Dissertationen zum Thema „Quarks orbital angular momentum“

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
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.
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.
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
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.
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.
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.
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.

The electron microscope is an ideal tool to prepare an electron into a specified quantum state, entangle that state with states in a specimen of interest, and measure the electron final state to indirectly gain information about the specimen. There currently exist excellent technologies to prepare both momentum eigenstates (transmission electron microscopy) and position eigenstates (scanning transmission electron microscopy) in a narrow band of energy eigenstates. Similarly, measurement of the momentum and position final states is straightforward with post-specimen lenses and pixelated detectors. Measurement of final energy eigenstates is possible with magnetic electron energy loss spectrometers. In 2010 and 2011, several groups independently showed that it was straightforward to prepare electrons into orbital angular momentum eigenstates. This disseratation represents my contributions to the toolset we have to control these eigenstates: preparation, application (interaction with specimen states), and measurement. My collaborators and I showed that phase diffraction gratings efficiently produce electron orbital angular momentum eigenstates; that control of orbital angular momentum can be used to probe chirality and local magnetic fields; and that there are several routes toward efficient measurement.

We shall present a theoretical description of paraxial beams, showing the propagation modes that arise from the solution of the paraxial equation in free space. We then discuss the angular momentum carried by light beams, with its decomposition in spin and orbital angular momentum and its quantization. We present the polarization and transverse modes of a beam as potential degrees of freedom to encode information. We define the Spin-Orbit modes and explain the experimental methods to produce such modes. We then apply the Spin-Orbit modes to perform a BB84 quantum key distribution protocol without a shared reference frame.We propose a Bell-like inequality criterion as a sufficient condition for the spin-orbit non-separability of a classical laser beam. We show that the notion of separable and non-separable spin-orbit modes in classical optics builds a useful analogy with entangled quantum states, allowing for the study of some of their important mathematical properties. We present a detailed quantum optical description of the experiment in which a comprehensive range of quantum states are considered.Following the study of Bell's inequalities we consider bipartite quantum systems characterized by a continuous angular variable θ. We show how to reveal non-locality on this type of system using inequalities similar to CHSH ones, originally derived for bipartite spin 1/2 like systems. Such inequalities involve correlated measurement of continuous angular functions and are equivalent to the continuous superposition of CHSH inequalities acting on two-dimensional subspaces of the infinite dimensional Hilbert space. As an example, we discuss in detail one application of our results, which consists in measuring orientation correlations on the transverse profile of entangled photons.

Dans une première partie introductive, nous rappelons la description théorique de la propagation de faisceaux optiques en terme des modes solutions de l'équation de propagation dans l'approximation paraxialle. Dans ce cadre, nous présentons les notions de moment cinétique transporté par les faisceaux lumineux, et de sa décomposition en moment cinétique intrinsèque (ou spin) et en moment angulaire.La seconde partie est consacrée au codage de l'information dans les degrés de libertés de polarisation et de modes transverses des faisceaux optiques. Les modes spin-orbites sont définis et un dispositif expérimental optique pour produire ces modes est présenté. Les modes spin-orbites sont alors exploités pour implémenter un protocole de distribution de clés BB84 ne nécessitant pas le partage à priori d'une base de référence.Dans une troisième partie, nous proposons un critère de type inégalité de Bell, qui constitue une condition suffisante pour caractériser la non-séparabilité en spin-orbite d'un faisceau optique classique. Nous montrons ensuite que la notion de modes spin-orbite séparable ou non-séparable constitue une analogie pertinente avec la notion d'intrication d'états quantiques et permet l'étude de certaines de ses propriétés fondamentales. Enfin, une implémentation expérimentale de cette simulation de tests de Bell avec des faisceaux optiques classiques est présentée, ainsi que sa description détaillée dans le cadre de l'optique quantique.Dans une dernière partie, nous nous intéressons à des inégalités de Bell, pour des états quantiques de systèmes quantiques à deux parties, qui sont caractérisées chacune par une variable continue de type angulaire (périodique). Nous montrons comment détecter la non-localité sur ce type de système, avec des inégalités qui sont similaires aux inégalités CHSH; inégalités qui avaient été développées originellement pour des systèmes de type spin 1/2. Nos inégalités, sont construites à partir de la mesure de la corrélation de fonctions angulaires. Nous montrons qu'elles sont en fait la superposition continue d'inégalités CHSH de type spin 1/2. Nous envisageons une possible implémentation expérimentale, où les corrélations mesurées sont les corrélations angulaires du profil transverse des photons intriqués
We shall present a theoretical description of paraxial beams, showing the propagation modes that arise from the solution of the paraxial equation in free space. We then discuss the angular momentum carried by light beams, with its decomposition in spin and orbital angular momentum and its quantization. We present the polarization and transverse modes of a beam as potential degrees of freedom to encode information. We define the Spin-Orbit modes and explain the experimental methods to produce such modes. We then apply the Spin-Orbit modes to perform a BB84 quantum key distribution protocol without a shared reference frame.We propose a Bell-like inequality criterion as a sufficient condition for the spin-orbit non-separability of a classical laser beam. We show that the notion of separable and non-separable spin-orbit modes in classical optics builds a useful analogy with entangled quantum states, allowing for the study of some of their important mathematical properties. We present a detailed quantum optical description of the experiment in which a comprehensive range of quantum states are considered.Following the study of Bell's inequalities we consider bipartite quantum systems characterized by a continuous angular variable θ. We show how to reveal non-locality on this type of system using inequalities similar to CHSH ones, originally derived for bipartite spin 1/2 like systems. Such inequalities involve correlated measurement of continuous angular functions and are equivalent to the continuous superposition of CHSH inequalities acting on two-dimensional subspaces of the infinite dimensional Hilbert space. As an example, we discuss in detail one application of our results, which consists in measuring orientation correlations on the transverse profile of entangled photons

Orbital angular momentum of light is a new field of research which is concerned with the mechanical and optical effects of light with a helical phase structure. In this thesis we ask fundamental questions on the properties of light carrying orbital angular momentum. We discuss the uncertainty relation for angle and angular momentum on the example of orbital angular momentum of light. The lower bound in the angular uncertainty relation is state dependent, which requires a distinction between states satisfying the equality in the uncertainty relation and states giving a minimum in the uncertainty product. We examine these special states and their uncertainty product. We show that for both kinds of states, the uncertainty product can be surprisingly large. We propose an experimentally testable criterion for an EPR paradox for orbital angular momentum and azimuthal angle. The criterion is designed for an experimental demonstration using orbital angular momentum of light. For the interpretation of future experimental results from the proposed setup, we include a model for the indeterminacies inherent to the angular position measurement. We show how angular apertures can be used to determine the angle, and we discuss the effects of this measurement on the proposed criterion. We show that for a class of aperture functions a demonstration of an angular EPR paradox, according to our criterion, is to be expected. The quantum theory of rotation angles is generalised to non-integer values of the orbital angular momentum. This requires the introduction of an additional parameter, the orientation of a phase discontinuity associated with fractional values of the orbital angular momentum. We apply our formalism to the propagation of light modes with fractional orbital angular momentum in the paraxial and non-paraxial regime.

