An algebraic q-deformed form for shape-invariant systems

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show that these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserves the shape-invariance property presented by the primary system. q-deformed generalizations of Morse, Scarf and Coulomb potentials are given as examples.

Ladder operators for subtle hidden shape-invariant potentials

Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics, we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance.

Excitons in undoped AlGaAs/GaAs wide parabolic quantum wells

In this work the electronic structure of undoped AlGaAs/GaAs wide parabolic quantum wells (PQWs) with different well widths (1000 and 3000 ) were investigated by means of photoluminescence (PL) measurements. Due to the particular potential shape, the sample structure confines photocreated carriers with almost three-dimensional characteristics. Our data show that depending on the well width thickness it is possible to observe very narrow structures in the PL spectra, which were ascribed to emissions associated to the recombination of confined 1s-excitons of the parabolic potential wells. From our measurements, the exciton binding energies (of a few meV) were estimated. Besides the exciton emission, we have also observed PL emissions associated to electrons in the excited subbands of the PQWs. © 2010 IOP Publishing Ltd.

Molecular properties of the PCO radical: heat of formation and the isomerization pathways

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Study of hadronic event-shape variables in multijet final states in pp collisions at root s=7 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Quantum motion in superposition of Aharonov-Bohm with some additional electromagnetic fields

The structure of additional electromagnetic fields to the Aharonov-Bohm field, for which the Schrodinger, Klein-Gordon, and Dirac equations can be solved exactly are described and the corresponding exact solutions are found. It is demonstrated that aside from the known cases (a constant and uniform magnetic field that is parallel to the Aharonov-Bohm solenoid, a static spherically symmetrical electric field, and the field of a magnetic monopole), there are broad classes of additional fields. Among these new additional fields we have physically interesting electric fields acting during a finite time or localized in a restricted region of space. There are additional time-dependent uniform and isotropic electric fields that allow exact solutions of the Schrodinger equation. In the relativistic case there are additional electric fields propagating along the Aharonov-Bohm solenoid with arbitrary electric pulse shape. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4714352]

Quantum Mechanics Insight into the Microwave Nucleation of SrTiO3 Nanospheres

An extensive investigation of strontium titanate, SrTiO3 (STO), nanospheres synthesized via a microwave-assisted hydrothermal (MAH) method has been conducted to gain a better insight into thermodynamic, kinetic, and reaction phenomena involved in STO nucleation and crystal growth processes. To this end, quantum chemical modeling based on the density functional theory and periodic super cell models were done. Several experimental techniques were employed to get a deep characterization of structural and optical features of STO nanospheres. A possible formation mechanism was proposed, based on dehydration of titanium and strontium clusters followed by mesoscale transformation and a self-assembly process along an oriented attachment mechanism resulting in spherical like shape. Raman and XANES analysis renders a noncentrosymmetric environment for the octahedral titanium, while infrared and first order Raman modes reveal OH groups which are unsystematically incorporated into uncoordinated superficial sites. These results seem to indicate that the key component is the presence of distorted TiO6 clusters to engender a luminescence property. Analysis of band structure, density Of states, and charge map shows that there is a close relationship among local broken symmetry, polarization, and energy split of the 3d orbitals of titanium. The interplay among these electronic and structural features provides necessary conditions to evaluate its luminescent properties under two energy excitation.

Coil-ring-coil block copolymers as building blocks of supramolecular hollow cylindrical brushes

This work describes the synthesis of a new class of rod-coil block copolymers, oligosubstituted shape persistent macrocycles, (coil-ring-coil block copolymers), and their behavior in solution and in the solid state.The coil-ring-coil block copolymers are formed by nanometer sized shape persistent macrocycles based on the phenyl-ethynyl backbone as rigid block and oligomers of polystyrene or polydimethylsiloxane as flexible blocks. The strategy that has been followed is to synthesize the macrocycles with an alcoholic functionality and the polymer carboxylic acids independently, and then bind them together by esterification. The ester bond is stable and relatively easy to form.The synthesis of the shape persistent macrocycles is based on two separate steps. In the first step the building blocks of the macrocycles are connected by Hagiara-Sogonaschira coupling to form an 'half-ring' as precursor, that contains two free acetylenes. In the second step the half-ring is cyclized by forming two sp-sp bonds via a copper-catalyzed Glaser coupling under pseudo-high-dilution conditions. The polystyrene carboxylic acid was prepared directly by siphoning the living anionic polymer chain into a THF solution, saturated with CO2, while the polydimethylsiloxane carboxylic acid was obtained by hydrosilylating an unsaturated benzylester with an Si-H terminated polydimethylsiloxane, and cleavage of the ester. The carbodiimide coupling was found to be the best way to connect macrocycles and polymers in high yield and high purity.The polystyrene-ring-polystyrene block copolymers are, depending on the molecular weight of the polystyrene, lyotropic liquid crystals in cyclohexane. The aggregation behavior of the copolymers in solution was investigated in more detail using several technique. As a result it can be concluded that the polystyrene-ring-polystyrene block copolymers can aggregate into hollow cylinder-like objects with an average length of 700 nm by a combination of shape complementary and demixing of rigid and flexible polymer parts. The resulting structure can be described as supramolecular hollow cylindrical brush.If the lyotropic solution of the polystyrene-ring-polystyrene block copolymers are dried, they remain birefringent indicating that the solid state has an ordered structure. The polydimethylsiloxane-ring-polydimethylsiloxane block copolymers are more or less fluid at room temperature, and are all birefringent (termotropic liquid crystals) as well. This is a prove that the copolymers are ordered in the fluid state. By a careful investigation using electron diffraction and wide-angle X-ray scattering, it has been possible to derive a model for the 3D-order of the copolymers. The data indicate a lamella structure for both type of copolymers. The macrocycles are arranged in a layer of columns. These crystalline layers are separated by amorphous layers which contain the polymers substituents.

