Indiana University-Purdue University Indianapolis (IUPUI) / This research investigates characteristics of PT (parity-time) symmetry breaking in a system of two optically-coupled, time-delayed semiconductor lasers. A theoretical rate equation model for the lasers' electric fields is presented and then reduced to a 2x2 Hamiltonian model, which, in the absence of time-delay, is PT-symmetric. The important parameters we control are the temporal separation of the lasers, the frequency detuning, and the coupling strength. The detuning is experimentally controlled by varying the lasers' temperatures, and intensity vs. detuning behavior are examined, specifically how the PT-transition and the period and amplitude of sideband intensity oscillations change with coupling and delay. Experiments are compared to analytic predictions and numerical results, and all are found to be in good agreement. Eigenvalues, eigenvectors, and exceptional points of the reduced Hamiltonian model are numerically and analytically investigated, specifically how nonzero delay affects existing exceptional points.

Des états électroniques localisés apparaissent dans les liens faibles entre électrodes supraconductrices : les états d’Andreev. Les expériences présentées dans cette thèse explorent les propriétés de cohérence quantique de ces états, en utilisant comme liens faibles des contacts à un atome entre des électrodes d’aluminium. Les contacts atomiques sont intégrés dans une cavité microonde qui permet à la fois de les isoler et de les sonder.Dans une première série d’expériences, il est montré qu’on peut utiliser les états d’Andreev pour définir un bit quantique, le « qubit d’Andreev », qu’on contrôle à l’aide d’impulsions micro-onde.Les mesures des temps de vie de cohérence de ce qubit sont analysées en détail.Dans une deuxième série d’expérience,l’interaction entre le qubit d’Andreev et le résonateur micro-onde est utilisée pour quantifier le nombre de photons présents dans le résonateur en fonction de la puissance d’impulsions microonde à sa fréquence propre.Enfin, des sauts quantiques et des sauts de parités ont observés dans des mesures continues de l’état du qubit d’Andreev. / Localized electronic states, called Andreev bound states, appear in weak-links placed between superconducting electrodes. The experiments presented in this thesis explore the coherence properties of these states. Single atom contacts between aluminum electrodes are used as weak links. In order to isolate and probe these states, the atomic contacts are integrated in amicrowave cavity.In a first series of experiments, it is shown that Andreev states can be used to define a quantumbit, “the Andreev qubit”, which is controlled using microwave pulses.Measurements of the lifetime and coherence time of this qubit are thoroughly analyzed.In a second series of experiments, the interaction between the Andreev qubit and the microwave cavity are used to determine the number of photons present in the cavity as a function of the power of microwave pulses at its eigenfrequency.Finally, quantum and parity jumps are observed in continuous measurements of the state of the Andreev dot.

The presence of excess free radicals in the body can result in severe health consequences because of oxidative damage to cells. Spin traps may be used as a probe to examine radical reactions in cells, but there is a need for less toxic and more lipid soluble examples. Melatonin is one of the numerous antioxidants used to scavenge free radicals in the body and reportedly one of the most efficient radical scavengers known. It is relatively nontoxic and easily crosses the lipid bilayer in cell membranes. Melatonin is thought to undergo a multistep oxidation process and this work investigates the potential for it to be used as a spin trap. The presence of electron withdrawing or donating groups added to melatonin may stabilize an intermediate and allow it to function as a spin trap. The essence of this study is to conduct a computational inquiry into the relative stability of melatonin, selected derivatives, and the partial oxidation products formed from the scavenging of hydroxyl radical. To determine this, geometries were optimized for each molecule at the DFT/B3LYP/6-31G(d) and HF/6-31G(d) levels of theory.