Orbital angular momentum (OAM) is a property of light that is widely used for applications in bioimaging, optical communication and optical manipulation, but is mainly limited to the infrared and visible spectra. Developing a table-top source of Extreme Ultraviolet (XUV) light containing an arbitrary amount of OAM is yet to be achieved. We accomplish this by exploiting high-harmonic generation (HHG), a process whereby an infrared pump beam produces high order harmonics. We experimentally demonstrate the conservation of OAM in HHG by measuring harmonics of order n containing n times the OAM of the pump (n = 11, 13, 15 in our experiment). These results agree with our theoretical model. We also show theoretically how to manipulate the HHG process to impart an arbitrary amount of OAM to the di fferent harmonics. We hence show the way to a table-top and flexible source of XUV light containing orbital angular momentum.

El control del Momento Angular Orbital (OAM por sus siglas en inglés) de la luz en sistemas óptico cuánticos puede proveernos de un grado adicional de libertad, lo cual nos puede permitir muchas aplicaciones en mecánica cuántica y tecnologías de la comunicación que tengan como eje central la óptica en su desarrollo. Luz laser con OAM, vórtices ópticos, son generalmente descritos por modos de Laguerre-Gausianos, los cuales tienen una distribución de intensidad tipo dona, con singularidades de fase en su frente de onda. En este caso particular los modos son de primer orden y la esfera de Poincaré da una conveniente representación geométrica para el subespacio expandido por esta base. Continuando la propuesta teórica hecha por B. Coutinho dos Santos et al. en 2007, en este proyecto estamos interesados en estudiar de forma experimental la dinámica de un Oscilador Paramétrico Óptico (OPO) bajo la inyección de un haz con OAM. El objetivo principal es caracterizar la conservación de OAM en los haces gemelos, nombrados "signal" y "idler" por razones históricas, provenientes del OPO inyectado, de acuerdo a una simetría no trivial en la esfera de Poincaré. Otro objetivo es el estudio teórico de la dinámica de los haces de luz gemelos, de acuerdo a parámetros experimentales reales del arreglo usado, y de ese modo mejorar la eficiencia en la creación de los fotones gemelos, lo cual permitiría el estudio experimental del entrelazamiento cuántico con este aparato. También, en la mira de este trabajo se encuentra, la medición y caracterización del "squeezing" que fue realizada en el recientemente montado OPO de la UFF.
The control of the Orbital Angular Momentum (OAM) of light in quantum optical system can provide an additional degree of freedom, that can enable many applications in quantum mechanics and optical communications. Lasers beams with OAM (optical vortices) are generally described by Laguerre-Gaussian modes, which have a doughnut intensity distribution with phase singularities in the wavefront. In the special case of first order OAM modes, the Poincaré sphere gives a convenient geometrical representation of those optical vortices. Following the theoretical proposal done by B.Coutinho dos Santos et. al in 2007, in this project we are interested in studying experimentally the dynamics of an Optical Parametric Oscillator under the injection of a seed beam with OAM. The main aim of this project is to characterize the OAM conservation in the twin beams, namely signal and idler, coming from the injected Optical Parametric Oscillator, according to the symmetry in the Poincaré sphere. We aim also at studying theoretically the dynamics of the twin beams generated, according to the real experimental parameters of the setup, to improve the twin beams creation efficiency, which will enable us to study experimentally quantum entanglement in this apparatus. Also, in the scope of this work, the measurements and characterization of squeezing was performed in the recent mounted OPO at UFF.
Tesis

This thesis presents theoretical, simulation and experimental based studies on emission/detection of orbital angular momentum (OAM) beams for the newly emerging integrated OAM photonics technology. The number of applications that utilise the OAM technology has been increasing since the time it has been discovered. Optical communication is one of the high potential applications of OAM beams because of the possibility of providing infinite number of states. This has been considered as the perfect solution for the increasing data load. In order to process the OAM concept in such optical systems, a number of methods have been proposed. In addition to these methods, a new PICs OAM interpretation method has been discussed in this study. The obtained results show that this method has the potential especially for high-capacity optical data transmission. Moreover, the purity of beams (in terms of reflection within the ring resonator) generated by an integrated vortex beam emitter which was proposed by our group-has been investigated for the first time in this study. The investigation showed that there is a disrupting feed-back beam exist within the system. However, its effect on the generated beam's purity is considerably low.

While the story of optical orbital angular momentum (OAM) dates back to the development of Maxwell's equations, the study of photon OAM by the physics community begins in earnest in the 1990s, led in part by a paper by Allen et al. describing the independent control of spin and orbital angular momentum in paraxial modes of light. The recognition of the orbital angular momentum of light in astronomy is a much more recent affair. This thesis explores the role of the OAM of light in astronomy and attempts to make the case for the measurement of photon OAM as a new tool in astronomy. Two contributions are made in order to prepare the groundwork for future endeavours: a laboratory assessment of the effectiveness of adaptive optics (AO) systems on atmospheric turbulence when measuring optical OAM, and an initial field test of an instrument measuring the optical OAM spectrum of the sun. Regarding the first study, the author finds that realistic atmospheric turbulence (1'' seeing) severely corrupts any incoming OAM signal at visible wavelengths, in spite of AO correction (<10% power recovered), however results suggest adequate correction at IR wavelengths. In the second study, an instrument to measure the OAM spectrum of a source is constructed and employed to measure the OAM spectrum of local regions of the sun. It represents the first measurement of its kind, distinguishing sunspots by analyzing their OAM spectrum and in addition, demonstrates the improvement of OAM measurements by implementing a lucky imaging routine. Finally, this thesis highlights a new avenue for further study into the measurement of OAM for observational astronomy. A new type of OAM measurement is proposed, capable of measuring rotations in the plane orthogonal to the line of sight. This measurement takes advantage of the rotational Doppler shift, an analogue of the translational Doppler shift, and an OAM interferometer designed to measure the associated phase shift is outlined. A future instrument is also proposed by combining the OAM interferometer with a high resolution spectrograph. This would allow for measurements of both the rotational and translational Doppler shifts, providing information about the three dimensional motion of an object.

Invoking Maxwell's classical equations in conjunction with expressions for the electromagnetic (EM) energy, momentum, force, and torque, we use a few simple examples to demonstrate the nature of the EM angular momentum. The energy and the angular momentum of an EM field will be shown to have an intimate relationship; a source radiating EM angular momentum will, of necessity, pick up an equal but opposite amount of mechanical angular momentum; and the spin and orbital angular momenta of the EM field, when absorbed by a small particle, will be seen to elicit different responses from the particle.

