Literatura científica selecionada sobre o tema "Quarks orbital angular momentum"

We have calculated the orbital angular momentum of quarks and gluons in the nucleon. The calculations are carried out in the next to leading order utilizing the so-called valon model. It is found that the average quark orbital angular momentum is positive, but small, and the average gluon orbital angular momentum is negative and large. We also report on some regularities about the total angular momentum of the quarks and the gluon, as well as on the orbital angular momentum of the separate partons. We have also provided partonic angular momentum, [Formula: see text] as a function of [Formula: see text].

We present a recent model calculation of the Wigner distributions for the quarks and the orbital angular momentum carried by the quarks. These Wigner distributions contain combined position and momentum space information of the quark distributions and are related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs).

Analytical and numerical results, for the orbital and spin content carried by different quark flavors in the baryons, are given in the chiral quark model with symmetry breaking. The reduction of the quark spin, due to the spin dilution in the chiral splitting processes, is transferred into the orbital motion of quarks and antiquarks. The orbital angular momentum for each quark flavor in the proton as a function of the partition factor κ and the chiral splitting probability a is shown. The cancellation between the spin and orbital contributions in the spin sum rule and in the baryon magnetic moments is discussed.

We discuss the quark phase-space or Wigner distributions of the nucleon which combine in a single picture all the information contained in the generalized parton distributions and the transverse-momentum dependent parton distributions. In particular, we present results for the distribution of unpolarized quarks in a longitudinally polarized nucleon obtained in a light-front constituent quark model. We show how the quark orbital angular momentum can be extracted from the Wigner distributions and compare it with alternative definitions.

For transversely polarized nucleons the distribution of quarks in the transverse plane is transversely shifted and that shift can be described in terms of Generalized Parton Distributions (GPDs). This observation provides a 'partonic' derivation of the Ji-relation for the quark angular momentum in terms of GPDs. Wigner distributions are used to show that the difference between the Jaffe-Manohar definiton of quark orbital angular momentum and that of Ji is equal to the change of orbital angular momentum due to the final state interactions as the struck quark leaves the target in a DIS experiment.

One of the continuing puzzles in QCD is the origin of the nucleon spin. All of the existing experimental data suggest that the contributions from the quark and gluon spins account only for about 50% of the nucleon spin. In order to account for the remaining 50%, one has to include the orbital angular momentum of the quarks and gluons. One way to establish if quarks carry significant angular momentum, is to perform a measurement of the Sivers function, which describes the correlation of the spin direction of the nucleon with the transverse momentum of the quark. We will describe the E1039 experiment at Fermilab, which will measure the Sivers asymmetry of the sea quarks via the Drell-Yan process, using a 120 GeV unpolarized proton beam on a transversely polarized NH 3 target.

Wigner distribution functions are the quantum analogue of the classical phase space distribution and being quantum implies that they are not genuine phase space distribution and thus lack any probabilistic interpretation. Nevertheless, Wigner distributions are still interesting since they can be related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) under some limit. We study the Wigner distribution of quarks and also the orbital angular momentum (OAM) of quarks in the dressed quark model.

We discuss the observables that have been recently put forth to describe quarks and gluons orbital angular momentum distributions. Starting from a standard parameterization of the energy momentum tensor in QCD one can single out two forms of angular momentum, a so-called kinetic term – Ji decomposition – or a canonical term – Jaffe-Manohar decomposition. Orbital angular momentum has been connected in each decomposition to a different observable, a Generalized Transverse Momentum Distribution (GTMD), for the canonical term, and a twist three Generalized Parton Distribution (GPD) for the kinetic term. While the latter appears as an azimuthal angular modulation in the longitudinal target spin asymmetry in deeply virtual Compton scattering, due to parity constraints, the GTMD associated with canonical angular momentum cannot be measured in a similar set of experiments.

Elastic nucleon form factors constrain the spatial distribution of quarks in the impact parameter plane. A recent analysis found that the average impact parameter of quarks strongly depends on their longitudinal momentum, and obtained an estimate of the orbital angular momentum carried by valence quarks in the proton.

Since the announcement of the proton spin crisis by the European Muon Collaboration there has been considerable progress in unravelling the distribution of spin and orbital angular momentum within the proton. We review the current status of the problem, showing that not only have strong upper limits have been placed on the amount of polarized glue in the proton but that the experimental determination of the spin content has become much more precise. It is now clear that the origin of the discrepancy between experiment and the naive expectation of the fraction of spin carried by the quarks and anti-quarks in the proton lies in the non-perturbative structure of the proton. We explain how the features expected in a modern, relativistic and chirally symmetric description of nucleon structure naturally explain the current data. The consequences of this explanation for the presence of orbital angular momentum on quarks and gluons is reviewed and comparison made with recent results from lattice QCD and experimental data.