Persistent currents in quantum rings

In this thesis, three different types of quantum rings arestudied. These are quantum rings with diamagnetic,paramagnetic or spontaneous persistent currents. It turns out that the main observable to characterizequantum rings is the Drude weight. Playing a key role inthis thesis, it will be used to distinguish betweendiamagnetic (positive Drude weight) and paramagnetic(negative Drude weight) ring currents. In most models, theDrude weight is positive. Especially in the thermodynamiclimit, it is positive semi-definite. In certain modelshowever, intuitivelysurprising, a negative Drude weight is found. This rareeffect occurs, e.g., in one-dimensional models with adegenerate ground state in conjunction with the possibilityof Umklapp scattering. One aim of this thesis is to examineone-dimensional quantum rings for the occurrence of anegative Drude weight. It is found, that the sign of theDrude weight can also be negative, if the band structurelacks particle-hole symmetry. The second aim of this thesis is the modeling of quantumrings intrinsically showing a spontaneous persistentcurrent. The construction of the model starts from theextended Hubbard model on a ring threaded by anAharonov-Bohm flux. A feedback term through which thecurrent in the ring can generate magnetic flux is added.Another extension of the Hamiltonian describes the energystored in the internally generated field. This model isevaluated using exact diagonalization and an iterativescheme to find the minima of the free energy. The quantumrings must satisfy two conditions to exhibit a spontaneousorbital magnetic moment: a negative Drude weight and aninductivity above the critical level. The magneticproperties of cyclic conjugated hydrocarbons likebenzene due to electron delocalization [magnetic anisotropy,magnetic susceptibility exaltation, nucleus-independent chemical shift (NICS)]---that have become important criteriafor aromaticity---can be examined using this model. Corrections to the presented calculations are discussed. Themost substantial simplification made in this thesis is theneglect of the Zeeman interaction of the electron spins withthe magnetic field. If a single flux tube threads a quantumring, the Zeeman interaction is zero, but in mostexperiments, this situation is difficult to realize. In themore realistic situation of a homogeneous field, the Zeemaninteraction has to be included, if the electrons have atotal spin component in the direction of the magnetic field,or if the magnetic field is strong.

Bottle microresonators for applications in quantum optics and all-optical signal processing

This thesis reports on the experimental realization, characterization and application of a novel microresonator design. The so-called “bottle microresonator” sustains whispering-gallery modes in which light fields are confined near the surface of the micron-sized silica structure by continuous total internal reflection. While whispering-gallery mode resonators in general exhibit outstanding properties in terms of both temporal and spatial confinement of light fields, their monolithic design makes tuning of their resonance frequency difficult. This impedes their use, e.g., in cavity quantum electrodynamics (CQED) experiments, which investigate the interaction of single quantum mechanical emitters of predetermined resonance frequency with a cavity mode. In contrast, the highly prolate shape of the bottle microresonators gives rise to a customizable mode structure, enabling full tunability. The thesis is organized as follows: In chapter I, I give a brief overview of different types of optical microresonators. Important quantities, such as the quality factor Q and the mode volume V, which characterize the temporal and spatial confinement of the light field are introduced. In chapter II, a wave equation calculation of the modes of a bottle microresonator is presented. The intensity distribution of different bottle modes is derived and their mode volume is calculated. A brief description of light propagation in ultra-thin optical fibers, which are used to couple light into and out of bottle modes, is given as well. The chapter concludes with a presentation of the fabrication techniques of both structures. Chapter III presents experimental results on highly efficient, nearly lossless coupling of light into bottle modes as well as their spatial and spectral characterization. Ultra-high intrinsic quality factors exceeding 360 million as well as full tunability are demonstrated. In chapter IV, the bottle microresonator in add-drop configuration, i.e., with two ultra-thin fibers coupled to one bottle mode, is discussed. The highly efficient, nearly lossless coupling characteristics of each fiber combined with the resonator's high intrinsic quality factor, enable resonant power transfers between both fibers with efficiencies exceeding 90%. Moreover, the favorable ratio of absorption and the nonlinear refractive index of silica yields optical Kerr bistability at record low powers on the order of 50 µW. Combined with the add-drop configuration, this allows one to route optical signals between the outputs of both ultra-thin fibers, simply by varying the input power, thereby enabling applications in all-optical signal processing. Finally, in chapter V, I discuss the potential of the bottle microresonator for CQED experiments with single atoms. Its Q/V-ratio, which determines the ratio of the atom-cavity coupling rate to the dissipative rates of the subsystems, aligns with the values obtained for state-of-the-art CQED microresonators. In combination with its full tunability and the possibility of highly efficient light transfer to and from the bottle mode, this makes the bottle microresonator a unique tool for quantum optics applications.