Applications of the orbital angular momentum (OAM) of light range from the next generation of optical communication systems to optical imaging and optical manipulation of particles. Here we propose a micron-sized semiconductor source that emits light with predefined OAM pairs. This source is based on a polaritonic quantum fluid. We show how in this system modulational instabilities can be controlled and harnessed for the spontaneous formation of OAM pairs not present in the pump laser source. Once created, the OAM states exhibit exotic flow patterns in the quantum fluid, characterized by generation-annihilation pairs. These can only occur in open systems, not in equilibrium condensates, in contrast to well-established vortex-antivortex pairs.

Vortex states are interesting fundamental quantum states whilst also finding many uses in photon optics. In 2010, propagating electron vortices were experimentally produced for the first time leading to the emergence of the field of electron phase shaping. This thesis details the production of electron states containing orbital angular momentum which produce a C-shaped intensity in the focal plane. This C-shaped intensity has a diameter of approximately 10 nm and can be used to lithographically pattern nanometre scale split rings. The broken rotational symmetry also allows rotations to be viewed. The design theory and orbital angular momentum analysis of the C-shaped states is presented. Experimental results of the first production of C-shaped electrons are then shown. The C-shaped electron beams have been applied to lithographic patterning and future potential applications of C-shapes for both electrons and photons are discussed. Photons have been shown to be able to couple total angular momentum,both spin and orbital contributions, to the orbital motion of two dimensional plasmon modes in chiral structures. The similar transfer of orbital angular momentum between propagating electron and plasmon modes has not yet been shown. This thesis provides the design of two dimensional spiral structures to support plasmon oscillations containing orbital angular momentum. Simulated electromagnetic fields show the addition of a spiralling boundary can allow eigenmodes with orbital angular momentum. In addition, the first analysis and electron energy loss experimental investigation of free space electron states containing OAM with flat chiral thin film structures supporting two dimensional surface plasmon modes is presented, showing some initial evidence of an energy signal dependent on the sign of topological charge.

Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. This study describes a new transform for pattern identification that interprets patterns as probability density functions, and has special properties with regards to classification. The transform, built upon the optimal transport theory, is invertible, with well defined forward and inverse operations. This study shows that the transform can be useful in ‘parsing out’ variations that are ‘Lagrangian’ (displacement and intensity variations) by converting these to ‘Eulerian’ (intensity variations) in transform space. This conversion is the basis for the main result that describes when the transforms can allow for linear classification to be possible in transform space. Demonstrated with computational experiments that used both real and simulated data, the transforms can help render a variety of real world problems simpler to solve. Moreover, making use of a newly developed theory suggesting a link between image turbulence and photon transport through the continuity equation, the transform is utilized to perform a decoding task for orbital angular momentum carrying beam patterns. Free space optical communications utilizing orbital angular momentum beams have recently emerged as a new technique for communications with potential for increased channel capacity. Turbulence due to changes in the index of refraction emanating from temperature, humidity, and air flow patterns, however, add nonlinear effects to the received patterns, thus making the demultiplexing task more difficult. The decoding technique is tested and compared against previous approaches using deep convolutional neural networks. Results show that the new method can obtain comparable classification accuracies (bit error rate) at a fraction of the computational cost, thus enabling higher bit rates.

The physical-layer security of a line-of-sight (LOS) free-space optical (FSO) link using orbital angular momentum (OAM) multiplexing is studied. We discuss the effect of atmospheric turbulence to OAM-multiplexed FSO channels. We numerically simulate the propagation of OAM-multiplexed beam and study the secrecy capacity. We show that, under certain conditions, the OAM multiplexing technique provides higher security over a single-mode transmission channel in terms of the total secrecy capacity and the probability of achieving a secure communication. We also study the power cost effect at the transmitter side for both fixed system power and equal channel power scenarios.

Three-dimensional (3D) displays project 3D images that give 3D perceptions and mimic real-world objects. Among the rich varieties of 3D displays, multiview displays take advantage of light’s various degrees of freedom and provide some of the 3D perceptions by projecting 2D subsampling of a 3D object. More 2D subsampling is required to project images with smoother parallax and more realistic sensation. As an additional degree of freedom with theoretically unlimited state space, orbital angular momentum (OAM) modes may be an alternative to the conventional multiview approaches and potentially project more images. This research involves exploring the possibility of encoding/decoding off-axis points in 2D images with OAM modes, development of the optical system, and design and development of a multiview colour display architecture. The first part of the research is exploring encoding/decoding off-axis points with OAM modes. Conventionally OAM modes are used to encode/decode the on-axis information only. Analysis of on-axis OAM beams referenced to off-axis points suggests representation of off-axis displacements as a set of expanded OAM components. At current stage off-axis points within an effective coding area are possible to be encoded/decoded with chosen OAM modes for multiplexing. Experimentally a 2D image is encoded/decoded with an OAM modes. When the encoding/decoding OAM modes match, the image is reconstructed. On the other hand, a dark region with zero intensity is shown. The dark region suggests the effective coding area for multiplexing. The final part of the research develops a multiview colour display. Based on understandings of off-axis representation of a set of different OAM components and experimental test of the optical system, three 1 mm monochromatic images are encoded, multiplexed and projected. Having studied wavelength effects on OAM coding, the initial architecture is updated to a scalable colour display consisting of four wavelengths.

The increasing demand for wireless connectivity and subsequently larger bandwidth requirements for high capacity connections have stretched the physical limits of existing wireless technologies in terms of bandwidth availability across the wireless frequency spectrum. Numerous research methods have been investigated and introduced in current wireless devices to overcome the problems relating channel capacity restriction. Some of these solutions are antenna diversity techniques such as multiple-input multiple-output (MIMO), and frequency diversity methods such as orthogonal frequency-division multiplexing (OFDM). In this thesis, orbital angular momentum (OAM) is successfully generated to transmit uncompressed high-definition (HD) video content at 4 Gbps rate over a 60 GHz wireless channel. As a prediction method, MA TLAB simulation was employed to design and create holographic plate (HP) masks and spiral phase plates (SPP). The MATLAB code was further utilized to control a printed circuit board (PCB) router drill to generate any desired models on copper or dielectric plates for example, holographic masks. It is believed for the first time, an experimental setup is exploited for generation of a 4 Gbps uncompressed video link over 60 GHz OAM wireless channel, and results are confirmed in tern:1s of received signal power and data rate throughput to illustrate the existence of OAM in 60 GHz channel. The achievements of this research wi~l contribute to the field of knowledge and it is concluded that it is a feasible prospect for multi-gigabit wireless communications to be achieved over OAM channels while improving the spatial diversity and spatial multiplexing of the wireless channel.