Premier aspect : Modélisation des GPDs via les fonctions d'onde du cône de lumière (FOCLs)L'étude améliore les moyens de trouver les fluctuations des nucléons en terme de quarks d'helicité définie. Elle utilise une représentation des distributions généralisées de partons (GPD) fondée sur des FOCLs de moment angulaire orbital de quark défini. Ces FOCLs sont importantes dans les développements de Fock des états hadroniques et sont des projections d'amplitudes à trois quarks. Les projections 3D du cône de lumière de ces amplitudes sont utilisées pour restaurer une interprétation probabiliste. Les amplitudes à trois quarks à projeter, à leur tour, sont des fonctions d'onde définies par des éléments de matrice de nucléon hors diagonale, ce qui permet d'obtenir des LFWF de nucléon de divers moments angulaires orbitaux définis (OAM).Avec ces FOCLs d'hélicité de quark définie, l'étude calcule les GPD par recouvrement. Cette approche permet d'isoler les contributions d'OAM défini aux GPDs des nucléons, aux fonctions de distribution des partons, aux facteurs de forme électromagnétiques et au rayon électrique du nucléon. L'importance de ce travail réside dans son potentiel à cartographier les contributions des états OAM de quark distincts à la structure du nucléon. Second aspect : repondération bayésienne des répliques de GPD en utilisant des données de simulation factice. Une étude systématique est présentée pour démontrer l'impact des données QCD sur réseau sur l'extraction des GPDs. Pour ce faire, un ensemble préalablement développé de modèles de GPDs basés sur des techniques d'apprentissage automatique est utilisé. La modélisation sous-jacente respecte les exigences théoriques, notamment la polynomialité, une forme de contrainte de positivité et des limites connues. Une attention particulière est accordée à l'estimation de l'incertitude découlant de la connexion complexe entre les GPDs et les processus expérimentaux, notamment la diffusion Compton à grande virtualité. Des données de QCD sur réseau factices sont stratégiquement incluses dans un cadre bayésien, réduisant l'incertitude associée aux modèles. L'accent est mis sur l'évaluation de l'impact de la précision, de la corrélation et de la couverture cinématique des données de simulation sur la réduction de l'incertitude, en particulier à obliquité modérée. Cela permet d'établir un lien entre les praticiens de la QCD sur réseau et la modélisation GPDs en examinant les contraintes sur les données simulées nécessaires pour maximiser la réduction de l'incertitude du côté de la modélisation des GPDs. En résumé, cette thèse de doctorat présente une exploration doublement axée sur la dynamique des quarks au sein de la structure nucléonique. Le premier aspect affine la modélisation des GPDs via les fonctions d'onde du cône de lumière (FOCLs), isolant les fluctuations de la projection d'hélicité des quarks et cartographiant la structure multidimensionnelle du nucléon. En complément, le deuxième aspect réalise une étude d'impact, incorporant des données de réseau factices pour contraindre la modélisation préalable des GPDs effectuée précédemment. Utilisant un cadre bayésien, ce travail affine les incertitudes résultant d'un modèle, éclairant ainsi les utilisations possibles des études de QCD sur réseau destinées à alimenter la modélisation des GPDs en combinaison et en complément des données expérimentales actuelles à venir<br>This PhD thesis encompasses two distinct yet interrelated aspects that contribute to the understanding of quark dynamics within the nucleon structure.First Aspect: GPD Modeling via LFWFsThe study improves ways to find quark helicity projection nucleon fluctuations. It uses a representation of Generalized Parton Distributions (GPDs) with definite quark orbital angular momentum Light Front Wave Functions (LFWFs). These LFWFs are important in Fock expansions of hadronic states, and are projections of three-quark amplitudes . The 3D light cone projections of such amplitudes are used to restore a probabilistic interpretation. The three-quark nucleon amplitudes to be projected, in turn, are wave functions defined through off-diagonal nucleon matrix elements, leading to the derivation of nucleon LFWFs of various definite orbital angular momenta (OAM).With these definite quark helicity LFWFs, the study calculates GPDs as combinations of their overlaps. This approach facilitates isolation of definite OAM contributions to nucleon GPDs, Parton Distribution Functions (PDFs), Electromagnetic Form Factors (FFs), and the electric nucleon radius. The significance of this work lies in its potential to map the contributions of distinct quark OAM states to nucleon structure.Second Aspect: Bayesian Reweighting of GPD Replicas Using Mock Lattice DataA systematic study is presented to demonstrate the impact of lattice QCD data on the extraction of GPDs. To achieve this, a previously developed set of GPD models based on machine learning techniques is employed. The underlying modeling adheres to theoretical requirements, including polynomiality, a form of positivity constraint, and known limits. Special attention is given to estimate uncertainty arising from the challenging connection between GPDs and experimental processes, notably deeply virtual Compton scattering (DVCS).Mock lattice QCD data inputs are strategically included in a Bayesian framework, reducing the uncertainty associated with the models. Emphasis is placed on assessing the impact of precision, correlation, and kinematic coverage of lattice data on uncertainty reduction, particularly at moderate skewness. This allows for a connection between lattice QCD practitioners and GPD modeling by investigating the constraints on lattice data necessary for the greatest reduction of uncertainty on the modeling side of nucleon GPD physics.In summary, this PhD thesis presents a dual-focused exploration of quark dynamics within the nucleon structure. The first aspect refines GPD modeling through LFWFs, isolating quark helicity projection nucleon fluctuations and delineating the multidimensional structure of the nucleon. Complementing this, the second aspect conducts an impact study, incorporating mock lattice data to constrain prior GPD modeling by colleagues of the candidate. Utilizing a Bayesian framework, the study refines uncertainties resulting from a prior model based on Goloskov and Kroll's phenomenological approach, and in doing so elucidates possible uses of directed lattice QCD studies intended to feed GPD modeling in combination and complement to current and future experimental data

