Neste trabalho apresentamos a produção de moléculas frias heteronucleares em uma armadilha magneto-óptica mista de 39K e 85Rb e detectadas no estado fundamental. A técnica de detecção consiste na fotoionização pulsada das moléculas que, após terem sido fotoassociadas, decaem através de emissão espontânea para estados ligados do potencial do estado molecular fundamental. A partir dos resultados da produção de moléculas frias KRb, estudamos-as com relação ao tipo de colisões que as originam, e à temperatura associada ao seu movimento translacional. Experimentos foram também realizados para comprovar que as moléculas detectadas são provenientes do estado fundamental. Finalmente, também estudamos neste trabalho, a taxa segundo a qual são formadas. Concomitantemente à produção de KRb, moléculas frias homonucleares 39K2 e 85Rb2 são também formadas, detectadas e caracterizadas. São apresentados também, os primeiros passos dados em direção à realização de espectroscopia fotoassociativa dos estados ligados das moléculas heteronucleares obtidas. / In this work, cold ground-state KRb molecules were produced by photoassociation in a two species magneto-optical trap (MOT) containing 39K and 85Rb. The KRb molecules are produced through photoassociation and detected in the ground state by multiphoton pulsed ionization. We have characterized their translational temperature and measured their formation rate constant. Homonuclear cold molecules 39K2 and 85Rb2 detected in their ground state were also formed in our trap and characterized as well. It is also reported our first efforts towards the realization of photoassociation spectroscopy of the heteronuclear molecules produced in our trap.

Durant les 15 dernières années, le couplage fort lumière-matière avec des matériaux organiques a attiré un intérêt croissant, notamment à cause des valeurs extrêmes que peut atteindre l'écart énergétique entre les modes couplés dans ces systèmes. Ces modes couplés sont des hybrides lumière-matière, aussi appelés états polaritons et notés habituellement P+ et P-. La valeur de I' écart énergétique entre les modes couplés, également appelé énergie de Rabi-splitting, est provoqué par une transition efficace de dipôle moments entre des molécules et aussi par des cavités ou des plasmons en surface de petits volumes en mode de micro-Fabry-Pérot métalliques (FP) qui sont utilisés dans ces études. Rabi-splittings - 1eV représente souvent une fraction importante de l'énergie de transition électronique, dans ce cas, le système est appelé dans le régime de couplage ultra-forte. Dans ce régime, la physico-chimie des molécules ou des propriétés des matériaux du système couplé peuvent être modifié. En effet, d'effet a déjà été montré sur les voies de relaxation dans le système couplé, les taux de réactions photochimiques, le travail d'extraction et de la conductivité des semi-conducteurs organiques dans l'obscurité, entre autres choses. Une étude récente a pu montrer que l'énergie de l'état non-excité dans une étude thermodynamique peut également être décalée dans le régime de couplage ultra-fort. De plus, le couplage fort ne se limite pas à des transitions électroniques, mais peut aussi être utilisé pour perturber les vibrations de l'état non-excité de molécules dans la région infrarouge. Tous ces résultats montrent que le couplage fort en lumière-molécule a beaucoup de potentiel pour le matériel et la science moléculaire et mérite donc une étude plus approfondie. / Over the past 15 years, light-matter strong coupling involving organic materials has been of increasing interest due to the very large energy splitting such systems exhibit between the two hybrid light-matter states, also known as the polaritonic states typically denoted P+ and P-. The large energy splitting, so-called Rabi splitting, is the result of the high transition dipole moments of the molecules and the small mode volumes of micro-metallic Fabry-Pérot (FP) cavities or surface plasmons used in these studies. Rabi-splittings -1 eV have been observed, often representing a significant fraction of the electronic transition energy in which case the system is said to be in the ultra-strong coupling regime. ln this regime the physical chemistry of molecules or the properties of materials of the coupied system should be modified. lndeed, it has already been shown to affect the relaxation pathways in the coupled system, the rates of photochemical reactions, thework-function and conductivity of organic-semiconductors in the dark, among other things. A recent thermodynamic study demonstrated that the ground state energy can also be shifted in theultra-strong coupling regime. Moreover, the strong coupling is not limited to electronic transitions, but also can be used to perturb the ground-state vibrations of molecules in the infrared region. Ali these results suggest that light-molecule strong coupling has much potential for material and molecular science and therefore merits further study.

