University, Diss., 2005--Düsseldorf.

Condensados de Bose-Einstein (BEC) são sistemas macroscópicos excelentes para a observação do comportamento quântico da matéria. Desde sua obtenção experimental em gases atômicos alcalinos diluídos aprisionados por campos magnéticos, há importantes aspectos relacionados a esse sistema que foram intensamente explorados, como os modos coletivos do BEC harmonicamente aprisionado, seu tunelamento através de barreiras de potencial e os estados excitados desse sistema, incluindo vórtice e sóliton. O último consiste de pacote de onda localizado, que propaga sem mudança de forma. Nesse trabalho, investigamos os novos aspectos que surgem da dinâmica de um sistema composto (condensado aprisionado contendo um sóliton). Há muitos estudos tratando cada parte separadamente: estado fundamental do BEC ou um sóliton em um BEC infinito uniforme estacionário. Estamos nos baseando nessas análises prévias, além da simulação numérica de campo médio do nosso sistema submetido a diferentes condições iniciais (BEC aprisionado no mínimo do potencial harmônico ou BEC deslocado na armadilha contendo um sóliton, além de uma deformação no potencial) para caracterizar a dinâmica desse sistema. Alguns dos nossos resultados puderam ser explicados por meio de predições analítica da chamada aproximação de Thomas-Fermi. Ao final, comparamos as simulações de campo médio (equação de Gross-Pitaevskii) com as advindas da teoria de múltiplos orbitais a fim de justificar o regime de validade da nossa teoria. / Bose-Einstein Condensates (BEC) are excellent macroscopic systems to observe the quantum behavior of matter. Since it experimental production in dilute atomic alkali gases trapped by magnetic fields, there are important aspects related to this system that have been intensely explored, like the collective modes of the harmonically trapped BEC, its tunneling through a potential barrier and the excited states of this system, that include the vortex and soliton. The latter consist of localized disturbances, which propagate without change of form. In this work, we investigate the singular aspects that coming from the dynamics of a composite system (trapped BEC containing a soliton). There are many studies that treat each part separately, that include a fundamental state BEC or a soliton inside a uniform infinite extent stationary BEC. We are basing on these previous analyses, besides mean-field numeric simulating our particular system submitted to diferent initial conditions (minimum harmonic potential trapped BEC or dislocated trapped BEC plus a soliton, in addition to a deformation in the potential) to characterize the tunneling dynamics. Some of our results could be explained using analytical predictions of the so called Thomas-Fermi approximation. At the end, we compar the meanfield simulations (Gross-Pitavskii equation) with the simulations from the multiple orbitals theory to justify the validity regime of our theory.

Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-02-20T14:43:25Z No. of bitstreams: 2 Tese - Francisco E. S. Feitosa.pdf: 967919 bytes, checksum: 5306fbcfacd272a247da3e3b41aaab96 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-02-20T14:43:39Z (GMT) No. of bitstreams: 2 Tese - Francisco E. S. Feitosa.pdf: 967919 bytes, checksum: 5306fbcfacd272a247da3e3b41aaab96 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2017-02-20T14:44:07Z (GMT) No. of bitstreams: 2 Tese - Francisco E. S. Feitosa.pdf: 967919 bytes, checksum: 5306fbcfacd272a247da3e3b41aaab96 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-02-20T14:44:07Z (GMT). No. of bitstreams: 2 Tese - Francisco E. S. Feitosa.pdf: 967919 bytes, checksum: 5306fbcfacd272a247da3e3b41aaab96 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-10-21 / In the first part of this thesis, we calculate the Gaussian curvature of surfaces isometrically immersed in homogeneous contact Riemannian 3—manifolds in terms of mean curvature and contact angle. Moreover, we find the Laplacian of the contact angle and, as an application, we characterize Hopf 's torus as the unique connected and compact surface in the class of homogeneous and simply connected 3—manifolds with isometry group of dimension 4 which has both constant mean curvature and contact angle. Furthermore, we present sufficient conditions to isometrically immerse surfaces in these 3—manifolds. In the second part, we present necessary and sufficient conditions for warped product to admit the structure of gradient almost Ricci soliton. Besides that, some results about existence and rigidity are presented. / Na primeira parte desta tese calculamos, em termos da curvatura média e do ângulo de contato, a curvatura Gaussiana de superfícies isometricamente imersas em 3—variedades Riemannianas de contato homogêneas. Também calculamos o Laplaciano do ângulo de contato. Como aplicação caracterizamos o Toro de Hopf como a única superfície conexa e compacta isometricamente imersa, com ângulo de contato e curvatura média ambos constantes, em uma classe de 3—variedades homogêneas simplesmente conexas com grupo de isometrias de dimensão quatro. Apresentamos ainda condições suficientes, em termos do ângulo de contato, para imergir isometricamente superfícies nestes ambientes. Na segunda parte, apresentamos condições necessárias e suficientes para que um produto warped admita estrutura de quase soliton de Ricci gradiente. Além disso, alguns resultados de existência e rigidez são apresentados.

In chapter 2, we study two Kaup-Newell-type matrix spectral problems, derive their soliton hierarchies within the zero curvature formulation, and furnish their bi-Hamiltonian structures by the trace identity to show that they are integrable in the Liouville sense. In chapter 5, we obtain the Riemann theta function representation of solutions for the first hierarchy of generalized Kaup-Newell systems. In chapter 3, using Hirota bilinear forms, we discuss positive quadratic polynomial solutions to generalized bilinear equations, which generate lump or lump-type solutions to nonlinear evolution equations, and propose an algorithm for computing higher-order lump or lump-type solutions. In chapter 4, we study mixed exponential and trigonometric wave solutions (called complexitons) to general bilinear equations, and propose two methods to find complexitons to generalized bilinear equations. We also succeed in proving that by choosing suitable complex coefficients in soliton solutions, multi-complexitons are actually real wave solutions from complex soliton solutions and establish the linear superposition principle for complexion solutions. In each chapter, we present computational examples.

