Light Scattering From an Atomic Gas Under Conditions of Quantum Degeneracy

Elastic light scattering from a macroscopic atomic sample existing in the Bose-Einstein condensate phase reveals a unique physical configuration of interacting light and matter waves. However, the joint coherent dynamics of the optical excitation induced by an incident photon is influenced by the presence of incoherent scattering channels. For a sample of sufficient length the excitation transports as a polariton wave and the propagation Green\u27s function obeys the scattering equation which we derive. The polariton dynamics could be tracked in the outgoing channel of the scattered photon as we show via numerical solution of the scattering equation for one-dimensional geometry. The results are analyzed and compared with predictions of the conventional macroscopic Maxwell theory for light scattering from a nondegenerate atomic sample of the same density and size

Experiments on synthetic dimensions in photonics

The first and introductory section of the dissertation presents the working principle of a one- and two-dimensional photonic mesh lattice based on the time-multiplexing technique. The basis of a random walk interrelated to the corresponding light and quantum walk is comprehensively discussed as well. The second part of the dissertation consists of three experiments on a one-dimensional photonic mesh lattice. Firstly, the Kapitza-based guiding light project models the Kapitza potential as a continuous Pauli-Schrödinger-like equation and presents an experimental observation of light localization when the transverse modulation is bell-shaped but with a vanishing average along the propagation direction. Secondly, the optical thermodynamics project experimentally demonstrates for the first time that any given initial modal occupancy reaches thermal equilibrium by following a Rayleigh-Jeans distribution when propagates through a multimodal photonic mesh lattice with weak nonlinearity. Remarkably, the final modal occupancy possesses a unique temperature and chemical potential that have nothing to do with the actual thermal environment. Finally, the quantum interference project discusses an experimental all-optical architecture based on a coupled-fiber loop for generating and processing time-bin entangled single-photon pairs. Besides, it shows coincidence-to-accidental ratio and quantum interference measurements relying on the phase modulation of those time bins. The third part of the dissertation comprises two experiments on a two-dimensional photonic mesh lattice. The first project discusses the experimental realization of a two-dimensional mesh lattice employing short- and long-range interaction. To some extent, the second project presents a nonconservative system based on a two-dimensional photonic mesh lattice exploiting parity-time (PT) symmetry

Game Theory Relaunched

The game is on. Do you know how to play? Game theory sets out to explore what can be said about making decisions which go beyond accepting the rules of a game. Since 1942, a well elaborated mathematical apparatus has been developed to do so; but there is more. During the last three decades game theoretic reasoning has popped up in many other fields as well - from engineering to biology and psychology. New simulation tools and network analysis have made game theory omnipresent these days. This book collects recent research papers in game theory, which come from diverse scientific communities all across the world; they combine many different fields like economics, politics, history, engineering, mathematics, physics, and psychology. All of them have as a common denominator some method of game theory. Enjoy

Magnetic micro-confinement of quantum degenerate gases

In this dissertation we explore the basic principles of the magnetic micro-confinement of the quantum degenerate gases where the approach of the so-called two-dimensional magnetic lattices has been theoretically and experimentally investigated. In this research a new generation of two-dimensional magnetic lattice has been proposed and considered as a developing phase for the previous approaches. Its advantage relies on introducing a simplified method to create single or multiple micro-traps of magnetic field local minima distributed, at a certain working distance, above the surface of a thin film of permanent magnetic material. The simplicity in creating the magnetic field local minima at the micro-scale manifests itself as a result of imprinting specific patterns through the thin film using suitable and available micro-fabrication techniques. In this approach, to create multiple micro-traps, patterned square holes of size αh X αh spaced by αs are periodically distributed across the x/y plane taking a two-dimensional grid configuration. These magnetic field local minima are recognized by their ability to trap and confine quantum single-particles and quantum degenerate gases at various levels of distribution in their phase spaces, such as ultracold atoms and virtual quantum particles. Based on the nature of the interaction between the external confining potential fields and the different types of quantum particles, this research is conducted through two separate but not different phases. We performed theoretical and/or experimental investigations, for both phases, at the vicinity of the magnetic micro-confinement and its suitability for trapping quantum particles. A special attention is paid to inspect the coherence in such systems defined in terms of providing an accessible coupling to the internal quantum states of the magnetically trapped particles. Such coherence is considered as one of the important ingredients for simulating condensed matter systems and processing quantum information

Robust and Model Predictive Control for Boundary Control Systems

Tässä väitöskirjassa tarkastellaan robustia ja mallia ennakoivaa säätöä reunasäätöjärjestelmien kannalta. Robustin säädön osalta tunnettuja tuloksia, erityisesti sisäisen mallin periaate, yleistetään tälle systeemiluokalle. Approksimatiivisen robustin reguloinnin käsite esitellään reunasäätöjärjestelmien viitekehyksessä, koska sisäisen mallin periaatteen nojalla tarkasti reguloivan robustin säätäjän konstruointi ei käytännössä ole mahdollista, jos säädettävän systeemin ulostulo on ääretönulotteinen. Lisäksi esitellään käytännöllinen säätäjärakenne, jota käyttämällä robusti regulointi voidaan saavuttaa tässä approksimatiivisessa mielessä. Mallia ennakoivaa säätöä (MPC) tarkastellaan ääretönulotteisten systeemien luokalle, joka kattaa osan reunasäätöjärjestelmistä. Jatkuva-aikaista järjestelmää approksimoidaan diskreettiaikaisella käyttäen Cayley-Tustin muunnosta, ja MPC-ongelma muodostetaan diskreettiaikaiselle systeemille. Diskreettiaikaiselle MPC-ongelmalle todistetaan optimaalinen ja stabiloiva ratkeavuus, mikä yleistää vastaavan äärellisulotteisen MPC-tuloksen tarkasteltujen ääretönulotteisten systeemien luokalle.In this thesis, robust and model predictive control are considered for boundary control systems. In terms of robust control, the existing results, especially the internal model principle, are generalized to cover this class of systems. The concept of approximate robust regulation for boundary control systems is presented, as, due to the internal model principle, in practice it is not possible to construct an exact robust regulating controller if the output space of the controlled system is infinite-dimensional. A practical controller design is presented to achieve robust regulation in this approximate sense. Model predictive control (MPC) is considered for the class of regular linear systems which includes regular boundary control systems. The continuous-time system is approximated by a discrete-time one by using the Cayley-Tustin transform, and MPC is considered for the discrete-time system. Stability and optimality are proved for the proposed discrete-time MPC designs, which extends the corresponding finitedimensional MPC designs to the class of regular linear systems