Orientadores: Narcizo Marques de Souza Neto, Flávio Cesar Guimarães Gandra / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-27T10:57:14Z (GMT). No. of bitstreams: 1 Veiga_LarissaSayuriIshibe_D.pdf: 10330689 bytes, checksum: 72bdd1a8fad1f82f880bb2c86fcd6a9e (MD5) Previous issue date: 2015 / Resumo: Este trabalho teve como objetivo a investigação de diversos mecanismos físicos provenientes das estruturas eletrônicas, magnéticas e cristalinas de sistemas ternários de terras raras e metais de transição 3d-5d através do uso das técnicas de espectroscopia de absorção de raios X e difração de raios X sob altas pressões. Dentre os fenômenos físicos estudados em função da compressão da rede cristalina induzida pela aplicação da pressão estão o magnetismo proveniente dos orbitais 4f e 5d nos sistemas ternários RERh4B4 (com RE = Dy e Er), os efeitos do campo elétrico cristalino e as interações de troca magnéticas nas perovskitas duplas 3d-5d (AFeOsO6, com A = Ca e Sr) e o acoplamento spin-órbita nos metais de transição 5d. As propriedades eletrônicas e magnéticas dos orbitais 4f e 5d das terras raras nos compostos da família RERh4B4 (RE = Dy e Er) foram investigadas através de experimentos de XANES e XMCD sob altas pressões na borda L3 do Dy e Er . Os sinais magnéticos das contribuições quadrupolar (2p3/2-> 4f) e dipolar (2p3/2->5d) presentes nos espectros de XMCD, em ambos os compostos, diminuem progressivamente em função da pressão. Este comportamento foi explicado em termos das interações de troca magnéticas entre os íons de terras raras, que são enfraquecidas pelas alterações locais da estrutura atômica induzidas pela compressão da rede cristalina. Já no sistema de perovskitas duplas, foi demonstrado que a compressão da estrutura Sr2FeOsO6, com um arranjo cristalino ordenado dos íons de Fe (3d) e Os (5d), permite o controle contínuo e reversível da coercividade e magnetização de saturação. Este efeito foi explicado em termos do aumento do campo elétrico cristalino em função da pressão, que altera as interações de troca magnéticas Fe-O-Os e transforma o material com magnetização remanente e coercividade praticamente nulas a pressão ambiente em outro com uma coercividade robusta (~0.5 T) e magnetização de saturação expressiva a pressões acima de ~10 GPa. Por fim, a última parte desta tese de doutorado foi dedicada ao uso da seletividade química e orbital da técnica de XANES na investigação do acoplamento spin-órbita nos elementos Pt (Pt0, 5d9) e Hf (Hf0, 5d2) sob altas pressões. Ao contrário do observado para a Pt, o cálculo do branching ratio a partir dos espectros de absorção nas bordas L2,3 do Hf revelaram que o acoplamento spin-órbita aumenta monotonicamente em função da pressão aplicada. Esse comportamento foi relacionado às propriedades supercondutoras e estruturais presentes nesse elemento sob altas pressões / Abstract: The scientific goal of this work has been the investigation of several physical mechanisms derived from the electronic, magnetic and structural properties of ternary rare earth and transition metal systems by means of X-ray absorption spectroscopy and X-ray diffraction techniques in a diamond anvil cell. Among the physical properties studied as a function of lattice compression induced by applied pressure are the magnetism of the 4f and 5d orbitals in tetragonal rare earth rhodium borides RERh4B4 (with RE = Dy e Er), the crystal electric field effects and magnetic exchange interactions in 3d-5d double perovskite systems (A2FeOsO6, with A = Ca e Sr) and the spin-orbit coupling in 5d transition metals. The electronic and magnetic properties of the rare earth 4f and 5d orbitals in the RERh4B4 (RE = Dy e Er) systems were investigated through high pressure XANES and XMCD experiments at Dy and Er L3 edges. For both compounds, the magnetic signals of the quadrupole (2p3/2->4f) and dipole (2p3/2->5d) contributions to the XMCD spectra progressively decrease as a function of pressure. This behavior was explained in terms of the magnetic exchange interactions between the rare earth ions, which are weakened by changes in