Ce travail de thèse traite des effets mécaniques rotationnels résultant de l'interaction son-matière en présence de transfert de moment angulaire de nature orbitale. Deux approches expérimentales sont mis en œuvre, toutes deux utilisant des ondes ultrasonores se propageant dans l'air et des objets de taille centimètrique obtenus par impression 3D imprimés et se comportant comme des miroirs structurés imprimant un profil de phase hélicoïdal au champ réfléchi. Le résultat principal consiste en la mesure directe quantitative du moment angulaire orbital porté par un faisceau vortex via deux approches indépendantes. La première est basée sur l’utilisation d’un miroir hélicoïdal placé à l’interface air-eau, et la seconde repose sur le développement d'un oscillateur mécanique de torsion forcé par le transfert de moment angulaire
We study the rotational mechanical effects resulting from sound-matter interaction in the presence of orbital angular momentum transfer. A set of experimental realizations are implemented by using ultrasonic waves propagating in the air and 3D printed centimeter-sized objects acting as structured mirrors imparting a helical phase profile to the reflected wave. The main result consists of the quantitative direct measurement of the orbital angular momentum carried by acoustic vortex beams via two independent approaches. The first one is based on the use of a freely rotating helical mirror placed at air-water interface, and the second one relies on the development of a torsional mechanical oscillator driven by acoustic orbital angular momentum

The vectorial nature (polarization) of light plays a significant role in light-matter interaction that leads to a variety of optical devices. The polarization property of light has been exploited in imaging, metrology, data storage, optical communication and also extended to biological studies. Most of the past studies fully explored and dealt with the conventional polarization state of light that has spatially symmetric electrical field geometry such as linear and circular polarization. Recently, researchers have been attracted to light whose electric field vector varies in space, the so-called optical vector vortex beam (VVB). Such light is expected to further enhance and improve the efficiency of optical systems. For instance, a radially polarized light under focusing condition is capable of a tighter focus more than the general optical beams with a uniform polarization structure, which improves the resolution of the imaging system [1]. Interaction of ultrafast laser pulses with matter leads to numerous applications in material processing and biology for imaging and generation of microfluidic systems. A femtosecond pulse, with very high intensities of (10^{12} - 10^{13} W/cm^2), has the potential to trigger a phenomenon of optical breakdown at the surface and therefore induce permanent material modification. With such high intensities and taking into account the fact that most materials possess large bandgap, the interaction is completely nonlinear in nature, and the target material can be modified locally upon the surface and even further in bulk. The phenomenon of optical breakdown can be further investigated by studying the nonlinear absorption. Properties like very short pulse duration and the high irradiance of ultrashort laser pulse lead to more precise results during the laser ablation process over the long pulsed laser. The duration of femtosecond laser pulse provides a high resolution for material processing because of the significant low heat-affected zone (HAZ) beyond the desired interaction spot generated upon irradiating the material. Under certain condition, the interaction of intense ultrashort light pulses with the material gives rise to the generation of periodic surface structures with a sub-micron periodicity, i.e., much smaller than the laser wavelength. The self-oriented periodic surface structures generated by irradiating the material with multiple femtosecond laser pulses results in improving the functionality of the material's surface such as controlling wettability, improving thin film adhesion, and minimizing friction losses in automobile engines, consequently, influences positively on many implementations. In this work, we introduced a new method to study complex polarization states of light by imprinting them on a solid surface in the form of periodic nano-structures. Micro/Nanostructuring of diamond by ultrafast pulses is of extreme importance because of its potential applications in photonics and other related fields. We investigated periodic surface structures usually known as laser-induced periodic surface structures (LIPSS) formed by Gaussian beam as well as with structured light carrying orbital angular momentum (OAM), generated by a birefringent optical device called a q-plate (QP). We generated conventional nano-structures on diamond surface using linearly and circularly polarized Gaussian lights at different number of pulses and variable pulse energies. In addition, imprinting the complex polarization state of different orders of optical vector vortex beams on a solid surface was fulfilled in the form of periodic structures oriented parallel to the local electric field of optical light. We also produced a variety of unconventional surface structures by superimposing a Gaussian beam with a vector vortex beam or by superposition of different order vector vortex beams. This thesis is divided into five chapters, giving a brief description about laser-matter interaction, underlying the unique characterization of femtosecond laser over the longer pulse laser and mechanisms of material ablation under the irradiation of fs laser pulse. This chapter also presents some earlier studies reported in formation of (LIPSS) fabricated on diamond with Gaussian. The second chapter explains the properties of twisted light possessing orbital angular momentum in its wavefront, a few techniques used for OAM generation including a full explanation of the q-plate from the fabrication to the function of the q-plate, and the tool utilized to represent the polarization state of light (SoP), a Poincar'e sphere. Finally, the experimental details and results are discussed in the third and fourth chapters, respectively, following with a conclusion chapter that briefly summarizes the thesis and some potential application of our findings.

ITC/USA 2013 Conference Proceedings / The Forty-Ninth Annual International Telemetering Conference and Technical Exhibition / October 21-24, 2013 / Bally's Hotel & Convention Center, Las Vegas, NV
We address the problem of detection in orbital angular momentum (OAM). The focus of our analysis will be on the power efficient Q-ary Pulse Position Modulation (Q - PPM). Free space optical signals sent through wireless channels are degraded by atmospheric turbulence. In this paper a novel detection approach based on a factor graph representation of OAM Q-PPM signalling is presented to equalize for the crosstalk among orbital angular momentum vortices. It will be shown that our proposed detection algorithm significantly outperforms the separate detection scenario in terms of error rate performance.

In this paper, we experimentally demonstrate simultaneous wavelength and orbital angular momentum (OAM) multiplexing/demultiplexing of 10 Gbit/s data streams using a new on-chip micro-component-tunable MEMS-based Fabry-Perot filter integrated with a spiral phase plate. In the experiment, two wavelengths, each of them carrying two channels with zero and nonzero OAMs, form four independent information channels. In case of spacing between wavelength channels of 0.8 nm and intensity modulation, power penalties relative to the transmission of one channel do not exceed 1.45, 0.79 and 0.46 dB at the hard-decision forward-error correction (HD-FEC) bit-error-rate (BER) limit 3.8 x 10 rectangle 3 when multiplexing a Gaussian beam and OAM beams of azimuthal orders 1, 2 and 3 respectively. In case of phase modulation, power penalties do not exceed 1.77, 0.54 and 0.79 dB respectively. At the 0.4 nm wavelength grid, maximum power penalties at the HD-FEC BER threshold relative to the 0.8 nm wavelength spacing read 0.83, 0.84 and 1.15 dB when multiplexing a Gaussian beam and OAM beams of 1st, 2nd and 3rd orders respectively. The novelty and impact of the proposed filter design is in providing practical, integrable, cheap, and reliable transformation of OAM states simultaneously with the selection of a particular wavelength in wavelength division multiplexing (WDM). The proposed on-chip device can be useful in future high-capacity optical communications with spatial-and wavelength-division multiplexing, especially for short-range communication links and optical interconnects. (C) 2017 Optical Society of America

