-built, frequency-stabilized diode laser systems, a high-power Yb:fiber laser, a multitude of supporting optics, and substantial timing and control electronics. This system allows us to cool and trap rubidium atoms at a temperature of about 30 μK. The results presented in this dissertation are summarized as follows. We successfully implemented a one-way barrier for neutral atoms and demonstrated its asymmetric nature. We used this new tool to compress the phase-space volume of an atomic sample and examined its significance as a physical realization of Maxwell's demon. We also demonstrated the robustness of the barrier's functionality to variations in several important experimental parameters. Lastly, we demonstrated the barrier's ability to cool an atomic sample, substantiating its potential application as a new cooling tool. This dissertation includes previously published coauthored material. / Committee in charge: Dr. Hailin Wang, Chair; Dr. Daniel A. Steck, Research Advisor; Dr. Jens U. Nockel; Dr. David M. Strom; Dr. Jeffrey A. Cina

Na perspectiva da aprendizagem significativa, o conhecimento prévio, ou subsunçor, do aprendiz é imprescindível para que ocorra a ancoragem cognitiva. As representações sociais, juntamente com outras ideias que compõem a ecologia representacional mental do aprendiz, podem ser relevantes em relação ao que se pretende aprender, pois atuam como subsunçores. Algumas dessas ideias podem ter sofrido a influência de meios de divulgação, que auxiliam na difusão de conceitos científicos – ou quase científicos – e podem influenciar o conhecimento das pessoas, por isso se faz necessário investigar qual o significado atribuído a tais conceitos na elaboração de representações sociais. À luz dos referenciais teóricos da aprendizagem significativa e das representações sociais, é apresentado um estudo, cujos objetivos são: 1) a partir das representações em relação à Física Quântica, identificadas no trabalho de mestrado, propor uma Unidade de Ensino Potencialmente Significativo (UEPS) para tratar deste tema a fim de investigar a possibilidade de modificação nessas representações; e 2) identificar possíveis representações sociais sobre outros conceitos de Física Moderna e Contemporânea que possam atuar como subsunçores no processo de aprendizagem significativa. Para alcançar os objetivos, a pesquisa é dividida em duas frentes de trabalho: a primeira dá continuidade à investigação do mestrado sobre o conceito de Física Quântica, buscando a evolução representacional, através da análise de mapas mentais e conceituais abordados no decorrer de uma proposta de ensino, e a segunda trata da investigação de outros conceitos que possam ser alvo de representações sociais, por meio de questionários de associação de palavras, para alcançar o grande público, como por exemplo, estudantes de Ensino Médio, universitários, moradores de uma mesma região, que compartilhem a mesma cultura, etc. Os resultados indicam a existência de possíveis representações sociais sobre os temas pesquisados e a possibilidade de mudança representacional utilizando a proposta de ensino sobre Mecânica Quântica. / In the perspective of the meaningful learning theory, previous knowledge, or subsumers, are indispensable for cognitive anchoring. Social representations, together with other ideas that compose the learner’s mental representation ecology, might be relevant regarding what is to be learned since they act as subsumers. Some of these ideas might have been influenced by the diffusion media, that help to disseminate scientific concepts – or almost cientifick – and might influence people’s knowledge. That’s why it is necessary to investigate the meaning assigned to these concepts in the construction of social representations. Under the frameworks of meaningful learning and social representations theories a research study was carried out with the following objectives: 1) from the social representations identified in the master’s degree study, regarding Quantum Mechanics, to construct a Potentially Meaningful Teaching Until (PMTU) to deal with this subject and to investigate the possibility of changing such representations; 2) to identify possible social representations about other concepts of Modern an Contemporary Physiscs that might act as subsuming concepts in meaningful learning. To reach these objectives the research was divided into two work fronts: the first one provides some continuation to the study carried out in the master’s degree about the concepts of Quantum Physics, looking for a conceptual evolution, through the use of mental and conceptual maps using during the teaching process, and the second one deals with the research of the other concepts that might be target of social representations, through word association questionnaires, to reach a large audience such as, for exemple, high school students, college students, citizens of a given region that share the same culture, etc. Research findings suggest the existance of possible social representations about the chosen topics and also the possibility of a representational change of them using a didactical proposal to teach Quantum Mechanics.