Entanglement in higher dimensions is an attractive concept that is a chal- lenge to realise experimentally. To this end, the entanglement of the orbital angular momentum (OAM) of photons holds promise. The OAM state-space is discrete and theoretically unbounded. In the work that follows, we investi- gate various aspects of OAM entanglement. We show how the correlations in OAM and its conjugate variable, angular position, are determined by phase- matching and the shape of the pump beam in spontaneous parametric down- conversion. We implement tests of quantum mechanics which have been previously done for other variables. We show the Einstein-Podolsky-Rosen paradox for OAM and angle, supporting the incompatibility of quantum me- chanics with locality and realism. We demonstrate violations of Bell-type inequalities, thereby discounting local hidden variables for describing the correlations we observe. We show the Hardy paradox using OAM, again highlighting the nonlocal nature of quantum mechanics. We demonstrate violations of Leggett-type inequalities, thereby discounting nonlocal hidden variables for describing correlations. Lastly, we have looked into the entan- glement of topological vortex structures formed from a special superposition of OAM modes and show violations of Bell-type inequalities confined to a finite, isolated volume.

A causa de la gran flexibilitat que ofereixen en la seva manipulació i control, els sistemes d’àtoms ultrafreds són ideals per simular un ampli ventall de models de matèria condensada i constitueixen una plataforma molt prometedora per a la implementació de noves tecnologies quàntiques. En aquest context, l’atomtrònica s’ha establert recentment com un nou camp de recerca que té per objectiu crear circuits d’ones de matèria amb àtoms ultrafreds en micro trampes òptiques versàtils, amb el doble propòsit d’explorar nous fenòmens físics i de construir dispositius quàntics com ara sensors o ordinadors. Els circuits atomtrònics més senzills estan formats per potencials en forma d’anell, els quals proporcionen camins tancats pels àtoms que admeten de manera natural estats de Moment Angular Orbital (MAO). Inspirats per aquests avenços, en aquesta tesi investiguem diversos sistemes que comparteixen la característica d’estar formats per àtoms ultrafreds en estats amb MAO en potencials amb simetria cilíndrica. El nostre interès es centra en tres aspectes dels estats amb MAO: el seu potencial per fabricar sensors, les seves aplicacions en la simulació de models de magnetisme quàntic, i les possibilitats que ofereixen per obtenir estats topològics. Primerament, considerem un Condensat de Bose-Einstein (CBE) atrapat en un únic potencial en forma d’anell i preparat en una superposició d’estats amb MAO que roten en direccions oposades. El perfil d’aquesta superposició mostra una línia de mínima densitat que gira a causa de la interacció no lineal entre els àtoms. Després de derivar una expressió que relaciona la freqüència d’aquesta rotació amb la força de les interaccions, proposem protocols que permeten fer servir el sistema com un sensor d’interaccions a dos cossos, camps magnètics i rotacions. A continuació, explorem diferents configuracions de potencials acoblats lateralment en les quals els àtoms ultrafreds experimenten una dinàmica d’efecte túnel governada per amplituds complexes amb fases que es poden variar modificant la geometria del sistema. En primer lloc, estudiem una xarxa en forma de cadena de diamant carregada amb àtoms no interactuants en estats amb MAO. En aquest sistema, les fases de les amplituds d’efecte túnel complexes donen lloc a una estructura de bandes topològica amb els seus corresponents estats de vora. A més, ajustant de manera adequada les amplituds d’efecte túnel es pot obtenir un espectre d’energies composat únicament de bandes planes. En aquest cas, el sistema mostra confinament d’Aharonov-Bohm. A continuació, analitzem una família de sistemes consistent en distribucions de potencials d’anell amb una geometria flexible plenes amb bosons fortament correlacionats en estats amb MAO. Ens centrem en el règim d’aïllant de Mott amb un àtom per trampa, en el qual es pot establir una correspondència entre estats amb MAO i d’espín-1/2. Mostrem que, ordenant les trampes de manera adequada, aquests sistemes poden simular diferents models d’espí d’interès relacionats amb un model de Heisenberg general. Seguidament, ens tornem a fixar en la cadena de diamant per investigar la física de dos bosons amb interacció atractiva en el límit en el qual totes les bandes són planes. En aquesta situació, l’energia cinètica no juga cap paper i les propietats del sistema venen determinades únicament per les interaccions. Mostrem que el sector de baixa energia de l’espectre d’estats de dos bosons es pot descriure en termes de models efectius d’una sola partícula que són topològicament no trivials. Finalment, estudiem una xarxa quadrada en dues dimensions amb diferents separacions fora i dintre de la cel·la unitat. Demostrem que aquest sistema constitueix un exemple d’aïllant topològic de segon ordre, presentant un moment quadrupolar finit i estats de cantonada protegits.<br>Debido a la gran flexibilidad que ofrecen en su manipulación y control, los sistemas de átomos ultrafríos son ideales para simular un amplio abanico de modelos de materia condensada y constituyen una plataforma muy prometedora para la implementación de nuevas tecnologías cuánticas. En este contexto, la atomtrónica se ha establecido recientemente como un nuevo campo de investigación cuyo objetivo es crear circuitos de ondas de materia con átomos ultrafríos manipulados mediante micro trampas ópticas versátiles, con el doble propósito de explorar nuevos fenómenos físicos y de construir dispositivos cuánticos como sensores u ordenadores. Los circuitos atomtrónicos más sencillos están formados por potenciales en forma de anillo, los cuales proporcionan caminos cerrados para los átomos que admiten de manera natural estados con Momento Angular Orbital (MAO). Inspirados por estos avances, en esta tesis investigamos diversos sistemas que comparten la característica de estar formados por átomos ultrafríos con carga de MAO en potenciales con simetría cilíndrica. Nuestro interés se centra en tres aspectos de los estados con MAO: su potencial para fabricar