In this work, we develop a new technique to determine the topological charge of a light beam with orbital angular momentum. Our technique is based on the diffraction by a triangular aperture. By performing numerical simulations, for Laguerre-Gaus beams and Bessel beams with different values of l, we found tha the diffraction pattern contains the signature of the topological charge of the beam. Our theoretical predictions for a triangular aperture were experimentally verifiel, demonstrating the the diffraction pattern reveals the topological charge of the light beam.
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Neste trabalho, desenvolvemos uma nova técnica para determinar a carga topológica de um feixe de luz com momento angular orbital. Nossa técnica é baseada na difração por uma abertura triangular. Através da realização de simulações numérica, para feixes Laguerre-Gauss e feixes Bessel com diferentes valores de l, descobrimos que o padrão de difração contém a assinatura da carga topológica do feixe. Nossas previsões teóricas para uma abertura triangular foram verificadas experimentalmente, demonstrando que o padrão de difração revela a carga topológica do feixe de luz. Esta técnica torna possível a determinação do módulo e do sinal da carga topológica de um feixe de luz de uma maneira simples e direta.

We report the design and experimental results for a two-chip T-cavity vertical external cavity surface emitting laser utilized for two-color collinear generation of Hermite-Gaussian and LaguerreGaussian (LG) transverse modes. A combination of intracavity mode-control elements and an external astigmatic mode converter was used to achieve high power LG modes. By incorporating intracavity birefringent filters in each arm of the T-cavity, wide wavelength tuning in excess of 12 nm of each mode is demonstrated. Output power exceeding 1.5W is measured for all the modes. Published by AIP Publishing.

It is well known that light can carry two different kind of angular momentum that together form the total angular momentum of photons. These two forms are the spin orbital angular momentum, associated with the circular polarisation of light, and the orbital angular momentum of light associated with a wavefront tilted with respect to the propagation axis. Any tilted wavefront generates an orbital component of the angular momentum but there are some special cases in which this property becomes particularly interesting. It is the case of optical vortices which form when the waveform is continuously and uniformly tilted to the propagation axis forming a spiral structure.

The aim of this work is to study the propagation of orbital angular momentum (OAM) of light for astrophysical applications and a method for OAM detection with optical telescopes. The thesis deals with the study of the orbital angular momentum (OAM) as a new observable for astronomers, which could give additional information with respect to those already inferred from the analysis of the intensity, frequency and polarization of light. Indeed, the main purpose of this work is to highlight that light can have a much more complex structure, and therefore can transport much more information. In particular, firstly we show that OAM can be imparted to light from interstellar media with a perturbed electron density function in the plane perpendicular to the propagation direction, revealing that the study of OAM could give information about the spatial structures of the traversed inhomogeneous media. The second part of the thesis deals with an experimental verification of the preservation of orbital angular momentum even for uncorrelated non-monochromatic wave beams, showing that this observable of light is preserved, thus we can aim at detecting it. Finally, if OAM can transport information, and if it is preserved in propagation, the obvious consequence is the study of its detection, in particular by an OAM mode sorter fitted to optical telescopes.
Lo scopo di questo lavoro è analizzare la propagazione del momento angolare orbitale (OAM) della luce per applicazioni astrofisiche e studiarne un metodo per la rilevazione con telescopi ottici. La tesi si occupa dello studio del momento angolare orbitale come un nuovo osservabile per gli astronomi, che potrebbe dare informazioni aggiuntive rispetto a quelle già deducibili dall'analisi della intensità, frequenza e polarizzazione della luce. Infatti, lo scopo principale di questo lavoro è di evidenziare come la luce possa avere una struttura molto più complessa, e quindi trasportare molte più informazioni. Inizialmente si dimostra che mezzi interstellari con una funzione di densità elettronica inomogenea nel piano perpendicolare alla direzione di propagazione della luce che li attraversa, possono conferire OAM. Ciò indica che lo studio dell' OAM può fornire informazioni sulle strutture spaziali dei mezzi attraversati non omogenei. Nella seconda parte della tesi viene esposta una verifica sperimentale della conservazione del momento angolare orbitale, anche per fasci d'onda non monocromatici e non coerenti . Viene così dimostrando che questo osservabile della luce si conserva, consentendone la rilevazione. Infine, osservato che l'OAM può trasportare informazioni, e che si conserva nella propagazione, si propone lo studio di un metodo per rivelarlo, in particolare di un uno spettrografo OAM per telescopi ottici.

In recent years there has been great interest in the applications of the interaction of the phase and intensity of laser light in atomic vapours. The generation of light beams with arbitrary phase and intensity patterns can now be easily achieved by using Spatial Light Modulators (SLMs). The transformation of quantized units of phase information to atomic vapours has implications in the fields of quantum optics for the realisation of sources of entangled photons, optical switching, and quantum information storage. Spatially shaped beams with non-trivial intensity geometries have found use in single atom quantum well traps and for the enhancement of density of standard Magneto Optical Traps. The work in this thesis is focussed around two main pro jects, involving the interaction of holographically shaped light beams with cold trapped atoms and with a hot atomic vapour respectively. An enhancement to the previously investigated technique of a SPontaneous force Optical Trap SPOT of 87 Rb is presented here which aims to solve various issues which naturally arise from compressing cold atoms in a Magneto Optical Trap (MOT) such as unavoidable heating during the compression. High density/high atom number traps are highly sought after in many experiments for more efficient transfer of atoms to Bose Einstein Condensates and for improved quantum storage capabilities in cold atom traps. The highest density achieved in our SPOT was 2.5 × 10^12 atoms cm−3 for 2 × 10^8 atoms at a temperature of approximately 100µK. This represents almost 2 orders of magnitude increase in density from the standard MOT setup with no adverse heating of the trap while maintaining 75% of the atoms. In the second part of this work hot atomic vapours are utilized for the efficient transfer of orbital angular momentum information from near infra-red pump fields, driving from 5S_1/2 to 5D_5/2 on a two-photon transition, to a cascade from 5D_5/2 to 6P_3/2 to 5S_1/2 generating 5230nm light and a coherent blue, 420nm, beam respecitively. This generation is performed using four wave mixing in 85 Rb. We observe the complete conversion of all input quantum information, the Orbital Angular Momentum (OAM) from the pump fields to the blue. In addition we show the additional phase coherence effects of this experiment through the use of simple superpositions of Laguerre-Gaussian (LG) modes showing that the process is indeed quantum in nature. A theoretical basis for the transfer of all OAM information to only the 420nm beam is also discussed here.

