Nesta tese de doutorado apresentamos os resultados de quatro tópicos referentes a estudos de propriedades elétricas que são interpretados com o auxílio da Teoria Quântica de Átomos em Moléculas (QTAIM). No primeiro deles, foram calculados momentos de dipolo e suas derivadas através de um novo formalismo de divisão de átomos em moléculas, baseado em campos de forças de Ehrenfest (CFE), sendo que estes dados são comparados com aqueles advindos da QTAIM. Desta forma, um modelo alternativo de partição em carga - fluxo de carga - fluxo de dipolo (CFCFD) é discutido para derivadas do momento dipolar. Os resultados gerais obtidos pelo formalismo CFE foram satisfatórios em termos quantitativos, embora QTAIM ainda fornece uma descrição mais apropriada destes fenômenos das polarizações atômicas e de suas variações durante vibrações. Na sequência, investigamos os Atratores Não Nucleares (NNAs), que são identificados através de uma análise QTAIM da densidade eletrônica. O nosso intuito foi descobrir novas moléculas que apresentam essa peculiaridade, bem como encontrar padrões entre os casos encontrados que permitam contribuir para o entendimento dos fatores que levam ao seu aparecimento. Para isso trabalhamos com moléculas diatômicas homonucleares de elementos representativos com números atômicos que variavam de Z=1 até Z=38 e moléculas heteronucleares formadas pela combinação dos mesmos. Os nossos dados mostram que NNAs podem ser encontrados em alguns pontos dentro da faixa de distâncias internucleares investigada para quase todos os sistemas diatômicos homonucleares, exceto para as moléculas de Hidrogênio, Hélio e Estrôncio. Por sua vez, encontramos trinta casos de NNAs em sistemas heteronucleares, muitos dos quais ainda inéditos na literatura. Descobrimos também que a polarizabilidade atômica aparentemente tem um papel importante na explicação dos casos encontrados. Tratamos também de moléculas contendo interações fracas como as de Van der Waals (moléculas tri-atômicas contendo um gás nobre ligado a um composto diatômico iônico) de modo a investigar os valores de dipolos atômicos QTAIM de uma maneira mais direta, ou seja, via comparação com um modelo simples para estes compostos. Por fim, estudamos moléculas em estados excitados, sendo que nossa análise focou em dois casos peculiares (CO e de CF2N2) que apresentam momento de dipolo nulo no estado fundamental, enquanto valores significativos desta propriedade são observados em seus primeiros estados excitados. Desta forma, QTAIM foi fundamental para compreender como o processo de excitação pode levar à mudanças tão significativas em tais propriedades elétricas. / In this PhD thesis we present the results of four different topics that refer to a study of electric properties interpreted with The Quantum Theory of Atoms and Molecules (QTAIM). First, dipole moments and their derivatives were calculated from a new formalism based on Ehrenfest Force Fields (EFF) and a comparison with data from QTAIM is carried out. Therefore, the Charge-Charge Flux-Dipole Flux (CCFDF) model was discussed for the dipole moment derivatives. The results from EFF were satisfactory in quantitative terms although QTAIM still seems to be better for the description of atomic polarization and its variations during vibrations. In the sequence, we investigated the Non-Nuclear Attractors (NNAs) that could be identified with the QTAIM formalism. Our intention was to discover new molecules that present this peculiarity, as well as to find trends among these cases that allow contributing for the understanding of the factors that lead to their appearance. For this purpose, we selected homonuclear diatomic molecules of elements presenting atomic numbers ranging from Z=1 to Z=38 and heteronuclear diatomic molecules containing these same elements. Our data shows that NNAs could be found in almost every homonuclear molecule expect by the systems formed by Hydrogen, Helium, and Strontium. On other hand, we have found 30 cases of NNAs in heteronuclear molecules, many of them seen for the first time. We also have noticed that the atomic polarizabilities play a main role in the understanding of these cases. We also treated molecules containing weak Van der Waals interactions (triatomic complexes presenting a noble gas bonded to a diatomic ionic molecule) in order to investigate the atomic dipole values obtained with QTAIM in a direct way, that is, by means of a comparison using a simple model for this kind of bonding. Finally, we studied molecules in excited states. Our focus was in two peculiar cases (CO and CF2N2), which present null dipole moments in their ground states but exhibit significant dipole moment values in their first excited states. Therefore, QTAIM was fundamental to understand how the excitation process can lead to important changes in electric properties.