the local atomic structure induced by compression of the crystal lattice. In the double perovskite system, it has been shown that compression of Sr2FeOsO6 structure with an ordered crystalline arrangement of iron (3d) and osmium (5d) transition metal ions, allows for continuous and reversible control of magnetic coercivity and saturation magnetization. This effect was explained in terms of enhanced crystal electric fields under high pressure, which alter the Fe-O-Os magnetic exchange interactions and transform the material with an otherwise mute response to magnetic fields into one with a strong coercivity (~0.5 T) and substantial saturation magnetization at pressures above ~10 GPa. Finally, the last part of this thesis is dedicated to the use of chemical and orbital selectivity of XANES technique as a tool to investigate the spin-orbit coupling in Pt (Pt0, 5d9) and Hf (Hf0, 5d2) elements under high pressures. Unlike observed for Pt, the calculated branching ratio determined from the integrated intensities of the Hf L2,3 white lines shows that the spin-orbit coupling increases monotonically as a function of applied pressure. This behavior was related to the superconducting and structural properties displayed by this element at high pressures / Doutorado / Física / Doutora em Ciências

Cette thèse de doctorat est dédiée à l’étude, avec des méthodes de calcul ab initio, desplasmons de surface et des états de surface de surfaces d’or, plate ou comportant desmarches (surface vicinale), par la simulation numérique de spectres de perte d’énergieélectronique (EEL) au moyen de la théorie de la fonctionnelle de la densité (DFT) et de lathéorie de perturbation de la fonctionnelle de la densité dépendant du temps (TDDFPT).L’influence du couplage spin-orbite (CSO) et celle de la géométrie de la surface ont étéétudiées. Dans l’or cristallin, j’ai étudié l’effet des électrons de semicoeur sur les spectresEEL à q = 0. J’ai montré en particulier que pour produire un spectre EEL sur une largegamme de fréquences, de 0 à 60 eV, il est nécessaire de tenir compte des électrons desemicoeur dans le pseudopotentiel, et qu’ils peuvent néanmoins être gelés dans le coeurpour l’étude de la partie basse en énergie du spectre EEL, pour des énergies inférieures à20 eV. J’ai réalisé des développements méthodologiques pour la TDDFPT avec CSO cou-plée à l’emploi de pseudopotentiels ultradoux, qui ont permis l’implémentation pratiquede cette approche dans les algorithmes de Liouville-Lanczos et de Sternheimer. J’ai utiliséavec succès ces approches qui m’ont permis de traiter des systèmes à plusieurs centainesd’atomes. J’ai examiné à nouveau le spectre EEL de l’or cristallin à q = 0, montrant enparticulier les traces d’un plasmon écranté dans le spectre EEL calculé sans inclure leseffets de CSO. J’ai ensuite montré que l’inclusion du CSO a un effet petit mais détectablesur le spectre EEL et le pic de plasmon, donnant un meilleur accord avec l’expérienceà q = 0. J’ai trouvé que la dispersion du plasmon acoustique (PAS) de la surface Au(111) est légèrement modifiée par le CSO, provenant du fait que la structure de bandesest elle-même modifiée par le dédoublement de Rashba de certains niveaux électroniques,dédoublement induit par le CSO. Puis, pour étudier les effets de géométrie, j’ai étudié lessurfaces vicinales (322), (455) et (788) de l’or. J’ai en particulier mené l’étude théoriquedes états électroniques de surface, et analysé l’évolution de l’état de surface de Shockleyentre la surface plate Au(111) et les surfaces ayant des marches dont les terrasses avaientdifférentes largeurs. J’ai montré la transition d’un état de surface résonant pour Au(322)à un état localisé pour Au(455) et pour Au(788), ainsi que le passage d’un état 2D étenduà travers la marche pour Au(322) à un état quasi-1D confiné dans la terrasse de la marchepour Au(455) et pour Au(788). Ces résultats sont en accord avec l’expérience, et avecceux d’un modèle de Kronig-Penney de potentiel périodique. J’ai calculé le spectre EELSpour la surface d’or (455) que j’ai modélisé par une tranche de 5 nm