Les besoins toujours croissants en terme de transfert de données numériques poussent au développement de nouvelles technologies pour accroître la capacité des réseaux, notamment en ce qui concerne les réseaux de fibre optique. Parmi ces nouvelles technologies, le multiplexage spatial permet de multiplier la capacité des liens optiques actuels. Nous nous intéressons particulièrement à une forme de multiplexage spatial utilisant le moment cinétique orbital de la lumière comme base orthogonale pour séparer un certain nombre de canaux. Nous présentons d’abord les notions d’électromagnétisme et de physique nécessaires à la compréhension des développements ultérieurs. Les équations de Maxwell sont dérivées afin d’expliquer les modes scalaires et vectoriels de la fibre optique. Nous présentons également d’autres propriétés modales, soit la coupure des modes, et les indices de groupe et de dispersion. La notion de moment cinétique orbital est ensuite introduite, avec plus particulièrement ses applications dans le domaine des télécommunications. Dans une seconde partie, nous proposons la carte modale comme un outil pour aider au design des fibres optiques à quelques modes. Nous développons la solution vectorielle des équations de coupure des modes pour les fibres en anneau, puis nous généralisons ces équations pour tous les profils de fibres à trois couches. Enfin, nous donnons quelques exemples d’application de la carte modale. Dans la troisième partie, nous présentons des designs de fibres pour la transmission des modes avec un moment cinétique orbital. Les outils développés dans la seconde partie sont utilisés pour effectuer ces designs. Un premier design de fibre, caractérisé par un centre creux, est étudié et démontré. Puis un second design, une famille de fibres avec un profil en anneau, est étudié. Des mesures d’indice effectif et d’indice de groupe sont effectuées sur ces fibres. Les outils et les fibres développés auront permis une meilleure compréhension de la transmission dans la fibre optique des modes ayant un moment cinétique orbital. Nous espérons que ces avancements aideront à développer prochainement des systèmes de communications performants utilisant le multiplexage spatial.
The always increasing need for digital data bandwidth pushes the development of emerging technologies to increase network capacity, especially for optical fiber infrastructures. Among those technologies, spatial multiplexing is a promising way to multiply the capacity of current optical links. In this thesis, we are particularly interested in current spatial multiplexing using the orbital angular momentum of light as an orthogonal basis to distinguish between a few optical channels. We first introduce notions from electromagnetism and physic needed for the understanding of the later developments. We derive Maxwell’s equations describing scalar and vector modes of optical fiber. We also present other modal properties like mode cutoff, group index, and dispersion. Orbital angular momentum is briefly explained, with emphasis on its applications to optical communications. In the second part, we propose the modal map as a tool that can help in the design of few mode fibers. We develop the vectorial solution of the ring-core fiber cutoff equation, then we extend those equations to all varieties of three-layer fiber profiles. Finally, we give some examples of the use of the modal map. In the third part of this thesis, we propose few fiber designs for the transmission of modes with an orbital angular momentum. The tools that were developed in the second part of this thesis are now used in the design process of those fibers. A first fiber design, characterized by a hollow center, is studied and demonstrated. Then a second design, a family of ring-core fibers, is studied. Effective indexes and group indexes are measured on the fabricated fibers, and compared to numerical simulations. The tools and the fibers developed in this thesis allowed a deeper comprehension of the transmission of orbital angular momentum modes in fiber. We hope that those achievements will help in the development of next generation optical communication systems using spatial multiplexing.

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Trabalhos anteriores já mostraram o dobramento do momento angular orbital de feixes após a geração de segundo harmônico em meios não lineares. Nesse trabalho pretendemos usar a polarização como parâmetro auxiliar para poder incidir em um cristal não linear dois feixes colineares com momentos angulares orbitais diferentes e obter na geração de seu segundo harmônico a soma de seus momentos angulares orbitais e veri car este resultado experimentalmente.
Previous work have already shown the orbital angular momentum doubling after second harmonic generation in non-linear media. In this work we intend to use the polarization as an auxiliary parameter to focus in a non-linear crystal two colinear beams with different orbital angular momentum and obtain in its second harmonic generation the sum of their orbital angular momentum and to verify it exeperimentally.

Twenty-odd years ago, scientists managed to produce several new techniques for manipulating certain properties of laser and microwave radiation. These new properties made it possible for the radiation to contain a lot more information than what was previously known. What they had discovered was that light could be twisted, thereby not only carrying polarization, also known as spin angular momentum (SAM) but also orbital angular momentum (OAM).Radar beams are used by scientists to probe the earth’s ionosphere. By measuring the echo of the radar waves one can deduce a lot of information, such as density and temperature of the plasma. In this thesis we will expand an existing program (iscatspb0.m) which computes the spectrum of plasma fluctuations as seen with an incoherent scatter radar, to having it incorporate radar beams carrying OAM, to see what new information of the plasma can be obtained.The three major findings in this thesis were what magnitude of the integer l is needed in order for the contribution of OAM to equal the contribution for the beam opening angle, how much the radar beam opening angle affected the measurements and in what way the spectrum obtained by a twisted beam is affected by different flows

We present the theory of orbital angular momentum of light (MAO), based on the basic concepts of electromagnetism, as well as some techniques from generation and characterization of light beams possessing MAO. We also present non-linear optical processes of parametric conversion spontaneous descendant (CPD) and stimulated (CPDE). We reviewed the problem of conservation of MAO in CPD in the scheme does not collinear, describing States of using Laguerre-Gauss beams MAO. We extend this study to the case in which Bessel beams are used to describe the States of MAO. Our results show that rape occurs on conservation law of MAO, which is attributed to deformation of the angular spectrum of beam pumping (pump) transferred to the twin photons. However, this violation can be advantageous because through breach of MAO have access to entangled States of dimension greater than those generated with collinear geometry. As an alternative to the note of the violation of the law of conservation in parametric down conversion process we proposed an experiment based on CPDE, where the experimental implementation is simpler. Using MAO as target and polarization qubit as qubit control, we experimentally a alternative to optical circuit proposal for Li-Ping et al. [16] for the implementation of the logic gate C-NOT. Also we present an application of logic gate C-NOT for the generation of entangled States of a single photon, which can be implemented with our optical circuit. The generation of entangled States, multidimensional, and the implementation quantum logic gates are important for the areas of information and quantum computation.
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Apresentamos a teoria do momento angular orbital da luz (MAO), baseada nos conceitos básicos do eletromagnetismo, bem como algumas técnicas de geração e caracterização de feixes de luz possuindo MAO. Apresentamos também os processos ópticos não lineares de conversão paramétrica descendente espontânea (CPD) e estimulada (CPDE). Revisamos o problema da conservação do MAO na CPD no regime não colinear, descrevendo os estados de MAO utilizando feixes Laguerre-Gauss. Extendemos este estudo para o caso em que feixes Bessel são usados para descrever os estados de MAO. Nossos resultados mostram que ocorre violação na lei de conservação do MAO, que é atribuída a deformação do espectro angular do feixe de bombeamento (pump) transferido para os fótons gêmeos. Entretanto, esta violação pode ser vantajosa, pois através da violação do MAO conseguimos ter acesso a estados emaranhados de dimensão maior do que aqueles gerados com geometria colinear. Como alternativa para a observação da violação da lei de conservação no processo de conversão paramétrica descendente, propusemos um experimento baseado na CPDE, onde a realização experimental é mais simples. Utilizando o MAO como qubit alvo e a polarização como qubit controle, realizamos experimentalmente um circuito ótico alternativo à proposta de Li-Ping e colaboradores [16] para a implementação da porta lógica C-NOT. Também apresentamos uma aplicação da porta lógica C-NOT para a geração de estados emaranhados de um único fóton, que pode ser implementada com nosso circuito ótico. A geração de estados emaranhados multidimensionais e a implementaçãode portas lógicas quânticas são importantes para as áreas de informação e computação quântica.