Nesta tese, utilizamos técnicas de química quântica para o estudo de sistemas contendo átomos de silício e nitrogênio. Nesse contexto, o trabalho aqui apresentado procurou concentrar-se em três tópicos principais: aglomerados de silício e nitrogênio, a superfície Si(100) e a interação de um átomo de nitrogênio com essa superfície. Estudamos inicialmente os aglomerados de fórmula SiNN e Si3N2, onde procuramos caracterizar de forma rigorosa a estabilidade e a natureza das ligações químicas das várias espécies. Com relação ao sistema SiNN, os resultados utilizando cálculos de alto nível mostraram a necessidade de novos dados experimentais para a caracterização inequívoca dessa espécie. Além disso, obtivemos os primeiros resultados para as propriedades de quatro novas estruturas. Estudamos a estrutura de várias espécies com fórmula Si3N2, e obtivemos como mínimo global uma estrutura planar contendo apenas ligações Si-N. Para a simulação da superfície Si(100) utilizamos os aglomerados de fórmula Si9H12 e Si15H16. Apenas a metodologia do Funcional da Densidade indicou a existência de uma estrutura distorcida para o Si9H12. Os cálculos CASSCF mostraram a necessidade do uso de funções multideterminantais. Com relação ao aglomerado Si15H16, obteve-se uma estrutura distorcida com os dímeros alternados como a forma mais estável. Entretanto, o uso do CASSCF mostrou ser a forma simétrica a mais estável. Com base no estudo dos aglomerados Si9H12 e Si15H16, partimos para a investigação dos mecanismos envolvidos no processo de interação e incorporação de átomos de nitrogênio na superfície de silício. Estruturas com simetria de spin quarteto e dupleto foram estudadas, sendo os mecanismos bastante semelhantes, com o nitrogênio interagindo inicialmente com um dos silícios dímeros para em seguida poder formar duas outras estruturas, uma com o nitrogênio ligado aos dois silícios dímeros e outra com o nitrogênio inserido no interior do aglomerado. Esta última estrutura corresponde à forma mais estável. Os resultados mostram claramente que a reação é bastante favorável do ponto de vista energético. Questionamos também o uso de vínculos durante a otimização das estruturas por impedir um devido relaxamento apropriado dos átomos de silício da primeira e segunda camadas. / In this thesis, quantum chemical techniques were used to study molecular systems containing silicon and nitrogen atoms. ln this context, the work was concentrated on three main topics: silicon-nitrogen clusters, the Si(100) surface, and the interaction of a nitrogen atom with that surface. We studied initially the clusters SiNN and Si3N2, where we tried to characterize with rigour the stability and the nature of the chemical bonds of the various species. Concerning the system SiNN, using high level calculation, the results showed the necessity of new experimental data for the unequivocal characterization of this species. Moreover, the properties of four new structures were described for the first time in this study. The structures of various species with formula Si3N2 were studied, and the global minimum corresponds to a planar structure containing only Si-N bonds. For the simulation of Si(100) surface, the clusters Si9H12 and Si15H16 were used. Density Functional Theory predicted the existence of an asymmetric geometry for the Si9H12 cluster. The CASSCF calculations showed the necessity of using multideterminantal wave functions. Concerning the Si15H16 cluster, the most stable structure corresponds to a distorted one with alternated dimers. However, the CASSCF methodology showed that the symmetric structure is the most stable. Based on the results for the Si9H12 and Si15H16 clusters, we started to investigate the mechanism involved in the interaction and incorporation of a nitrogen atom into the silicon surface. Structures with quartet and doublet spin symmetry were studied, being their mechanisms very similar, with the nitrogen atom interacting initially with one silicon dimer; after that two other structures can be formed, one with the nitrogen bonded to two silicon dimers, and the other with the nitrogen bonded to one silicon dimer and two internal silicons. This last structure corresponds to the most stable species. The results show clearly that the reaction is very favorable energetically. The use of geometrical constraints during the optimization was questioned since it prevents the proper relaxation of the silicon atoms in the first and second layers.