d’or séparée de sesvoisines (répétées périodiquement) par 5 nm de vide. J’ai identifié la signature du plas-mon acoustique de surface. J’ai montré que, pour un moment transféré perpendiculaireà la marche de la surface, la dispersion du PAS n’est pas modifiée par rapport à celle duPAS de la surface plate Au(111) pour q < 0.125 Å −1 . Cependant, pour des valeurs plusgrandes du moment transféré, le pic du PAS a une énergie plus basse que celle du PASde Au(111), montrant les signes du confinement du PAS et suggérant que deux types dePAS peuvent se produire: un plasmon intra(sous)bande, similaire à celui de la surfaceAu(111), et un plasmon inter(sub)band, caractéristique de cette surface vicinale. / The PhD thesis is devoted to the ab initio study of surface plasmons and surface states offlat and vicinal surfaces of Au through the simulation of electron energy loss (EEL) spectraby means of the density functional theory (DFT) and the time-dependent density func-tional perturbation theory (TDDFPT). The influence of the spin-orbit coupling (SOC)and of the surface geometry has been investigated. In bulk Au I have studied the effect ofthe inclusion of semi-core electrons on the EEL spectrum at q = 0 and the plasmon peakposition and intensity. In particular, I have shown that in order to reproduce the EELspectrum on a wide frequency range (0-60 eV) it is important to account for semi-coreelectrons in the pseudopotential although they can be frozen in the core in studies of thelow energy part of the spectrum (below 20 eV). I have made methodological developmentsfor TDDFPT with SOC in the ultrasoft pseudopotential scheme that led to the practicalimplementation of SOC in the Liouville-Lanczos and Sternheimer approaches. I have thensuccessfully applied these approaches that allowed me to model systems with hundreds ofatoms. I have revisited the plasmonic excitations in bulk Au, pointing out that, in partic-ular, one can observe traces of an unscreened s-like bulk plasmon in the EEL spectrum atq = 0 calculated without SOC. I have also demonstrated that SOC has a small but notice-able effect on the Au EEL spectrum and plasmon peak, mainly modifying the unscreeneds-like plasmon peak and thus bringing the calculated spectrum into a better agreementwith experimental results at q = 0. Moreover I have observed that the dispersion ofthe acoustic surface plasmon (ASP) on the Au(111) surface is slightly modified by SOC,because the ASP comes from the surface state that itself is modified by SOC through theRashba splitting. To investigate the effect of geometry I have studied the vicinal (322),(455) and (788) surfaces of Au. In particular I have performed the theoretical study of thesurface states, analyzing the evolution of the Shockley surface state from the flat Au(111)surface towards the surfaces with terraces of different width. I have shown the surfaceresonance-to-surface state transition from (322) to (455) and (788) surfaces. I have shownalso the transition from the average-surface-modulated to the terrace-modulated statefrom (322) to (455) and (788) surfaces, as well as the transition from the extended 2Dstate to the quasi-1D state confined within the terrace. These results are in agreementwith experiments and results obtained with the Kronig-Penney periodic potential model.I have performed the EEL spectrum calculations for the Au(455) surface which I havemodeled with a 5 nm sized slab separated from its periodic neighbors by 5 nm of vacuum.I have identified signatures of the ASP in these spectra, showing that indeed, for the caseof the transferred electron wavevector momentum perpendicular to the step, the ASPdispersion is not changed with respect to the ASP dispersion of the Au(111) surface forq < 0.125 Å −1 . For bigger values of q, however, the ASP peak has a lower energy com-pared to the ASP peak of the Au(111) surface, showing signs of the ASP confinement, andsuggesting that two types of the ASP could occur: an intra(sub)band plasmon, similarto the Au(111) surface plasmon, and an inter(sub)band plasmon, characteristic of thisvicinal surface.