sensores, sus aplicaciones en la simulación de modelos de magnetismo cuántico, y las posibilidades que ofrecen para obtener estados topológicos. Empezamos considerando un condensado de Bose-Einstein (CBE) atrapado en un único potencial en forma de anillo y preparado en una superposición de estados con MAO que rotan en direcciones opuestas. El perfil de esta superposición muestra una línea de mínima densidad que gira debido a la interacción no lineal entre los átomos. Después de deducir una expresión que relaciona la frecuencia de esta rotación con la fuerza de las interacciones, proponemos protocolos que permiten utilizar el sistema como un sensor de interacciones a dos cuerpos, campos magnéticos y rotaciones. A continuación, estudiamos diferentes configuraciones de potenciales acoplados lateralmente en las que los átomos ultrafríos experimentan una dinámica de efecto túnel gobernada por amplitudes complejas con fases que se pueden variar modificando la geometría del sistema. En primer lugar, exploramos una red en forma de cadena de diamante llena con átomos no interactuantes en estados con MAO. En este sistema, las fases de las amplitudes de efecto túnel complejas dan lugar a una estructura de bandas topológica con sus correspondientes estados de borde. Además, ajustando de forma adecuada las amplitudes de efecto túnel, se puede obtener un espectro de energías compuesto únicamente de bandas planas. En este caso, el sistema muestra confinamiento de Aharonov-Bohm. En segundo lugar, analizamos una familia de sistemas consistente en distribuciones de potenciales de anillo con una geometría flexible llenas con bosones fuertemente correlacionados en estados de MAO. Nos centramos en el régimen de aislante de Mott con un átomo por trampa, en el que se puede establecer una correspondencia entre estados con MAO y de espín-1/2. Mostramos que, ordenando las trampas de manera adecuada, estos sistemas pueden simular diferentes modelos de espín de interés relacionados con un modelo de Heisenberg general. Seguidamente nos volvemos a fijar en la cadena de diamante para investigar la física de dos bosones con interacción atractiva en el límite en el que todas las bandas son planas. En esta situación, la energía cinética no juega ningún papel y las propiedades del sistema vienen determinadas únicamente por las interacciones. Mostramos que el sector de baja energía del espectro de estados de dos bosones se puede describir en términos de modelos efectivos de una sola partícula que son topológicamente no triviales. Finalmente, estudiamos una red cuadrada en dos dimensiones con diferentes separaciones fuera y dentro de la celda unidad. Demostramos que este sistema constituye un ejemplo de aislante topológico de segundo orden, presentando un momento cuadrupolar finito y estados de esquina protegidos.<br>Due to their high degree of tunability and controllability, ultracold atom systems constitute an ideal playground for simulating a wide variety of condensed matter models and are one of the most promising platforms for the implementation of novel quantum technologies. In this context, the emerging field of atomtronics aims at realizing matter-wave circuits with ultracold atoms in versatile optical micro-traps. These efforts have a two-fold purpose: exploring new fundamental physics and constructing quantum devices such as sensors or computers. The simplest atomtronic circuits are formed by ring-shaped potentials, which provide closed loops for the atoms that naturally support Orbital Angular Momentum (OAM) states. Motivated by these advances, in this thesis we investigate different systems that have the common characteristic of being formed by ultracold atoms carrying OAM in cylindrically symmetric potentials. Our interest is focused on three aspects of OAM states: their potential use for sensing purposes, their applications as quantum simulators of models of quantum magnetism, and the possibilities that they offer for realizing topological phases of matter. We start by considering a Bose Einstein Condensate (BEC) trapped in a single ring potential and prepared in a superposition of counter-rotating OAM states. The density profile of this state has a minimal line that rotates due to the non-linear interaction between the atoms. After deriving an expression that relates the frequency of this rotation with the strength of the interactions, we propose protocols to use the system as a device for sensing two-body interactions, magnetic fields and rotations. Next, we explore several configurations of side-coupled potentials where ultracold atoms in OAM states experience tunnelling dynamics that are governed by complex amplitudes with phases that can be tuned by modifying the geometry of the system. First, we study a lattice with a diamond chain shape filled with non-interacting ultracold atoms carrying OAM. In this system, the phases in the tunnelling rates give rise to a topological band structure with its corresponding protected edge states. Furthermore, a proper tuning of the tunneling parameters may lead to an energy spectrum composed entirely of flat bands. In this scenario, the system exhibits Aharonov-Bohm caging. We then analyse a family of systems consisting of arrays of ring potentials with a flexible geometry filled with strongly correlated bosons in OAM states. We focus on the Mott insulator regime at unit filling, for which one can establish a correspondence between OAM and spin-1/2 states. We demonstrate that by properly arranging the traps, these systems can realize different spin models of interest related to a general Heisenberg model. Then, we turn our attention back to the diamond chain to examine the physics of two attractively interacting bosons in the limit when all bands are flat. In this situation, the kinetic energy is frozen and the properties of the system are solely determined by the interactions. We show that the low-energy sector of the two-boson spectrum can be described in terms of effective single-particle models that are topologically non-trivial. Finally, we investigate a two-dimensional square lattice with different intra- and inter-cell spacings in the non-interacting limit. We show that this system constitutes an example of a second-order topological insulator, displaying a finite quadrupole moment and protected corner states.