The ALPHA experiment at CERN is an ongoing project which tests fundamental symmetries between matter and antimatter by producing and trapping antihydrogen atoms in order to perform precision spectroscopic measurements. A logical next step is to form the antihydrogen molecular ion (consisting of one positron and two antiprotons). This system possesses net charge, and can therefore be trapped electrostatically, making repeated measurements possible. Moreover it has been suggested that the molecule has the potential to allow for higher-precision comparisons with ordinary matter than have been attained with the atom. Since both momentum and energy have to be conserved in a collision, a simple collision process between an antihydrogen atom (“Hbar”) and an antiproton (“pbar”) does not suffice in order to form the molecular ion. However it is possible, upon mixing of the two species, for a pbar colliding with an Hbar in the ground electronic state to form a metastable molecular state (i.e., a resonance) which is weakly coupled to a stable molecular state (i.e., a bound state) via spontaneous quadrupole transition. During the time a metastable ion exists, a second pbar can happen to undergo a Coulomb collision with the metastable molecular ion. The quadrupole electrostatic interaction with this secondary antiproton acts as a time-dependent perturbation on the molecular system which can strengthen the coupling between resonance and bound state. Hence a collision with a secondary pbar can induce a transition to a bound state whereby the excess energy is carried off by the secondary pbar. This work aims to determine the efficiency of the process just described. On the theoretical side, the following is done: a study is conducted on the topic of resonance scattering as it relates to the problem in consideration; building on this study a generalized time-dependent perturbation theory is constructed which is valid for transitions to and from resonant states as well as bound states. On the numerical side: the effective potential for pbar-Hbar scattering in the ground electronic state is obtained numerically within the adiabatic approximation; the energies and lifetimes of the resonant states of the molecular ion are estimated; a temperature-dependent rate coefficient is obtained for the process described which, in order to obtain a proper rate, needs to be multiplied by the square of the density of the antiproton plasma and by the number of antihydrogen atoms. It is concluded that at current capacity for trapping and storage of pbar and Hbar the process examined is not competitive with respect to other formation routes which have been proposed for the molecular ion.

Includes bibliographical references. / The tendency in theoretical physics, particularly in the past few decades, has been towards unification: over the years it has emerged that increasingly many physical phenomena can be explained by a common underlying theory. Symmetry principles, both global and local, play an important role in this unification programme. Global symmetries often account for approximate regularities we observe in nature - local or gauge symmetries are understood as basic symmetries which lie at the heart of the interactions of the constituents of matter.

Durant cette thèse, nous avons abordé l'étude de la réactivité en phase gazeuse des biomolécules. L’avènement des techniques d’ionisation douces telle que l’ionisation par éléctronébulisation, a rendu possible ces dernières années, la formation d'ions en phase gazeuse sans dégrader la biomolécule étudiée.La Dissociation Induite par Collision (CID) est un cas particulier de spectrométrie de masse en tandem, que nous avons utilisée durant ce travail. Le principe du CID est d'activer les modes rovibrationnelles d’un système moléculaire ionique par collision avec un gaz inerte, ce qui augmente la probabilité de fragmentation de l'ion. Bien qu'étant une technique très utile d'un point de vue analytique, la spectrométrie de masse en tandem ne donne pas d'informations sur les mécanismes des réactions se produisant dans la cellule de collision; afin d’obtenir ces informations, les simulations de dynamique chimiques apparaissent comme un outil satisfaisant. En effet, en utilisant la dynamique directe, nous évitons ainsi d'explorer la totalité de la surface d'énergie potentielle, qui devient compliquée lors de l’étude d’édifices moléculaires de grande taille. Etant donné que les simulations de dynamique chimiques sont limitées à de courtes échelles, de l’ordre de la dizaine de picosecondes, nous avons également employé la théorie unimoléculaire RRKM (Rice-Ramsperger-Kassel-Marcus) pour étudier la réactivité à des temps plus longs, en vue de comprendre les processus réactionnels se produisant à l’issue du processus de relaxation vibrationnelle intramoléculaire (IVR). Durant ce travail de thèse, nous avons choisi d'étudier comme système modèle de base nucléique la molécule d'uracile. Par ailleurs,nous avons aussi étudié la réactivité en phase gazeuse de sucres (cellobiose, maltose et gentiobiose), qui ont été au préalable dérivatisés afin de localiser la charge sur la molécule et ainsi simplifier l’étude théorique associée. / In the present thesis, we address the study of the reactivity of biomolecules in the gasphase.The advent of soft ionization techniques such as electrospray ionization, made possible, in the last years, the gentle formation of ions in the gas phase without breaking the molecule understudy.Collision Induced Dissociation (CID) is aparticular case of tandem mass spectrometrydynamics simulations are pointed like asatisfactory tool. Using direct dynamics weavoid exploring the whole potential energysurface, which becomes really complicatedwhen dealing with big molecules.Since chemical dynamics simulations arerestricted to the short time scale reactivity,typically ~10ps, we make use of the Rice–Ramsperger–Kassel–Marcus (RRKM)unimolecular theory to study the reactivity atUniversité Paris-SaclayEspace Technologique / Immeuble DiscoveryRoute de l’Orme aux Merisiers RD 128 / 91190 Saint-Aubin, Francethat we use in the present thesis. The aim of CIDis to activate the rovibrational modes of an ionicmolecular system by collisions with an inert gas,increasing the probability of the ion of beingfragmented.Despite being a really useful technique, tandemmass spectrometry does not give informationabout the mechanisms of the reactions takingplace in the collision cell; in order to obtain suchinformation, chemicallonger time scales to understand reaction pathsthat take place after intramolecular vibrationrelaxation (IVR).In the present thesis we have chosen to study asmodel system of nucleobase the uracil molecule.Furthermore, we also studied the gas-phase reactivity of carbohydrates (cellobiose, maltose and gentiobiose), which were preliminarily derivatized in order to simplify the charge localization, and consequently the theoretical study.