In this doctoral thesis we investigate several experiments exploring the light orbital angular momentum and the Fraunhofer diffraction of light. Our investigations goes from coherent propagation, continue through incoherent propagation, arriving at semiclassical states used to explore one fundamental problem in quantum mechanics, i. e., the Born’s rule. Therefore, concerning coherent propagation of light with orbital angular momentum, we were first involved with studies about Fraunhofer diffraction of this type of light, by a single slit and by a square aperture. In the former work we studied the Fraunhofer diffraction when the slit center is aligned with the vortex center and when it is out of the vortex center. Concerning the work related to the square aperture, we show that the diffraction by such aperture is not sufficient to characterize the topological charge. Continuing the works, we also investigate the Fraunhofer diffraction of light with orbital angular momentum of fractional topological charge in the real space. An interesting phenomenon, the birth of a vortex, was studied at Fraunhofer plane, showing new conclusions in the study of fractional topological charges. Our studies continued with the Fraunhofer propagation of vortices in incoherent light, unveiling strong correlations between incoherent vortices. Finally, we explored semiclassical aspects of light with orbital angular momentum. Firstly, the topological charge determination via the spatial probability distribution of detection of photons diffracted by a triangular aperture. After, the validation of the Born’s rule using diffraction, by three slits disposed in a triangular configuration, of photons with an extra phase, i. e., the azimuthal phase added to the path phase.
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Nesta tese de doutorado investigamos diversos experimentos que exploram o momento angular orbital da luz e a difração de Fraunhofer. Nossas investigações abrangeram desde propagação coerente, passando por propagação incoerente, chegando a estados semiclássicos usados para explorar uma questão fundamental da mecânica quântica, a saber, a regra de Born. Portanto, no que concerne à propagação de luz coerente com momento angular orbital, estivemos envolvidos primeiramente com estudos da difração de Fraunhofer deste tipo de luz, por uma fenda simples e por uma abertura quadrada. No primeiro trabalho estudamos a difração de Fraunhofer quando o centro da fenda está alinhado com o centro do vórtice e quando está deslocado do centro do vórtice. Quanto ao trabalho relacionado à abertura quadrada, mostramos que a difração de Fraunhofer por tal abertura não permite caracterizar a carga topológica. Prosseguindo os trabalhos, investigamos também a difração no plano de Fraunhofer de luz com momento angular de carga fracionária no plano real. Um interessante fenômeno, o nascimento de um vórtice, foi estudado no plano de Fraunhofer, mostrando novas conclusões nos estudos relacionados à carga fracionária. Nossos estudos continuaram com a propagação de Fraunhofer de vórtices em luz incoerente, revelando fortes correlações entre vórtices incoerentes. Por fim, exploramos aspectos semiclássicos da luz com momento angular orbital. Primeiramente, a determinação da carga topológica via distribuição de probabilidade espacial de detecção de fótons difratados por uma abertura triangular. Posteriormente, a validação da regra de Born utilizando difração, por três fendas simples dispostas na forma triangular, de fótons com uma fase extra, ou seja, a fase azimutal, adicionada à fase de caminho.

To address key challenges for both quantum communication and quantum computing applications in a simultaneous manner, we propose to employ the photon angular momentum approach by invoking the well-known fact that photons carry both the spin angular momentum (SAM) and the orbital angular momentum (OAM). SAM is associated with polarization, while OAM is associated with azimuthal phase dependence of the complex electric field. Given that OAM eigenstates are mutually orthogonal, in principle, an arbitrary number of bits per single photon can be transmitted. The ability to generate/analyze states with different photon angular momentum, by using either holographic or interferometric methods, allows the realization of quantum states in multidimensional Hilbert space. Because OAM states provide an infinite basis state, while SAM states are 2-D only, the OAM can also be used to increase the security for quantum key distribution (QKD) applications and improve computational power for quantum computing applications. The goal of this paper is to describe photon angular momentum based deterministic universal quantum qudit gates, namely, {generalized-X, generalized-Z, generalized-CNOT} qudit gates, and different quantum modules of importance for various applications, including (fault-tolerant) quantum computing, teleportation, QKD, and quantum error correction. For instance, the basic quantum modules for quantum teleportation applications include the generalized-Bell-state generation module and the QFT-module. The basic quantum module for quantum error correction and fault-tolerant computing is the nonbinary syndrome calculator module. The basic module for entanglement assisted QKD is either the generalized-Bell-state generation module or the Weyl-operator-module. The possibility of implementing all these modules in integrated optics is discussed as well. Finally, we provide security analysis of entanglement assisted multidimensional QKD protocols, employing the proposed qudit modules, by taking into account the imperfect generation of OAM modes.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this thesis we discuss some fundamental aspects of the quantum theory from a contemporaneous point of view, where we could develop three works. In the first we analyze theoretically an atomic double-slit interferometer. It has been shown that if the energy eigenstates of the atom are correlated with its particle and wave behaviors, complementary phenomena can be measured simultaneously, indicating a reinterpretation of the complementarity principle. We also demonstrate that this experiment possesses quantum erasure properties. In the second we present a two-particle interferometer in order to analyze the way in which decoherence affects quantum interference. It has been shown how the environmental constituents, here considered as photons, can destroy the oscillations in the coincidence detection rate of the particles. Due to the temporal characteristic of this kind of interference, we name this process as quantum temporal decoherence. In the last work we study the existence of a novel complete family of exact and orthogonal solutions of the paraxial wave equation. The complex amplitude of these beams is proportional to the confluent hypergeometric functions, which we name hypergeometric modes of type-II (HyG-II). It is formally demonstrated that a hyperbolic-index medium can generate and support the propagation of such a class of beams. Since these modes are eigenfunctions of the photon orbital angular momentum, we conclude that an optical fiber with hyperbolic-index profile could take advantage over other graded-index fibers by the capacity of data transmission.
Nesta tese discutimos alguns aspectos fundamentais da teoria quântica de um ponto de vista mais contemporâneo, onde também pudemos desenvolver três trabalhos. No primeiro analisamos teoricamente um interferômetro de fenda dupla para átomos. Mostramos que se os autoestados de energia do átomo estão correlacionados com os comportamentos de partícula e de onda do mesmo, fenômenos complementares podem ser medidos simultaneamente, indicando uma reinterpretação do princípio da complementaridade. O mesmo aparato também apresentou propriedades de apagador quântico. No segundo apresentamos um interferômetro de duas partículas e a maneira como a decoerência afeta o grau de interferência. Mostramos como os constituintes do ambiente, aqui considerados como fótons, podem destruir a oscilação na taxa de coincidência de detecção das partículas. Devido a sua característica temporal, chamamos este processo de decoerência temporal quântica. No último trabalho estudamos a existência de uma nova família de soluções ortogonais da equação paraxial da luz. A amplitude complexa desses feixes são proporcionais às funções hipergeométricas confluentes, que denominamos modos hipergeométricos do segundo tipo (HyG-II). Demonstramos formalmente que um meio com um perfil hiperbólico de índice de refração pode gerar e suportar essa classe de feixes. Uma vez que esses modos são autofunções do momento angular orbital do fóton, concluímos que uma fibra ótica com este perfil de índice, em certas situações, poderia levar vantagem em relação a outras fibras com índice variável na capacidade de transmissão de dados.