The desire to increase the amount of information that can be encoded onto a single photon has driven research in many areas of optics. One such area is the study of the orbital angular momentum (OAM) carried by a light beam. These beams have helical phase-fronts and carry an orbital angular momentum of l_hbar per photon, where the integer l is unbounded, giving a large state space in which to encode information. In the work that follows I discuss the development of new methods to measure the OAM carried by a light beam. An adaptation of a previously outlined interferometric technique is presented, resulting in a compact, robust measurement tool while dramatically reducing the number of degrees of freedom required for alignment. A new approach to sorting OAM is discussed, inspired by the simple example of the discrimination of plane waves focussed by a lens within direction space. This new approach is a telescopic system comprising two bespoke optical elements that transform OAM states into transverse momentum states; the various stages of development are outlined. Further to the development of this technique, investigations into the effects of misalignment and atmospheric turbulence on a communication link are presented. Outwith the area of optical communications, it is shown that by analysing the orbital angular momentum of light scattered from a spinning object we can observe a frequency shift many times greater than the rotation rate.

Electron vortex beams are beams of freely propagating electrons that possess orbital angular momentum. Recently predicted and experimentally verified, electron vortices are hoped to lead to new developments in several areas, in particular electron microscopy, as well as other areas as diverse as spintronics and quantum information. This thesis introduces and examines key concepts relating to electron vortices, and as an introduction, the major developments relating to electron vortices over the past few years are outlined and discussed. The Bessel beam is derived as a suitable solution to the Schrodinger equation for an electron beam carrying orbital angular momentum. The linear and orbital angular momenta of such a beam are discussed alongside the use of electron vortices in manipulation of nanoparticles. Being a charged particle the electron vortex carries electromagnetic fields; the magnetic field is found to have an axial component, unique to the vortex beam. Coupling between the spin and orbital angular momentum of the electron propagating within its own field is found to be negligible in typical electron microscope contexts. Electron vortices are found to have a similar form as the more widely known optical vortices, but key differences between electrons and photons lead to fundamentally different behaviour in many circumstances. The main differences between electron and optical vortices are outlined throughout this thesis. Interactions between the electron and optical vortices and matter, in the form of a hydrogenic atom, are considered. In contrast to the optical vortex, interactions between atomic matter and the electron vortex are found to lead to transfer of orbital angular momentum, opening the possibility of using electron vortices in the electron microscope to probe magnetism at nano- or atomic-scales. The premise and requirements of such experiments are discussed.

Thesis (Ph.D.)--Boston University<br>Internet data traffic capacity is rapidly reaching limits imposed by nonlinear effects of single mode fibers currently used in optical communications. Having almost exhausted available degrees of freedom to orthogonally multiplex data in optical fibers, researchers are now exploring the possibility of using the spatial dimension of fibers, via multicore and multimode fibers, to address the forthcoming capacity crunch. While multicore fibers require complex manufacturing, conventional multimode fibers suffer from mode coupling, caused by random perturbations in fibers and modal (de)multiplexers. Methods that have been developed to address the problem of mode coupling so far, have been dependent on computationally intensive digital signal processing algorithms using adaptive optics feedback or complex multiple-input multiple-output algorithms. Here we study the possibility of using the orbital angular momentum (OAM), or helicity, of light, as a means of increasing capacity of future optical fiber communication links. We first introduce a class of specialty fibers designed to minimize mode coupling and show their potential for OAM mode generation in fibers using numerical analysis. We then experimentally confirm the existence of OAM states in these fibers using methods based on fiber gratings and spatial light modulators. In order to quantify the purity of created OAM states, we developed two methods based on mode-image analysis, showing purity of OAM states to be 90% after 1km in these fibers. Finally, in order to demonstrate data transmission using OAM states, we developed a 4-mode multiplexing and demultiplexing systems based on free-space optics and spatial light modulators. Using simple coherent detection methods, we successfully transmit data at 400Gbit/s using four OAM modes at a single wavelength, over 1.1 km of fiber. Furthermore, we achieve data transmission at 1.6Tbit/s using 10 wavelengths and two OAM modes. Our study indicates that OAM light can exist, and be long lived, in a special class of fibers and our data transmission demonstrations show that OAM could be considered an additional degree of freedom for data multiplexing in future optical fiber communication links. Our studies open the doors for other applications such as micro-endoscopy and nanoscale imaging which require fiber based remote delivery of OAM light.