Les gaz d'atomes ultrafroids offrent des possibilités sans précédent pour la réalisation et la manipulation des systèmes quantiques. Le contrôle exercé sur les interactions entre particules permet d'atteindre le régime de fortes interactions, pour des espèces d'atomes à la fois fermioniques et bosoniques. Dans la limite unitaire, où la force d'interaction est à son maximum, des propriétés universelles émergent. Pour les atomes bosoniques, celles-ci comprennent l'effet Efimov, l'existance surprenante d'une séquence infinie d'états liés à trois corps. Dans cette thèse, nous avons étudiés un système de bosons unitaires. Partant des cas à deux et à trois corps, nous avons montrés que le modèle choisi capturait correctement les caractéristiques universelles de l'effet Efimov. Pour le modèle à N-corps, nous avons développé un algorithme de Monte Carlo quantique capable de réaliser les différentes phases thermodynamiques du système : gaz normal à haute-température, condensat de Bose-Einstein, et liquide d'Efimov. Un unique composant de notre modèle resterait pertinent à la limite de température infinie, à savoir la répulsion corps dur à trois corps, qui constitue une généralisation du potentiel classique entre sphères dures. Pour ce modèle, nous avons proposé une solution au problème d'empilement compact en deux et trois dimensions, fondée sur une Ansatz analytique et sur la technique de recuit simulé. En étendant ces résultats à une situation de pression finie, nous avons montré que le système présente une transition de fusion discontinue, que nous avons identifié à travers la méthode de Monte Carlo. / Ultracold atomic gases offer unprecedented possibilities to realize and manipulate quantum systems. The control on interparticle interactions allows to reach the strongly-interacting regime, with both fermionic and bosonic atomic species. In the unitary limit, where the interaction strength is at its maximum, universal properties emerge. For bosonic atoms, these include the Efimov effect, the surprising existence of an infinite sequence of three-body bound states. In this thesis, we have studied a system of unitary bosons. Starting from the two- and three-body cases, we have shown that the chosen model correctly captures the universal features of the Efimov effect. For the corresponding many-body problem, we have developed a quantum Monte Carlo algorithm capable of realizing the different thermodynamic phases in which the system may exist: The high-temperature normal gas, Bose-Einstein condensate, and Efimov liquid. A single ingredient of our model would remain relevant in the infinite-temperature limit, namely the three-body hard-core repulsion, which constitutes a generalization of the classical hard-sphere potential. For this model, we have proposed a solution to the two- and three-dimensional packing problem, based on an analytical ansatz and on the simulated-annealing technique. Extending these results to finite pressure showed that the system has a discontinuous melting transition, which we identified through the Monte Carlo method.

Produire et faire interagir entre eux des photons optiques de façon contrôlée sont deux conditions nécessaires au développement de communications quantiques à longue distance, et plus généralement au traitement quantique d’information codée sur des photons. Cette thèse présente une étude expérimentale de solutions possibles a ces deux problèmes, en utilisant la conversion des photons en excitations collectives (polaritons) dans un nuage d’atomes froids, placé dans le mode d’une cavité optique de faible finesse (~100). Dans un premier temps, des polaritons entre états atomiques fondamentaux sont utilisés pour « mettre en mémoire » une excitation unique dans le nuage. Celle-ci est ensuite convertie efficacement en un photon unique, dont le champ est analysé par tomographie homodyne. La fonction de Wigner de l’état à un photon est reconstruite a partir des données expérimentales, et présente des valeurs négatives, démontrant que les degrés de liberté de ce photon (mode spatio-temporel et état quantique) sont complètement contrôlés. Dans un second temps, les photons sont couplés à des polaritons impliquant des états de Rydberg. Les fortes interactions dipolaires entre ces derniers se traduisent par des non-linéarités optiques dispersives très importantes, qui sont caractérisées dans un régime d’excitation classique. Ces non-linéarités peuvent être amplifiées jusqu’à ce qu’un seul photon suffise à modifier totalement la réponse du système, permettant en principe de générer des interactions effectives entre photons. / Controllably producing optical photons and making them interact are two key requirements for the development of long-distance quantum communications, and more generally for photonic quantum information processing. This thesis presents experimental studies on possible solutions to these two problems, using the conversion of the photons into collective excitations (polaritons) in a cold atomic cloud, inside the mode of a low-finesse optical cavity (~100). Firstly, ground-state polaritons are used to store a single excitation in the cloud memory. This polariton is then efficiently converted into a single photon, whose field is characterized via homodyne tomography. The single photon state’s Wigner function is reconstructed from the experimental data and exhibits negative values, demonstrating that the photon’s degrees of freedom (spatio-temporal mode and quantum state) are well controlled. Secondly, photons can be coupled to polaritons involving Rydberg states. The strong dipolar interactions between these give rise to very strong optical dispersive nonlinearities, that are characterized in a classical excitation regime. These nonlinearities can be amplified until a single photon is enough to modify the entire system’s response, allowing in principle for the generation of effective photon-photon interactions.