Title: A new method for the solution of the Schrödinger equation Author: Jakub Kocák Department: Department of Physical and Macromolecular Chemistry Supervisor: doc. RNDr. Filip Uhlík, Ph.D. Abstract: In this thesis we study method for the solution of time-independent Schrö- dinger equation for ground state. The wave function, interpreted as probability density, is represented by samples. In each iteration we applied approximant of imaginary time propagator. Acting of the operator is implemented by Monte Carlo simulation. Part of the thesis is dedicated to methods of energy calculation from samples of wave function: method based on estimation of value of wave function, method of convolution with heat kernel, method of averaged energy weighed by wave function and exponential de- cay method. The method for the solution was used to find ground state and energy for 6-dimensional harmonic oscillator, anharmonic 3-dimensional octic oscillator and hydrogen atom. Keywords: imaginary time propagation, Monte Carlo method, variational principle, ground state 1

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Made available in DSpace on 2016-06-02T20:27:38Z (GMT). No. of bitstreams: 1 3466.pdf: 565162 bytes, checksum: 770041f07c68eda588bd0c501dabe93d (MD5) Previous issue date: 2011-02-10 / Financiadora de Estudos e Projetos / In this work we analyze the existence of radially symmetric solutions, positive solutions as well as the existence of ground state solutions for a class of Klein-Gordon-Maxwell equations when the nonlinearity exhibits critical behavior. For the positive and ground state solutions we prove existence results when a potential V is introduced. In order to obtain such results, we use variational methods / Neste trabalho analisamos a existência de soluções radialmente simétricas, soluções positivas, bem como a existência de soluções ground state para uma classe de equações do tipo Klein-Gordon-Maxwell quando a não-linearidade exibe comportamento crítico. Para as soluções positivas e do tipo ground state provamos resultados de existência quando um potencial V é introduzido. A fim de obtermos tais resultados, usamos métodos variacionais.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-25T13:08:29Z No. of bitstreams: 1 arquivototal.pdf: 1324370 bytes, checksum: 6a689c99393e6b9a2a7f27c49ef07a8d (MD5) / Made available in DSpace on 2017-08-25T13:08:29Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1324370 bytes, checksum: 6a689c99393e6b9a2a7f27c49ef07a8d (MD5) Previous issue date: 2017-02-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In thisworkwestudytheexistenceofgroundstatesforthefollowingclassofcoupled systems involvingnonlinearSchrödingerequations 8<: 􀀀 u + V1(x)u = f1(x; u) + (x)v;x 2 RN; 􀀀 v + V2(x)v = f2(x; v) + (x)u; x 2 RN; where thepotentials V1 : RN ! R, V2 : RN ! R are nonnegativeandrelatedwith the couplingterm : RN ! R by j (x)j < pV1(x)V2(x), forsome 0 < < 1. In the case N = 2, thenonlinearities f1 e f2 havecriticalexponentialgrowthinthesense of Trudinger-Moserinequality.Inthecase N 3, thenonlinearitiesarepolynomials with subcriticalandcriticalexponentintheSobolevsense.Westudyalsothefollowing class ofnonlocalcoupledsystems 8<: (􀀀 )1=2u + V1(x)u = f1(u) + (x)v;x 2 R; (􀀀 )1=2v + V2(x)v = f2(v) + (x)u; x 2 R; where (􀀀 )1=2 denotes thesquarerootoftheLaplacianoperatorandthenonlinearities havecriticalexponentialgrowth.Ourapproachisvariationalandbasedon minimization techniqueovertheNeharimanifold / Neste trabalhoestudamosaexistênciadegroundstatesparaaseguinteclassede sistemas acopladosenvolvendoequaçõesdeSchrödingernão-lineares 8<: 􀀀 u + V1(x)u = f1(x; u) + (x)v;x 2 RN; 􀀀 v + V2(x)v = f2(x; v) + (x)u; x 2 RN; onde ospotenciais V1 : RN ! R, V2 : RN ! R são não-negativoseestãorelacionados com otermodeacomplamento : RN ! R por j (x)j < pV1(x)V2(x), paraalgum 0 < < 1. Nocaso N = 2, asnão-linearidades f1 e f2 possuemcrescimentocrítico exponencialnosentidodadesigualdadedeTrudinger-Moser.Nocaso N 3, asnão- linearidades sãopolinômioscomexpoentesubcríticoecríticonosentidodeSobolev. Estudamos aindaaseguinteclassedesistemasacopladosnão-locais 8<: (􀀀 )1=2u + V1(x)u = f1(u) + (x)v;x 2 R; (􀀀 )1=2v + V2(x)v = f2(v) + (x)u; x 2 R; onde (􀀀 )1=2 denota ooperadorraízquadradadolaplacianoeasnão-linearidades possuemcrescimentocríticoexponencial.Nossaabordagemévariacionalebaseadana técnica deminimizaçãosobreavariedadedeNehari.