Orbital Angular Momentum (OAM) is a fundamental property of electromagnetic fields, associated to helicity of waves phase fronts. Like frequency and polarization, it represents a degree of freedom of an electromagnetic field and can be used for its identification. In fact, two waves with the same frequency but different OAM values can be distinguished from each other when their whole phase fronts are collected. Electromagnetic fields with nonzero OAM form an orthogonal basis and can be discriminated, without any digital post processing, at the physical layer. For this reason, they represent an interesting tool for the development of new multiplexing systems that better exploit the electromagnetic spectrum. Within this context, this thesis presents the main results of theoretical and experimental studies on the application of OAM waves to radio multiplexing systems. It starts by considering the state-of-the-art of radio OAM waves, in order to identify features and applications concerning telecommunications. Then, it examines special parabolic antennas, also known as conformal antennas, that can generate and recognize electromagnetic waves at radio frequency with integer values of OAM. These antennas are then employed in practical experiments to test long-range multiplexing system prototypes, where three channels are transmitted and received on the same frequency and polarization state. The experiments study the difficulties of exploiting OAM modes orthogonality over long distances. In fact, due to diffraction, the size of field distributions increases more and more during propagation. Therefore, over long distances, it is necessary to use large antennas to collect their whole phase fronts. To overcome this problem and reduce the size of the received fields two interesting solutions are presented. The first one concerns a particular effect of field concentration that can be obtained superimposing electromagnetic waves with integer and consecutive values of OAM. The second one, on the contrary, studies the generation process for a special class of OAM fields, called higher order vortex beams, that are characterized by a more compact intensity distribution. Hence, the thesis considers the possibility of distinguish radio waves with different OAM values by receiving only a small portion of the phase fronts. This latter study, developed by using MIMO systems theory and theoretical models on OAM beams propagation, focuses also in the comparison between general multiplexing systems based on today MIMO technology with the ones based on OAM waves. The analysis of long-range systems is then concluded by examining, both theoretically and experimentally, the superposition of waves with opposite values of OAM. These fields, in fact, are characterized by a more regular distribution and can be useful in simplifying the structure of OAM-based communication systems. In the end, the thesis considers short range communications where OAM waves are used not only for multiplexing purposes but also to increase, directly at the physical layer, the communication security.<br>Il momento angolare orbitale, normalmente identificato con l’acronimo inglese OAM (Orbital Angular Momentum), é una proprietá fondamentale dei campi elettromagnetici legata alla loro distribuzione; campi con OAM diverso da zero sono infatti caratterizzati da intensitá a forma di ciambella e da fronti d’onda che si avvolgono a spirale. Al pari della frequenza, anche l’OAM rappresenta un grado di libertá di un’onda elettromagnetica e puó essere utilizzato per la sua identificazione. Infatti, due campi aventi la stessa frequenza ma diverso valore di OAM possono essere distinti quando i loro fronti d’onda vengono ricevuti interamente. Questa caratteristica fa sí che i campi elettromagnetici con OAM formino una base ortogonale e che possano essere distinti direttamente a livello fisico, senza il bisogno di post processing digitale. Le onde con OAM sono quindi particolarmente interessanti per lo sviluppo di nuovi sistemi radio multiplexing sia su lunga che su breve distanza, argomento esaminato sia teoricamente che sperimentalmente nella presente tesi. Lo studio inizia con l’esame dello stato dell’arte sulle onde radio con OAM per individuarne caratteristiche ed applicazioni legate alle telecomunicazioni. Viene quindi studiato un particolare tipo di antenne paraboliche, dette anche “conformate”, in grado di generare e di riconoscere onde radio con diversi valori di OAM. Usando queste antenne, viene quindi condotto uno studio sperimentale per valutare un prototipo di sistema multiplexing su lunga distanza, composto da tre canali isofrequenziali. L’esperimento evidenzia le difficoltá, precedentemente individuate nella fase di studio, riguardanti l’implementazione di un simile sistema. Durante la propagazione, infatti, i fronti d’onda si espandono a causa della diffrazione e risulta complicato riceverli interamente senza l’impiego di antenne ingombranti. Questo comporta una notevole difficoltá nello sfruttamento dell’ortogonalitá fra onde radio con OAM su lunghe distanze e costituisce un forte limite all’implementazione di un sistema multiplexing. Per ovviare a questo problema la tesi esamina tre possibili soluzioni. Nella prima considera un metodo per concentrare la distribuzione di un campo elettromagnetico con OAM mediante la sovrapposizione di modi interi e consecutivi. Nella seconda, studia la generazione di campi con OAM detti “di ordine superiore”, (higher order vortex beams), caratterizzati da una distribuzione di intensitá piú compatta. Nella terza, infine, esamina la possibilitá di distinguere due onde radio con diverso OAM mediante una ricezione parziale del loro campo elettromagnetico. Quest’ultima soluzione, analizzata mediante il formalismo dei sistemi MIMO e di modelli teorici sulla propagazione delle onde con OAM, consente anche di operare un confronto generale fra sistemi multiplexing basati sulle odierne tecniche MIMO e quelli basati su onde radio con OAM. Lo studio di sistemi a lunga distanza si conclude quindi esaminando le sovrapposizioni di campi elettromagnetici con valori opposti di OAM. Queste infatti, essendo caratterizzate da una distribuzione semplice e regolare, possono costituire un’interessante opzione per semplificare la struttura di sistemi di comunicazione basati su onde con OAM. Infine, nell’ultima parte, la tesi esamina sistemi multiplexing su breve distanza dove i campi elettromagnetici con OAM vengono utilizzati non solo per implementare un multiplexing ma anche per aumentare, direttamente a livello fisico, la sicurezza della comunicazione.