Hyperbranched polyether polyols as building blocks for complex macromolecular architectures

The present thesis deals with the development of new branched polymer architectures containing hyperbranched polyglycerol. Materials investigated include hyperbranched oligomers, hyperbranched polyglycerols containing functional initiator-cores at the focal point, well-defined linear-hyperbranched block copolymers and also negatively charged hyperbranched polyelectrolytes.rnHyperbranched oligoglycerols (DPn = 7 and 14) have been synthesized for the first time. The materials show narrow polydispersity (Mw/Mn ca. 1.45) and a very low content in cyclic homopolymers. 13C NMR evidences the dendritic structure of the oligomers and the DB could be calculated (44% and 52%). These new oligoglycerols were compared with the industrial products obtained by polycondensation which exhibit narrow polydispersity (Mw/Mn<1.3) butrnmultimodal distribution in SEC. Detailed 13C NMR and Maldi-ToF studies reveal the presence of branched units and cyclic compounds. In comparison, the hyperbranched oligoglycerols comprise a very low proportion of cyclic homopolymer which render them very interesting materials for biomedical applications for example.rnThe site isolation of the core moiety in dendritic structure offers intriguing potential with respect to peculiar electro-optical properties. Various initiator-cores (n-alkyl amines, UVabsorbing amines and benzophenone) for the ROMBP of glycidol have been tested. The bisglycidolized amine initiator-cores show the best control over the molecular weight and the molecular weight distribution. The photochemical analyses of the naphthalene containingrnhyperbranched polyglycerols show a slight red shift, a pronounced hypochromic effect (decrease of the intensity of the band) compared with the parent model compound and the formation of a relative compact structure. The benzophenone containing polymers adopt an open structure in polar solvents. The fluorescence measurements show a clear “dendritic effect” on the fluorescence intensities and the quantum yield of the encapsulated benzophenone.rnA convenient 3-step strategy has been developed for the preparation of well-defined amphiphilic, linear-hyperbranched block copolymers via hypergrafting. The procedure represents a combination of carbanionic polymerization with the alkoxide-based, controlled ring-opening multibranching polymerization of glycidol. Materials consisting of a polystyrene linear block and a hyperbranched polyglycerol block exhibit narrow polydispersity (1.01-1.02rnfor 5.4% to 27% wt. PG and 1.74 for 52% wt. PG) with a high grafting efficiency. The strategy was also extended to materials with a linear polyisoprene block.rnDetailed investigations of the solution properties of the block copolymers with linear polystyrene blocks show that block copolymer micelles are stabilized by the highly branched block. The morphology of the aggregates is depending on the solvent: in chloroform monodisperse spherical shape aggregates and in toluene ellipsoidal aggregates are formed. On graphite these aggregates show interesting features, giving promising potential applications with respect to the presence of a very dense, functional and stable hyperbranched block.rnThe bulk morphology of the linear-hyperbranched block copolymers has been investigated. The materials with a linear polyisoprene block only behave like complex liquids due to the low Tg and the disordered nature of both components. For the materials with polystyrene, only the sample with 27% wt. hyperbranched polyglycerol forms some domains showing lamellae.rnThe preparation of hyperbranched polyelectrolytes was achieved by post-modification of the hydroxyl groups via Michael addition of acrylonitrile, followed by hydrolysis. In aqueous solution materials form large aggregates with size depending on the pH value. After deposition on mica the structures observed by AFM show the coexistence of aggregates andrnunimers. For the low molecular weight sample (PG 520 g·mol-1) extended and highly ordered terrace structures were observed. Materials were also successfully employed for the fabrication of composite organic-inorganic multilayer thin films, using electrostatic layer-bylayer self-assembly coupled with chemical vapor deposition.