Since the last few decades frustrated spin systems have attracted much interest. These studies are motivated by the rich variety of their unusual magnetic properties and potential applications. In this thesis, excitation spectra of the weakly coupled dimer system Ba3Cr2O8, the spin-1/2 chain material with distorted diamond structure Cu3(CO3)2(OH)2 (natural mineral azurite), and the quasi-twodimensional antiferromagnet with triangle spin structure Cs2CuBr4 have been studied by means of high-field electron spin resonance. Two pairs of gapped modes corresponding to transitions from a spin-singlet ground state to the first excited triplet state with zero-field energy gaps, of 19.1 and 27 K were observed in Ba3Cr2O8. The observation of ground-state excitations clearly indicates the presence of a non-secular term allowing these transitions. Our findings are of crucial importance for the interpretation of the field-induced transitions in this material (with critical fields Hc1 = 12.5 T and Hc2 = 23.6 T) in terms of the magnon Bose-Einstein condensation. The natural mineral azurite, Cu3(CO3)2(OH)2, has been studied in magnetic fields up to 50 T, revealing several modes not observed previously. Based on the obtained data, all three critical fields were identified. A substantial zero-field energy gap, Δ = 9.6 K, has been observed in Cs2CuBr4 above the ordering temperature. It is argued that contrary to the case for the isostructural Cs2CuCl4, the size of the gap can not be explained solely by the uniform Dzyaloshinskii-Moriya interaction, but it is rather the result of the geometrical frustration stabilizing the spin-disordered state in Cs2CuBr4 in the close vicinity of the quantum phase transition between a spiral magnetically ordered state and a 2D quantum spin liquid.

Les molécules aromatiques protonées jouent un rôle important dans les réactions de substitution électrophile aromatique, et dans différents processus biologiques. Ces molécules sont présentes aussi dans d’autres milieux tels que les flammes de combustion, les plasmas de divers hydrocarbures, les ionosphères planétaires (Titan) et le milieu interstellaire. Les molécules protonées sont très stables car elles ont des couches électroniques complètes mais elles sont en général très sensibles à leur environnement local car elles sont chargées : une étude en phase gazeuse est nécessaire pour déterminer leurs propriétés intrinsèques. Jusqu’à présent, très peu de chose était connu sur les molécules protonées isolées en phase gazeuse, seulement quelques résultats étaient disponibles. Ce manque de données venait de la difficulté de générer des molécules protonées en phase gazeuse et surtout de les produire à basse température (la protonation est une réaction exothermique). Récemment, des progrès ont permis d’étudier les molécules protonées en phase gazeuse à très basse température, en particulier par le développement des sources ioniques couplées avec des techniques d'expansion de jet supersonique. Grâce à cette technique on a enregistré le spectre photo fragmentation de l’état fondamental vers le premier état excité (S1←S0) de différentes molécules aromatiques protonées en phase gazeuse. Les molécules que nous avons étudiées peuvent être regroupées en quatre familles : Les molécules polycycliques aromatiques protonées linéaires (benzène, naphtalène, anthracène, tétracène, pentacène). Les molécules polycycliques aromatiques protonées non linéaires (fluorène, phénanthrène, pyrène). Les molécules protonées contenant un hétéro atome (benzaldéhyde, salicylaldéhyde, 1-naphthol et 2-naphthol, indole, aniline). Les agrégats protonés (dimère de benzène, naphtalène (H2O)n, n=1,2,3. naphtalène (NH3)n, n=1,2,3, benzaldéhyde (Ar , N2)). Dans les spectres enregistrés presque toutes les transitions électroniques S1←S0 sont décalées vers le rouge (basse énergie) par rapport à celui des molécules parentes neutres. Ce décalage est dû au caractère transfert de charge du premier état excité. Certains spectres sont résolus vibrationnellement, alors que pour d'autres molécules le spectre ne présente pas de progression vibrationnelle à cause d’un dynamique très rapide de l’état excité menant par des intersections coniques à l’état fondamental. Les spectres d’absorption des molécules protonées sont plus riches en vibrations par comparaison avec les molécules neutre. Cela reflète le changement relativement important de géométrie de l’état excité dû à son caractère transfert de charge. Les résultats expérimentaux ont été complétés par des calculs ab-initio qui ont permis de localiser la transition électronique, déterminer la structure géométrique et électronique, les modes de vibration et, pour certaines de ces molécules, la dynamique de l’état excité. Les calculs sont en général en très bon accord avec les expériences. / Protonated aromatic molecules play an important