Studying the orbital angular momentum (OAM) of light has become rather fashion- able in the 21st century. Yet, most of major advances in OAM related research have been conducted in the visible regime of light. A significant portion OAM research revolves around using OAM radiation to perform some function that is deemed useful. Examples of this are optical trapping, micro-machine manipulation and the development of advanced communication systems. Photon entanglement measurements also make use of OAM radiation. Interest in probing radiation for naturally generated OAM is far less popular. For example, interest in building OAM sensitive telescopes was sparse at the beginning of this thesis, however the first reported detection of astrophysical OAM was published in 2013. This thesis aims to tackle these two areas of sparse research by developing the components and understanding in order to build OAM sensitive millimetre-wavelength telescopes. Spiral phase plates (SPPs) are the device of choice. The majority of the thesis sets out to test three different SPPs, in order to compare and contrast different methods for their manufacture and design. Electromagnetic theory of OAM and its generation is reviewed first. Then, each SPP is modelled numerically fol- lowed by in-depth modelling of each plate by using the computational electromagnetic package FEKO. Finally, each plate is measured with a three dimensional field scanner developed as part of this thesis. Development of a new modular SPP design concludes this thesis.

Thesis (PhD)--Stellenbosch University, 2014.<br>ENGLISH ABSTRACT: High-dimensional quantum entanglement offers an increase in information capacity per photon; a highly desirable property for quantum information processes such as quantum communication, computation and teleportation. As the orbital angular momentum (OAM) modes of light span an infinite-dimensional Hilbert space, they have become frontrunners in achieving entanglement in higher dimensions. In light of this, we investigate the potential of OAM entanglement of photons by controlling the parameters in both the generation and measurement systems. We show the experimental procedures and apparatus involved in generating and measuring entangled photons in two-dimensions. We verify important quantum tests such as the Einstein, Podolsky and Rosen (EPR) paradox using OAM and angle correlations, as well as a violation of a Bell-type inequality. By performing a full state tomography, we characterise our quantum state and show we have a pure, highly entangled quantum state. We demonstrate that this method can be extended to higher dimensions. The experimental techniques used to generate and measure OAM entanglement place an upper bound on the number of accessible OAM modes. As such, we investigate new methods in which to increase the spiral bandwidth of our generated quantum state. We alter the shape of the pump beam in spontaneous parametric down-conversion and demonstrate an effect on both OAM and angle correlations. We also made changes to the measurement scheme by projecting the photon pairs into the Bessel-Gaussian (BG) basis and demonstrate entanglement in this basis. We show that this method allows the measured spiral bandwidth to be optimised by simply varying the continuous radial parameter of the BG modes. We demonstrate that BG modes can be entangled in higher dimensions compared with the commonly used helical modes by calculating and comparing the linear entropy and fidelity for both modes. We also show that quantum entanglement can be accurately simulated using classical light using back-projection, which allows the study of projective measurements and predicts the strength of the coincidence correlations in an entanglement experiment. Finally, we make use of each of the techniques to demonstrate the effect of a perturbation on OAM entanglement measured in the BG basis. We investigate the self-healing property of BG beams and show that the classical property is translated to the quantum regime. By calculating the concurrence, we see that measured entanglement recovers after encountering an obstruction.<br>AFRIKAANSE OPSOMMING: Hoë-dimensionele kwantumverstrengeldheid bied ’n toename in inligtingskapasiteit per foton. Hierdie is ’n hoogs wenslike eienskap vir kwantum inligting prosesse soos kwantum kommunikasie, berekening en teleportasie. Omdat die orbitale hoekmomentum (OAM) modusse van lig ’n oneindig dimensionele Hilbertruimte beslaan, het dit voorlopers geword in die verkryging van verstrengeling in hoër dimensies. In die lig hiervan, ondersoek ons die potensiaal van OAM verstrengeling van fotone deur die parameters in beide die generering en meting stelsels te beheer. Ons toon die eksperimentele prosedures en apparaat wat betrokke is by die generering en die meet van verstrengelde fotone in twee dimensies. Ons verifieer kwantumtoetse, soos die Einstein, Podolsky en Rosen (EPR) paradoks vir OAM en die hoekkorrelasies, sowel as ’n skending van ’n Bell-tipe ongelykheid. Deur middel van ’n volledige toestand tomografie, karakteriseer ons die kwantum toestand en wys ons dat dit ’n suiwer, hoogs verstrengel kwantum toestand is. Ons toon ook dat hierdie metode uitgebrei kan word na hoër dimensies. Die eksperimentele tegnieke wat tydens die generasie en meet van OAM verstrengeling gebruik is, plaas ’n bogrens op die aantal toeganklik OAM modusse. Dus ondersoek ons nuwe metodes om die spiraal bandwydte van ons gegenereerde kwantum toestand te verhoog. Ons verander die vorm van die pomp bundel in spontane parametriese af-omskakeling en demonstreer die uitwerking daarvan op beide OAM en die hoekkorrelasies. Ons het ook veranderinge aan die meting skema gemaak deur die foton pare op die Bessel-Gauss (BG) basis te projekteer. Ons wys dat hierdie metode die gemeetde spiraal bandwydte kan optimeer deur eenvoudig die kontinue radiale parameter van die BG modes te verander. Ons demonstreer dat BG modusse verstrengel kan word in hoër dimensies as die heliese modusse, wat algemeen gebruik word, deur berekeninge te maak en te vergelyk met lineêre entropie en vir beide modusse. Ons wys ook dat kwantumverstrengling akkuraat nageboots kan word, met behulp van die klassieke lig terug-projeksie, wat die studie van projeksie metings toelaat en voorspel die krag van die saamval korrelasies in ’n verstrengeling eksperiment. Ten slotte, gebruik ons elk van die tegnieke om die effek van ’n storing op OAM verstrengling wat in die BG basis gemeet is, te demonstreer. Ons ondersoek die self-genesingseienskap van BG bundels en wys dat die klassieke eienskap vertaal na die kwantum-gebied. Deur die berekening van die konkurrensie (concurrence), sien ons dat die gemeetde verstrengeling herstel word nadat ’n obstruksie ondervind is.