Coarse-graining and quantum-classical adaptive coupling in soft matter

Die vorliegende Arbeit untersucht den Zusammenhang zwischen Skalen in Systemen weicher Materie, der für Multiskalen-Simulationen eine wichtige Rolle spielt. Zu diesem Zweck wurde eine Methode entwickelt, die die Approximation der Separierbarkeit von Variablen für die Molekulardynamik und ähnliche Anwendungen bewertet. Der zweite und größere Teil dieser Arbeit beschäftigt sich mit der konzeptionellen und technischen Erweiterung des Adaptive Resolution Scheme'' (AdResS), einer Methode zur gleichzeitigen Simulation von Systemen mit mehreren Auflösungsebenen. Diese Methode wurde auf Systeme erweitert, in denen klassische und quantenmechanische Effekte eine Rolle spielen.rnrnDie oben genannte erste Methode benötigt nur die analytische Form der Potentiale, wie sie die meisten Molekulardynamik-Programme zur Verfügung stellen. Die Anwendung der Methode auf ein spezielles Problem gibt bei erfolgreichem Ausgang einen numerischen Hinweis auf die Gültigkeit der Variablenseparation. Bei nicht erfolgreichem Ausgang garantiert sie, dass keine Separation der Variablen möglich ist. Die Methode wird exemplarisch auf ein zweiatomiges Molekül auf einer Oberfläche und für die zweidimensionale Version des Rotational Isomer State (RIS) Modells einer Polymerkette angewandt.rnrnDer zweite Teil der Arbeit behandelt die Entwicklung eines Algorithmus zur adaptiven Simulation von Systemen, in denen Quanteneffekte berücksichtigt werden. Die Quantennatur von Atomen wird dabei in der Pfadintegral-Methode durch einen klassischen Polymerring repräsentiert. Die adaptive Pfadintegral-Methode wird zunächst für einatomige Flüssigkeiten und tetraedrische Moleküle unter normalen thermodynamischen Bedingungen getestet. Schließlich wird die Stabilität der Methode durch ihre Anwendung auf flüssigen para-Wasserstoff bei niedrigen Temperaturen geprüft.

Self-Absorption and Luminescence Quantum Yields of Dye-Zeolite L Composites

Electronic absorption and fluorescence spectra based on transmission measurements of thin layers obtained from new perylene−zeolite L composites and new dye1,dye2−zeolite L sandwich composites, the latter acting as antenna systems, have been investigated and analyzed. The influence of extra- and intraparticle self-absorption on the spectral shape and fluorescence quantum yield is discussed in detail. Due to its intraparticle origin, self-absorption and re-emission can often not be avoided in organized systems such as dye−zeolite L composites where a high density of chromophores is a prerequisite for obtaining the desired photophysical properties. We show, however, that it can be avoided or at least minimized by preparing dye1,dye2−zeolite L sandwich composites where donors are present in a much larger amount than the acceptors because they act as antenna systems.

Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits

A quantum simulator of U(1) lattice gauge theories can be implemented with superconducting circuits. This allows the investigation of confined and deconfined phases in quantum link models, and of valence bond solid and spin liquid phases in quantum dimer models. Fractionalized confining strings and the real-time dynamics of quantum phase transitions are accessible as well. Here we show how state-of-the-art superconducting technology allows us to simulate these phenomena in relatively small circuit lattices. By exploiting the strong non-linear couplings between quantized excitations emerging when superconducting qubits are coupled, we show how to engineer gauge invariant Hamiltonians, including ring-exchange and four-body Ising interactions. We demonstrate that, despite decoherence and disorder effects, minimal circuit instances allow us to investigate properties such as the dynamics of electric flux strings, signaling confinement in gauge invariant field theories. The experimental realization of these models in larger superconducting circuits could address open questions beyond current computational capability.

High efficient luminescence in type-II GaAsSb-capped InAs quantum dots upon annealing

The photoluminescence efficiency of GaAsSb-capped InAs/GaAs type II quantum dots (QDs) can be greatly enhanced by rapid thermal annealing while preserving long radiative lifetimes which are ∼20 times larger than in standard GaAs-capped InAs/GaAs QDs. Despite the reduced electron-hole wavefunction overlap, the type-II samples are more efficient than the type-I counterparts in terms of luminescence, showing a great potential for device applications. Strain-driven In-Ga intermixing during annealing is found to modify the QD shape and composition, while As-Sb exchange is inhibited, allowing to keep the type-II structure. Sb is only redistributed within the capping layer giving rise to a more homogeneous composition.