We investigate two medium-facilitated interactions between properties of light upon propagation through optical fiber. The first is interaction between the spin and intrinsic orbital angular momentum in a linear optical medium. This interaction gives rise to fine structure in the longitudinal momenta of fiber modes and manifests in rotational beating effects. We probe those beating effects experimentally in cutback experiments, where small segments are cut from the output of a fiber to probe the evolution of both output polarization and spatial orientation, and find agreement between theoretical predictions and measured behavior. The second is nonlinear optical interaction due to cross- and self-phase modulation between the complex-valued temporal amplitude profile of pump pulses and the amplitude profiles of generated signal and idler pulses in optical fiber photon-pair sources utilizing the four-wave mixing process named modulation instability. We develop a model including the effects of these nonlinear phase modulations (NPM) describing the time-domain wave function of the output biphoton in the low-gain regime. Assuming Gaussian temporal amplitude profiles for the pump pulse, we numerically simulate the structure of the biphoton wave function, in symmetric and asymmetric group velocity matching configurations. Comparing the overlap of the joint temporal amplitudes with and without NPM indicates how good of an approximation neglecting NPM is, and we investigate the effects of NPM on the Schmidt modes. We find that effects of NPM are small on temporally separable sources utilizing symmetric group velocity matching, but appreciably change the state of temporally entangled sources with the same group velocity matching scheme. For sources designed to produce entangled biphotons, our simulations suggest that NPM increases the Schmidt number, which may increase entanglement resource availability with utilization of a phase-sensitive detection scheme. We find that NPM effects on temporally separable sources designed with asymmetric group velocity matching produce non-negligible changes in the state structure. The purity is unaffected at perfect asymmetric group velocity matching, but if the pump is detuned from the correct wavelength, the purity degrades. The largest changes to the state due to NPM occur in long fibers with long pulse durations and low repetition rates.

Magneto-optical materials such as permalloy can be used to create artificial spin- ice (ASI) lattices with antiferromagnetic ordering. Magneto-optical materials used to create diffraction lattices are known to exhibit magnetic scattering at the half- order Bragg peak while in the ground state. The significant drawbacks of studying the magneto-optical generation of OAM using x-rays are cost, time, and access to proper equipment. In this work, it is shown that the possibility of studying OAM and magneto-optical materials in the spectrum of visible light at or around 2 eV is viable. Using spectroscopic ellipsometry it is possible to detect a change in the magnetization of thin permalloy films with thicknesses between 5 and 20 nm. Patterns consistent with OAM were found at 1.95 eV using a square lattice with a 4𝜋 radial phase shift in the antiferromagnetic ground state. Evidence of magnetic scattering at the half-order Bragg peak using 1.95 eV was also found.

Des interactions entre la matière et la lumière sont à l'origine de phénomènes opto-mécaniques. L'une des caractéristiques distinctives de l'interaction lumière-matière est l'interaction spin-orbite de la lumière. Cette dernière s'étudie au sein d'un domaine de recherche émergent consacré à l'étude des effets opto-mécaniques en présence de l'interaction entre la polarisation et des degrés de liberté spatiaux de la lumière. En particulier, ce travail vise à observer directement la manifestation (i) des forces latérales et (ii) des couples optiques gauches qui sont des effets opto-mécaniques contre-intuitifs. On utilise pour cela des milieux non homogènes et anisotropes comme ingrédients essentiels à la fabrication d’éléments optiques spin-orbite. Nous rapportons tout d'abord, les tentatives d’observations expérimentales directes, à partir des résultats préliminaires obtenus préalablement dans notre groupe de recherche. Nous présentons ensuite de nouvelles propositions d'expérimentations ainsi qu'une généralisation adaptée au cas des forces latérales. Par conséquent, nous rapportons d’une observation directe à l’échelle du millimètre des forces latérales optiques et des couples optiques gauches dépendantes du spin en effectuant une étude complète. Il ressort de l'analyse des deux phénomènes que leurs vitesses peuvent être augmentées en réduisant l'inertie ou la taille des éléments optiques spin-orbite au point de rendre les phénomènes significatifs à l'échelle microscopique et intéressants pour les applications technologiques. Nous faisons un rapport chronologique de notre travail expérimental consistant à observer le moment de force orienté à gauche à l'échelle du micromètre en utilisant des versions miniaturisées des échantillons précédents. Comme la dernière tentative n’était pas concluante, nous finissons par proposer de nouvelles stratégies prometteuses pour manipuler de tels micro-objets
Interactions between light and matter cause optomechanical phenomena, where a distinctive feature of light-matter interaction, namely, the spin-orbit interaction of light, takes place within an emerging research area dedicated to the study of optomechanical effects in the presence of the interplay between polarization and spatial degrees of freedom of light. In particular, this work aims to directly observe the manifestation of (i) lateral forces and (ii) left-handed torques, which are counterintuitive optomechanical effects, by using inhomogeneous and anisotropic media as a critical ingredient for the manufacture of spin-orbit optical elements. Hence, we report on their direct experimental observations attempts, starting from the preliminary results obtained in our group before this work, and then present our new proposals and further generalization to the case of lateral forces. Consequently, we report on a millimeter-scale direct observation of optical spin-dependent lateral forces and left-handed torques with a full study. From the analysis of both phenomena, it turns out that their speed can be increased by reducing the spin-orbit optical elements inertia or size, making the phenomena relevant at microscopic-scale and interesting for technological applications. Thus, we account for our experimental journey chronologically, to observe the left-handed torque at micrometer-scale with samples that correspond to miniaturized versions of previous ones. Since the last results were inconclusive, we finish by proposing new strategies of manipulation of such micro-elements with promising implementation