La plupart des objets quantiques individuels développés jusqu’à aujourd’hui ne permettent pas de satisfaire toutes les conditions nécessaires pour la construction d’un simulateur quantique. Une possibilité pour obtenir un système quantique robuste est de combiner plusieurs de ces approches. Dans cette thèse, nous décrivons les résultats obtenus sur deux systèmes expérimentaux développés dans ce but.La première partie de cette thèse décrit un système hybride d’atomes neutres couplés à des qubits supraconducteurs, en construction à l’Université du Maryland. La solution envisagée pour placer un ensemble d’atomes froids à proximité de la surface supraconductrice est de piéger les atomes dans le champ évanescent se propageant autour d’une fibre optique nanométrique. Nous avons développé un dispositif permettant la production de fibres optiques nanométriques de transmission optique supérieure à 99.95% dans le mode fondamental. Nous avons également optimisé la transmission de quelques modes d’ordres supérieurs, ce qui pourra s’avérer utile pour le piégeage d’atomes.La seconde partie de cette thèse décrit un système développé à l’Institut d’Optique et comprenant des atomes neutres piégés dans des matrices de pinces optiques. Dans ce cas, nous excitons les atomes dans des états de Rydberg afin de bénéficier de fortes interactions interatomiques. Nous avons caractérisé les interactions de van der Waals et les interactions résonantes entre deux atomes individuels, et démontré le caractère cohérent de l’interaction dipolaire. Nous avons enfin simulé la dynamique d’une chaine élémentaire de spins dans une matrice de trois atomes / Most platforms that are being developed to build quantum simulators do not satisfy simultaneously all the requirements necessary to implement useful quantum tasks. Robust systems can be constructed by combining the strengths of multiple approaches while hopefully compensating for their weaknesses. This thesis reports on the progress made on two different setups that are being developed toward this goal.The first part of this thesis focuses on a hybrid system of neutral atoms coupled to superconducting qubits that is under construction at the University of Maryland. Sub-wavelength diameter optical fibers allow confining an ensemble of cold atoms in the evanescent field surrounding the fiber, which makes them ideal for placing atoms near a superconducting surface. We have developed a tapered fiber fabrication apparatus, and measured an optical transmission in excess of 99.95% for the fundamental mode. We have also optimized tapered fibers that can support higher-order optical modes with high transmission, which may be useful for various optical potential geometries.The second part of this thesis focuses on a system of neutral atoms trapped in arrays of optical tweezers that has been developed at the Institut d’Optique. Placing the atoms in highly excited Rydberg states allows us to obtain strong interatomic interactions. Using two individual atoms, we have characterized the pairwise interactions in the van der Waals and resonant dipole-dipole interaction regimes, providing a direct observation of the coherent nature of the interaction. In a three-atom system, we have finally simulated the dynamics of an elementary spin chain

Cette thèse de doctorat a été réalisée au sein du III-VLab, en partenariat avec l’Institut d’Electronique du Sud (IES). L’objectif de ce travail de thèse vise d’une part à l’optimisation des performances des diodes laser DFB émettant à 780 nm et le développement d’une source plus compacte (MOPA) à 780nm, intégrant de façon monolithique l’oscillateur maître (laser à rétro-action répartie ou DFB) et l’amplificateur de puissance, et d’autre part, à appréhender les phénomènes de bruit, permettant d’évaluer la qualité technologique des lasers. Les développements autour de la longueur d’onde 780 nm, se sont organisés en plusieurs thématiques : les lasers Fabry-Perot et DFB, les amplificateurs (SOA), les MOPA et l’étude du bruit des lasers. Nous avons étudié des structures de différentes épaisseurs de puits quantiques (160Å, 135 Å et 145 Å). La comparaison des performances globales des différentes structures de lasers larges, loin d’être évidente, nous a permis de choisir celle intégrant un puits quantique de 160 Å, pour la réalisation des lasers Fabry-Perot à ruban étroit (3µm à 4µm). Nous avons obtenu sur des lasers larges, de 3 mm de long, bruts de clivage, une puissance d’environ 5 watts par face pour un courant d’injection continu autour de 10 A. Les simulations et caractérisations