We derive two hierarchies of 1+1 dimensional soliton-type integrable systems from two spectral problems associated with the Lie algebra of the special orthogonal Lie group SO(3,R). By using the trace identity, we formulate Hamiltonian structures for the resulting equations. Further, we show that each of these equations can be written in Hamiltonian form in two distinct ways, leading to the integrability of the equations in the sense of Liouville. We also present finite-dimensional Hamiltonian systems by means of symmetry constraints and discuss their integrability based on the existence of sufficiently many integrals of motion.

La thèse montre des solutions pour la réalisation de circuits photoniques intégrés utilisant le caractère volumétrique et les très faibles pertes en propagation des solitons spatiaux. On s'intéresse aux éléments de base : interconnexions, sources et router optique (comme dispositif d'élaboration). Interconnexions et sources sont réalisé dans le niobate de lithium (LN) qui fournis des structures avec une très longue durée temporelle. Le fonctionnement d'un router optique est démontré dans le semiconducteur photo-réactif (PR) InP:Fe en raison de sa sensitivité aux longueurs d'onde infrarouges (IR) et à son temps de réponse rapide. On montre que les pertes en propagation dans les interconnexions solitoniques peuvent être réduites à nouveau en utilisant un faisceau en polarisation ordinaire qui augmente la variation d'indice de réfraction induite. La réalisation de sources intégrées solitoniques est étudié pour avoir émission en bleu à 400nm et en IR à 1530nm. Celles en bleu sont obtenues par génération de deuxième harmonique ; le rôle du bleu pour la formation des solitons est montré et ses propriétés physiques étudiées. Celles en IR sont obtenues en dopant le LN avec des ions (actifs) d'erbium. Leurs effets sur les paramètres PR sont présentés et les solitons spatiaux sont obtenus en excitant l'absorption soit du LN soit de l'erbium. L'amplification de la luminescence est étudié numériquement. Le routage optique dans le InP:Fe est obtenu en faisant interagir deux solitons cohérents et en changeant leur phase relative. L'augmentation de la séparation ou leur fusion est analysé en fonction de la distance entre eux, température et intensité de la lumière / Solutions for the realization of integrated photonic circuits with the advantages that spatial solitons offer, like their volumetric nature and the very low propagation losses are shown. Interconnections, sources and optical router (as signal elaboration device) are investigated. Interconnections and sources are experimentally demonstrated in lithium niobate (LN) that provides long-lasting structures thanks to its very long dielectric relaxation time. The optical router working principle is realized in the photorefractive semiconductor InP:Fe because of its sensitivity in infrared radiation and its fast response time. To improve solitonic interconnections, an analysis based on propagation losses in function of light polarization and LN anisotropy is done. The key role played by an ordinary polarized beam on the induced refractive index variation is exploited. Integrated sources in solitonic waveguides for the emission of blue at 400nm and of an infrared beam at 1530nm are investigated. Sources emitting in blue are obtained via a second harmonic generation process ; blue seed role in spatial soliton formation is demonstrated and its physical properties are investigated as well. The infrared one is achieved by doping LN with (active) erbium ions. Their effects on the photorefractive parameters are exploited and spatial solitons realized both pumping direcly erbium absorption lines and the LN ones. Luminescence amplification is studied numerically. Optical routing in InP:Fe is achieved by making two coherent solitons interact by changing their relative phase. Separation increasing or fusion is analyzed in function of mutual distance, temperature and light intensity

No description available.

京都大学 / 0048 / 新制・課程博士 / 博士(エネルギー科学) / 甲第20018号 / エネ博第341号 / 新制||エネ||68(附属図書館) / 33114 / 京都大学大学院エネルギー科学研究科エネルギー基礎科学専攻 / (主査)教授 岸本 泰明, 教授 中村 祐司, 准教授 田中 仁 / 学位規則第4条第1項該当 / Doctor of Energy Science / Kyoto University / DFAM

No description available.

One of the most intriguing properties of light-matter interaction is the ability of an electromagnetic field to exert mechanical forces on polarizable objects. This phenomenon is a direct consequence of the fact that light carries momentum, which in turn can be transferred to matter. Mediated by scattering, this interaction usually manifests itself as a “pushing force” in the direction of beam propagation. However, it is possible to judiciously engineer these optical forces, either by tailoring particle polarizability, and/or by structuring the incident light field. As a simple example, a tightly focused laser beam demonstrates strong gradient forces, which may attract and even trap particles with positive polarizability in the focal volume. The opposite occurs in the regime of negative polarizability, where particles are expelled from the regions of highest intensity. Based on this fundamental principle, one can actively shape the beam using spatial light modulators to manipulate individual objects as well as ensembles of particles suspended in a liquid. In the latter case, a modulation of the local particle concentration is associated with changes of the effective refractive index. The result is an artificial nonlinear medium, whose Kerr-type response can be readily tuned by the parameters of its constituent particles. In the course of this work, we introduce a new class of synthetic colloidal suspensions exhibiting negative polarizabilities, and observe for the first time robust propagation and enhanced transmission of self-trapped light over long distances. Such light penetration in strongly scattering environments is enabled by the interplay between optical forces and self-activated transparency effects. We explore various approaches to the design of negative-polarizability arrangements, including purely dielectric as well as metallic and hybrid nanoparticles. In particular, we find that plasmonic resonances allow for extremely high and spectrally tunable polarizabilities, leading to unique nonlinear light-matter interactions. Here, for the first time we were able to observe plasmonic resonant solitons over more than 25 diffraction lengths, in colloidal nanosuspensions.