role in electrophilic aromatic substitution reactions, fundamental reactions in organic chemistry and in various biological processes. The interstellar medium is another environment which is likely to contain the protonated aromatic molecules, that’s because these molecules are stable chemically since they are close shell electronic structure. These molecules were also identified in others environments such as combustion flames, plasmas of various hydrocarbons and the upper atmosphere of Titan. Protonated molecules are usually very sensitive to their local environment; a gas phase study is required to determine their intrinsic properties. Until now, very little is known about the isolated protonated molecules, only a few results are available in the literature. This lack of data is due to the difficulties of the production and the cooling of these molecules in gas phase. The technical progress we have done has enabled the study of protonated molecules in the gas phase at very low temperatures, using an ion sources, supersonic jet and the laser induced photofragmentation techniques. Using this technique, we have recorded many electronic spectra (S1←S0) of different protonated molecules. We can regroup the studied molecules into four: Linear protonated polycyclic aromatic molecules (benzene, naphthalene, anthracene, tetracene, pentacene). Nonlinear protonated polycyclic aromatic molecules (fluorene, phenanthrene, pyrene). Protonated molecules containing an hetero atom (benzaldehyde, salicylaldehyde, 1-naphthol and 2-naphthol, indole, aniline). Protonated cluster (dimer of benzene, naphthalene (H2O)n, n = 1,2,3. Naphthalene (NH3)n, n = 1,2,3, benzaldehyde (Ar, N2)). Most of those spectra are red-shifted compare to the spectrums of neutral parent molecules. This red-shift is due to charge transfer character of the first excited state. Some spectra are vibrationally resolved, while for other molecules the spectrum do not shows any vibrational progression. This behaviour is explained by the dynamic of the excited state, this dynamic being usually is very fast, sometimes leading to the ground state through a conical intersection. The spectra of protonated molecules are very active vibrationally in comparison with neutral molecules, many vibrational modes forbidden for neutral molecule becomes active for the protonated one (Franck-Condon factor is not zero). This is reflecting the charge transfer character of the excited state. The experimental results were complemented by ab-initio calculations, which have allowed determining the electronic transition, the geometric and electronic structure of the molecule, the vibrational modes, and for some of these molecules the dynamics of excited state. Calculations are generally in very good agreement with experiments.

The ability of physics to provide an understanding of our Universe lies in the essential interrelation between experiment and theory. But physics does not provide us only reliable representations of the causes acting in nature. Its powerful experimental devices and theoretical methods are the underlying reason of the explosive technological development of our time. LiNbO3 and LiTaO3 represent only one example of the essential impact of both experimental and theoretical investigations on their technological applications. Particularly, LiNbO3 has been the subject of many experimental studies due to its applications in electro-optic and integrated optical devices. Also, the doped LiNbO3 with rare-earth and transition metals could be used, for instance, as a material for tunable lasers. The previous theoretical studies devoted to LiNbO3 and LiTaO3 focused on their electronic structure, being an attempt to understand the microscopic origin of the paraelectric-to-ferroelectric phase transition of these materials. The ab initio lattice dynamics investigations performed so far were mainly aimed to identify the role of the individual atoms vibrations in the energetic of the phase transition. The lack of a reliable model for the zone-center lattice dynamics in these compounds motivated us to investigate this issue by means of ab initio frozen-phonon calculations. On the background of the obtained phonon frequencies and eigenvectors, we unambiguously identified all zone-center modes for LiNbO3 and the A1 ones for LiTaO3. Due to the above mentioned enlargement of the technological applications of LiNbO3 by doping with various ions, we focused on the analysis of the ground-state properties of this material when doped with Fe and Cr. Even if the theoretical approach used in our calculations is not predictive with respect to the optical properties of the physical systems in study, a certain insight on this problem could be gained from the analysis of the effect of the atomic positions relaxation on the impurities energy levels localized in the optical band gap.