électro-optiques menées sur des lasers ridge Fabry-Perot, ont servi à affiner le dessin des DFB à 780 nm, par rapport aux briques de base existantes du III-V Lab, et à proposer des structures à cavités optiques larges et super-large (LOC et SLOC) optimisées, en termes de puissance, qualités de faisceau et spectrale.Les mesures de bruits, appuyées d’un modèle de bruit électrique, ont permis d’extraire une valeur du paramètre de Hooge de 2,1.10^-3 pour les lasers ridge, en accord avec la littérature, et qui correspond à une bonne qualité de matériau et technologique des lasers. Différents types d’amplificateurs optiques évasés ont été dessinés, réalisés et caractérisés. Les caractérisations des diverses géométries de SOA, ont donné dans l’ensemble, des valeurs de gain comprises entre 19dB et 25dB. Nous avons obtenu respectivement pour les structures d’amplificateurs à guidages entièrement par l’indice (GI), entièrement par le gain (GG) et mixte (GM), des puissances de 500mW, 750mW et 1W. L’ensemble des résultats obtenus avec ces structures sont prometteurs pour l’intégration monolithique avec le DFB. En ce qui concerne le MOPA, trois approches ont été étudiées: MOPA droit, DFB et amplificateur tiltés de 7° (par rapport à la normale aux faces clivées), et la plus prometteuse mais plus complexe, intégrant le DFB droit et l’amplificateur tilté de 7°, avec une section courbe entre les deux. La prise en compte de l’ensemble des résultats lasers Fabry-Perot, DFB et des résultats d’amplificateurs, nous ont permis de proposer des dessins MOPA originaux. Le dessin du masque réalisé, intègre toutes ces configurations de MOPA, et en plus, des SOA et DFB, qui seront utilisés comme témoins de test lors des caractérisations. / This thesis has been realized in III-VLab in collaboration with the South Electronic Institute in Montpellier. The aim of this work focuses in one hand, on the performance improvement of DFB's diode lasers emitting at 780 nm, and the advanced design of a compact semiconductor laser diode (Master Oscillator Power Amplifier), integrating monolithically the master oscillator (DFB for Distributed Feedback laser); in the other hand, using the noise phenomenon’s studies as a tool, for validating of our laser technologies. The Developments round the 780 nm wavelength, have been divided into different thematic: Fabry-Perot and DFB, Semiconductor Optical Amplifiers (SOA), MOPA, and the lasers noise’s study. We have studied structures with different quantum well thickness (160Å, 135 Å and 145 Å). The comparison of global performances of broad area lasers from these different structures, far to being obvious, allowed us to choose the one that integrates the 160-Å-thickness of quantum-well, for the realization of ridge Fabry-Perot lasers of 3 to 4-µm-of width. We obtained with broad area lasers, as cleaved, with 3-mm cavity lengths, an output power around 5 watts per facet, in continuous bias current around 10 AModellings and electro-optics characterizations performed on ridge Fabry-Perot lasers, allowed to refine DFB lasers at 780 nm, in comparison of the existing building blocks in the lab; we proposed new optimized structures with Large and Super Large Optical Cavities(LOC and SLOC), in terms of optical output power, beam and spectral qualities.The noise measurements with electrical noise modelling, allowed us to extract a value of Hooge’s parameter of 2,1.10^-3, quite in agreement with literature for such lasers, which corresponds to a good material quality and laser technology.Different types of flared SOA have been designed, realized and characterized. The characterizations of various SOA geometries, have given in general, values of gain between 19 dB to 25 dB. With SOAs of types: fully Index Guiding (IG), fully Gain Guiding (GG) and Mixed Guiding (MG), we have respectively obtained 500 mW, 750 mW and 1 W. All the results obtained with these structures are promising for monolithic integration with DFB. Regarding the MOPA, three approaches have been studied. The straight MOPA, the approach of SOA and DFB with 7° tilt(relative to the normal to cleaved facets), and the most complex, but promising approach, integrating the SOA with 7° tilt, and straight DFB, with a bend section between them. By taking into account all the results obtained on Fabry-Perot lasers, DFB, and SOA results, we were able to propose original MOPA designs. The layout drawing has been realized, all the MOPA configurations and additional, DFB and SOA devices, have been included on it. They will be used as test structures for characterizations.