Orbital angular momentum (OAM) is one of the most recently discovered properties of light, and it is only in the past decade its quantum properties have been the subject of experimental investigations and have found applications. Unlike polarization, which is only bidimensional, orbital angular momentum provides, with relative ease, unprecedented access to a theoretically unbounded discrete state space. The process of spontaneous parametric down-conversion has long been used as a source of two-photon states that can be entangled in several degrees of freedom, including OAM. In this thesis, the properties of the natural OAM spectrum associated with the entangled states produced by parametric down-conversion were investigated. Chapters 2 and 3 describe the production and detection of tunable high-dimensional OAM entanglement in a down-conversion system. By tuning the phase-matching conditions and improving the detection stage, a substantial increase in the half-width of the OAM correlation spectrum was observed. The conjugate variable of OAM, angular position, was also considered when examining high-dimensional states entangled in OAM. In order to efficiently determine their dimension, high-dimensional entangled states were probed by implementing a technique based on phase masks composed of multiple angular sectors, as opposed to narrow single-sector analysers. Presented in chapter 4, this technique allows the measurements of tight angular correlations while maintaining high optical throughput. The states so produced were then used for a number of applications centred around the concept of mutually unbiased bases. One can define sets of mutually unbiased bases for arbitrary subspaces of the OAM state space. Two bases are mutually unbiased if the measurement of a state in one basis provides no information about the state as described in the other basis. Complete measurements in mutually unbiased bases of high-dimensional OAM spaces are presented in chapter 5. Measurements in sets of mutually unbiased bases are integral to quantum science and can be used in a variety of protocols that fully exploit the large size of the OAM state space; we describe their use in efficient quantum state tomography, quantum key distribution and entanglement detection. Caution is however necessary when dealing with state spaces embedded in higher-dimensional spaces, such as that provided by OAM. Experimental tests of Bell-type inequalities allow us to rule out local hidden variable theories in the description of quantum correlations. Correlations inconsistent with the states observed, or even with quantum mechanics, known as super-quantum correlations, have however been recorded previously in experiments that fail to comply with the fair-sampling conditions. Chapter 6 describes an experiment that uses a particular choice of transverse spatial modes for which super-quantum correlations persist even if the detection is made perfectly efficient. The sets of modes carrying OAM allow a complete description of the transverse field. The ability to control and combine additional degrees of freedom provides the possibility for richer varieties of entanglement and can make quantum protocols more powerful and versatile. One such property of light, associated with transverse modes possessing radial nodes in the field distribution, can be accessed within the same type of experimental apparatus used for OAM. In chapter 7, the radial degree of freedom is explored, together with OAM, in the context of Hong-Ou-Mandel interference.