Résumé: Ce travail se veut une analyse conceptuelle de certains développements récents dans les fondements mathématiques de la Mécanique Classique et de la Mécanique Quantique qui ont permis de formuler ces deux théories dans un même langage. Du point de vue algébrique, l’ensemble des observables d’un système physique, soit-il classique ou quantique, est décrit par une algèbre de Jordan-Lie. Du point de vue géométrique, l’espace des états de tout système est décrit par un espace uniforme de Poisson avec transition de probabilité. Ces deux structures mathématiques sont ici interprétées comme une manifestation du double rôle constitutif des propriétés en physique : elles sont à la fois des quantités et des transformations. Il s’agit alors de comprendre l’articulation précise entre ces deux rôles. Au cours de l’analyse, il apparaîtra que la Mécanique Quantique peut être vue comme se distinguant de la Mécanique Classique par une condition de compatibilité entres les quantités et les transformations.D’autre part, cette thèse met en évidence l’existence d’une tension fondamentale entre une certaine façon abstraite de concevoir les structures mathématiques, présente dans la pratique de la physique mathématique, et la nécessité de spécifier des états ou des observables particulières. Il devient alors important de comprendre comment, dans le formalisme, se construit un schéma d’indexation. La “poursuite de l’individuation” est l’analyse de différentes techniques mathématiques vues comme tentatives de résolution ce problème. En particulier,nous discuterons comment la théorie des groupes permet d’y apporter une solution partielle. / This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the set of observables of a physical system, be it classical or quantum, is described by a Jordan-Lie algebra. From the geometric point of view, the space of states of any system is described by a uniform Poisson space with transition probability. Both these structures are here perceived as formal translations of the fundamental two fold role of properties in Mechanics: they are at the same time quantities and transformations. The question becomes then to understand the precise articulation between these two roles. The analysis will show that Quantum Mechanics canbe thought as distinguishing itself from Classical Mechanics by a compatibility condition between properties-as-quantities and properties-as-transformations. Moreover, this dissertation shows the existence of a tension between a certain ‘abstractway’ of conceiving mathematical structures, used in the practice of mathematical physics, and the necessary capacity to specify particular states or observables. It then becomes important to understand how, within the formalism, one can construct a labelling scheme. The “Chasefor Individuation” is the analysis of diferent mathematical techniques which attempt to overcome this tension. In particular, we discuss how group theory furnishes a partial solution

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