Ce travail vise à contribuer à l’amélioration de notre connaissance de l’électrodynamique quantique des états liés, par des mesures de haute précision dans des états exotiques de la matière. Bien que notre connaissance de l’électrodynamique quantique des états liés et du problème relativiste à plusieurs corps aient fait des progrès importants ces dernières années, il reste des questions fondamentales dont la résolution nécessite d’augmenter le nombre et la précision des tests expérimentaux. La première partie de ce travail a été réalisée dans le cadre de l’expérience récente sur les ions muoniques d’hélium (μ4He+ et μ3He+) conduite par la collaboration CREMA. Cette expérience vise à fournir de nouvelles valeurs précises pour les rayons de charge moyens des noyaux des isotopes stables de l’hélium. Ces valeurs sont extraites de la mesure du déplacement de Lamb, c’est-à-dire, de la mesure de la différence d’énergie entre les États 2S − 2P. Une mesure des énergies de transition d’une précision d’au moins 50 ppm, permet de déterminer les rayons de charge des noyaux des isotopes d’hélium avec une incertitude de 0,03%, dix fois plus précise que les résultats précédents obtenus à partir de la diffusion d’électrons. La deuxième partie de ce travail a été de réaliser des mesures de haute précision de transitions de rayons X dans des ions fortement chargés, à l’aide d’un spectromètre à double cristal plan. Ces ions étaient produits dans le plasma d’une source d’ions de type ECRIS (electron-cyclotron resonance ion source). Le spectromètre utilisé est non seulement capable de fournir des mesures de haute précision, mais aussi des mesures sans référence à des énergies de transition théorique ou expérimentales. Quatre énergies de transition de n = 2 → n = 1 ont été mesurées pour des ions d’argon de trois états de charge différents, héliumoïde, lithiumoïde et berylliumoïde, avec une précision meilleure que 3 ppm. La largeur naturelle de chaque raie a également été obtenue expérimentalement. Les résultats trouvés sont en excellent accord avec les calculs théoriques les plus récents. / This work aims to provide insight on Bound-State Quantum-Electrodynamics (BSQED) by experimental fundamentals high-precision tests in exotic states of matter. Although BSQED and the relativistic many-body problem have been undergoing important progress, there are still some issues that require the increase of the number and accuracy of experimental fundamental tests. The first part of this work was done within the framework of the recent experiment in muonic helium ions (μ4He+ and μ3He+) by the CREMA collaboration. This experiment, aims to provide new accurate values for the root-mean-square (rms) charge radii of the helium isotopes nuclei that are extracted from the measurement of the Lamb Shift, i.e., the measurement of the energy difference between the 2S − 2P states. With the goal of measuring the transition energies with an accuracy of at least 50 ppm, the rms charge radii of the helium isotopes will be determined with an uncertainty of 0.03%, a factor of ten more precise than previous results obtained from electron scattering. The second part of this work aims the high-precision measurement of x-ray transitions in Highly-Charged Ions (HCI) using a Double-Crystal Spectrometer (DCS). These ions were produced in the plasma of an Electron-Cyclotron Resonance Ion Source (ECRIS). This kind of spectrometer is able not only to provide high-precision measurements but also reference-free measurements, without reference to any theoretical or experimental energy. Four transitions energies from n = 2 → n = 1 have been measured in an argon plasma in three different charge states, He-, Be- and Li-like, with an accuracy of better than 3 ppm. Besides the energies, the natural width of each transition has also been experimentally obtained. The obtained results are in excellent agreement with the most recent theoretical calculations.

En la literatura sobre mecànica quàntica és freqüent trobar descriptors basats en la densitat de parells o la densitat electrònica, amb un èxit divers segons les aplicacions que atenyin. Per tal de que tingui sentit químic un descriptor ha de donar la definició d'un àtom en una molècula, o ésser capaç d'identificar regions de l'espai molecular associades amb algun concepte químic (com pot ser un parell solitari o zona d'enllaç, entre d'altres). En aquesta línia, s'han proposat diversos esquemes de partició: la teoria d'àtoms en molècules (AIM), la funció de localització electrònica (ELF), les cel·les de Voroni, els àtoms de Hirshfeld, els àtoms difusos, etc.L'objectiu d'aquesta tesi és explorar descriptors de la densitat basats en particions de l'espai molecular del tipus AIM, ELF o àtoms difusos, analitzar els descriptors existents amb diferents nivells de teoria, proposar nous descriptors d'aromaticitat, així com estudiar l'habilitat de totes aquestes eines per discernir entre diferents mecanismes de reacció. / In the literature, several electronic descriptors based in the pair density or the density have been proposed with more or less success in their pratical applications. In order to be chemically meaningful the descriptor must give a definition of an "atom" in a molecule, or instead be able to identify some chemical interesting regions (such as lone pair, bonding region, among others). In this line, several molecular partition schemes have been put forward: atoms in molecules (AIM), electron localization function (ELF), Voronoi cells, Hirshfeld atoms, fuzzy atoms, etc. The goal of this thesis is to explore the density descriptors based on the molecular partitions of AIM, ELF and fuzzy atom, analyze the existing decriptors at several levels of theory, propose new aromaticity descriptors, and study its ability to discern between different mechanisms of reaction.

Extensive theoretical studies on the ground and excited state properties of systems containing heavy atoms have shown that accurate prediction of transition energies and related properties requires the incorporation of both relativistic and higher order correlation and relaxation effects as these effects are strongly inter- wined. The relativistic and dynamical electron correlation effects can be incor- porated in many-electron systems through a variety of many-body methods like configuration interaction (CI), coupled cluster method (CCM) etc. which are very powerful and effective tool for high precision description of electron correlation in many-electron systems. In this thesis, we investigate the relativistic and correlation effects in heavy atomic and molecular systems using these two highly correlated many-body methods. It is well recognized that, heavy polar diatomic molecules such as BaF, YbF, TlF, PbO, etc. are the leading experimental candidates for the search of violation of Parity (P ) and Time-reversal (T ) symmetry. The experimental detection of such P,T-odd effects in atoms and molecules has important consequences for the theory of fundamental interactions or for physics beyond the standard model (SM). For instance, a series of experiments on TlF have already been reported which provide the tightest limit available on the tensor coupling constant C , proton electric dipole moment (EDM) dp , etc. Experiments on YbF and BaF molecules are also of fundamental significance to the study of symmetry violation in nature, as these experiments have the potential to detect effects due to the electron EDMde. It is therefore imperative that high precession calculations are necessary to interpret these ongoing (and perhaps forthcoming) experimental outcome. For example, the knowledge of the effective electric field E(characterized by Wd) at the unpaired electron is required to link the experimentally determined P,T-odd frequency shift with the electron EDM de. We begin with a brief review of P,T-odd effects in heavy atoms and polar diatomics and the possible mechanisms which can give rise to such effects, in particular, the one arises due to the intrinsic electron EDM de. The P,T-odd interaction constant Wd is computed for the ground (2∑ ) state of YbF and BaF molecules using all-electron DF orbitals at the restricted active space (RAS) CI level. The RASCI space used for both systems in this calculation is sufficiently large to incorporate important core-core, core-valence, and valence-valence electron correlation effects. In addition to Wd, we also report the dipole moment (µe ) for these systems to assess the reliability of the method. The basis set dependency of Wd is also analyzed. The single reference coupled cluster (SRCC) method, developed by the cluster expansion of a single determinant reference function, is one of the most sophisticated method for treating dynamical correlation effects in a size-extensive manner. The non-uniqueness of the exponential nature of the wave operator diversifies the methods in multi-reference context. The multi-reference coupled cluster (MRCC) strategies fall within two broad classes: (a) State-Universal (SU), a Hilbert-space approach and (b) Valence-Universal (VU), a Fock-space approach. In this thesis, we shall be mainly concerned with the VU-MRCC which unlike SU-MRCC uses a single wave operator that not only correlates the reference functions, but also all the lower valence (or the so called subdued) sectors, obtained by deleting the occupancies systematically. The linear response theory (LRT) or equation of motion (EOM) method is another possible alternative which is nowadays extensively used to compute the atomic and molecular properties. Although, the CCLRT or EOM-CC method is not fully extensive in nature, this method has some distinct advantages over the traditional VU-MRCC theory. Further, for one-valence problem like ionization processes, the CCLRT/EOM-CC is formally equivalent to VU-MRCC, and hence, size-extensive. In this thesis, the core-extensive CCLRT and core-valence extensive (all electron) VU-MRCC methods are applied to compute the ground and excited state properties of various atomic and molecular systems (HCl, CuH, Ag, Sr, Yb and Hg) using nonrelativistic and relativistic (for heavy atoms) spinors. The similarities and differences in the structure of these two formalisms are also addressed. We also investigate the ground and excited state properties of HCN which is a system of astrophysical importance. This system has raised interest among the astrophysicists due to its detection in the atmosphere of Titan and Carbon stars. HCN has also been identified via radio-techniques in both comets and interstellar atmosphere. In the ash-photolysis of oxazole, iso-oxazole, and thiozole a transient band system was observed in the region 2500-3050 Å. This band system was attributed to a meta-stable form of HCN, i.e, either HNC or triplet HCN. We carry out detailed theoretical investigations using CCLRT and complete active space self-consistent field (CASSCF) method to characterize this unidentified band and other experimentally observed transitions.

Precise measurements of both absolute frequencies and small frequency differences of atomic energy levels have played an important role in the development of physics. For example, high precision measurements of absolute frequencies of the 2S½ → 2P ½ transition (D1 line) of alkali atoms form an important link in the measurement of the fine structure constant, α. Similarly, precise interferometric measurements of the local gravitational acceleration (g) rely on the knowledge of the absolute frequencies of the 2S½ → 2P 3/2 transition (D2line) in alkali atoms. Difference frequency measurements of hyperfine structure and isotope shifts of atomic energy levels provide valuable information about the structure of the nucleus, which in turn helps in fine tuning the atomic wave functions used in theoretical calculations. The work reported in this thesis starts with the development and refinement of high precision measurement of absolute frequencies using a ring-cavity resonator. The measurement technique is relatively simple and cost-effective, but the accuracy is comparable to that achieved with the frequency comb technique (10¯11) when the accuracy is limited by the natural linewidth of the transition being measured. The technique combines the advantages of using tunable diode lasers to access atomic transitions with the fact that the absolute frequency of the D2 line in87Rb is known with an accuracy of 6 kHz. A frequency-stabilized diode laser locked to this line is used as a frequency reference, along with a ring-cavity resonator whose length is locked to the reference laser. For a given cavity length, an unknown laser locked to an atomic transition has a small frequency offset from the nearest cavity resonance. We use an acousto-optic modulator (AOM) to compensate for this frequency offset. The measured offset is combined with the cavity mode number to obtain a precise value for the frequency of The unknown laser. We have used this technique for absolute frequency measurements Of the D lines in133Cs and 6,7Li, and the 398.8nm line in Yb. We have also developed a technique to measure the ‘difference frequency’ of atomic energy levels using a single diode laser and an AOM. In this technique, the laser is first locked to a given hyperfine transition. The laser frequency is then shifted using the AOM to another hyperfine transition and the AOM frequency is locked to this difference. Thus the AOM frequency directly gives a measurement of the hyperfine interval. Applying this AOM technique we have measured the hyperfine interval of the D1 lines of all alkali atoms with high precision. We have further developed a technique of coheren-tcontrol spectroscopy (CCS) using co-propagating control and probe beam that is useful for highresolution spectroscopy. In this technique, the probe beam is locked to a transition and its absorption signal is monitored while the control beam is scanned through neighbouring transition. As the control comes into resonance with another transition, the probe absorption is reduced and the signal shows a Doppler free dip. This technique allows us to resolve transitions that are otherwise swamped by crossover resonances in conventional saturated absorption spectroscopy (SAS). We have applied this technique to measure hyperfine intervals in the D2 line of several alkali atoms. Thus, we were able to do high-precision measurements of both absolute and difference frequency of atomic transitions. The precision of the absolute frequency measurement is finally limited by the accuracy of 6 kHz with which the reference frequency is known. The nearby two photon transition in Rb, i.e. the 5S1/2→5D3/2 transition at 778 nm, is known with an accuracy of 1 kHz. In future, we hope to improve the accuracy of our technique using this transition as the reference. This thesis is organized as follows: In Chapter1,we give a brief introduction to our work.. We review the importance of frequency measurements and precision spectroscopy, followed by a comparison of the frequency comb and our ring cavity technique. In Chapter2, we describe measurements of the absolute frequency of the D lines of 133Cs using the ring cavity. We give a detailed discussion of the technique, the Possible sources of errors, and ways to check for the errors. The measurement of the absolute frequency of the D lines of Cs allows a direct comparison to frequency comb measurements, and thus acts as a good check on our technique. In Chapter 3, we describe the absolute frequency and isotope shift measurements in the 398.8 nm line in Yb. We probed this line by frequency doubling the output of a tunable Ti:Sapphire laser. We obtained< 60 kHz precision in our measurements and were able to resolve several discrepancies in previous measurements on this line. In Chapter 4, we describe the measurement of hyperfine structure in the D1 lines of alkali atoms. We used conventional saturated-absorption spectroscopy in a vapor cell to probe different hyperfine transitions and then used our AOM technique to measure the hyperfine interval with high precision. In Chapter 5 we discuss our measurements of hyperfine structure in the D2 lines of several alkali atoms. In the case of 23Na and 39K, the closely-spaced hyperfine transitions are not completely resolved in conventional saturatedabsorption spectroscopy due to the presence of cross over resonances. We have used coherent control spectroscopy to obtain crossover-free spectra and then measured the hyperfine intervals using an AOM. This technique was also used for high resolution spectroscopy in the D2 line of 133Cs. Finally, we describe our measurements of hyperfine structure in the D2 line of Rb using normal saturated absorption spectroscopy. Chapter 6, describes the relative and absolute frequency measurements in the D lines of6,7 Li at 670nm. High-precision measurements in lithium are of special interest because theoretical calculations of atomic properties in this simple three electron system are fairly advanced. Lithium spectroscopy poses an experimental challenge and we describe our efforts in doing highresolution spectroscopy on this system. Chapter 7 describes the hyperfine spectroscopy on the1P 1 state of 173Yb. Measurement of hyperfine structure in 173Yb has a problem because two of the hyperfine transitions overlap with the transition in 172Yb. In our earlier work (described in chapter 4), we had solved this problem by using multipeak fitting to the partially resolved spectrum. Here, we directly resolve the hyperfine transitions by using transverse laser cooling to selectively deflect the 173Yb isotope. In Chapter 8 , we give a broad conclusion to the work reported in this thesis and suggest future avenues of research to continue the work commenced here.