Computational chemistry has gained interest as a characterization tool to predict photoluminescence, reactivity and structural properties of organic and transition metal complexes. With the rise of methods including relativity, these studies have been expanded to the accurate modeling of luminescence spectra of complexes with considerable spin-orbit splitting due to heavy metal centers as well as the reaction pathways for these complexes to produce natural products such as hydrogen gas. These advances have led to the synthesis and utility of more effective catalysis as well as the development of more effective organic light emitting diodes (OLEDs) through the incorporation of organometallic complexes as emitters instead of typical organic emitters. In terms of significant scientific advancement presented in this work is in relation to the discovery of significant spin-orbit splitting in a gold(I) alkylphosphine complex, where the splitting results in the states that emit in different colors of the visible region of the electromagnetic spectrum. This work also reveals the discovery both computationally and experimentally, of a genuine polar-covalent bond between two-closed shell metals. This work highlights a complex with an incredibly short gold(I) – copper(I) intermetallic distance leading to a vibrational frequency and dissociation energy that is on par with those of other systems with single-bonded metal centers. Lastly, this work outlines a strategy for the production of hydrogen gas through the use of trinuclear cyclic coinage metal complexes as catalysis to split hydrohalic acids.

In the last decade, a large number of studies have been devoted to the peculiarities of correlated physics found in the quasi-two-dimensional square lattice iridium oxides. It was shown that this 5d family of transition metal oxides has strong structural and electronic similarities to the famous 3d family of copper oxides. Moreover, a delicate interplay of on-site spin-orbit coupling, Coulomb repulsion and crystalline electric field interactions is expected to drive various exotic quantum states. Many theoretical proposals were made in the last decade including the prediction of possible superconductivity in square-lattice iridates emerging as a sister system to high-Tc cuprates, which however met only limited experimental confirmation. One can, therefore, raise a general question: To what extent is the low-energy physics of the quasi-two-dimensional square-lattice iridium oxides different from other transition metal oxides including cuprates? In this thesis we investigate some of the effects which are usually neglected in studies on iridates, focusing on quasi-two-dimensional square-lattice iridates such as Sr2IrO4 or Ba2IrO4. In particular, we discuss the role of the electron-phonon coupling in the form of Jahn-Teller interaction, electron-hole asymmetry introduced by the strong correlations and some effects of coupling scheme chosen to calculate multiplet structure for materials with strong on-site spin-orbit coupling. Thus, firstly, we study the role of phonons, which is almost always neglected in Sr2IrO4, and discuss the manifestation of Jahn-Teller effect in the recent data obtained on Sr2IrO4 with the help of resonant inelastic x-ray scattering. When strong spin-orbit coupling removes orbital degeneracy, it would at the same time appear to render the Jahn-Teller mechanism ineffective. We show that, while the Jahn-Teller effect does indeed not affect the antiferromagnetically ordered ground state, it leads to distinctive signatures in the spin-orbit exciton. Second, we focus on charge excitations and determine the motion of a charge (hole or electron) added to the Mott insulating, antiferromagnetic ground-state of square-lattice iridates. We show that correlation effects, calculated within the self-consistent Born approximation, render the hole and electron case very different. An added electron forms a spin-polaron, which closely resembles the well-known cuprates, but the situation of a removed electron is far more complex. Many-body configurations form that can be either singlets and triplets, which strongly affects the hole motion. This not only has important ramifications for the interpretation of angle-resolved photoemission spectroscopy and inverse photoemission spectroscopy experiments of square lattice iridates, but also demonstrates that the correlation physics in electron- and hole-doped iridates is fundamentally different. We then discuss the application of this model to the calculation of scanning tunneling spectroscopy data. We show that using scanning tunneling spectroscopy one can directly probe the quasiparticle excitations in Sr2IrO4: ladder spectrum on the positive bias side and multiplet structure of the polaron on the negative bias side. We discuss in detail the ladder spectrum and show its relevance for Sr2IrO4 which is in general described by more complicated extended t-J -like model. Theoretical calculation reveals that on the negative bias side the internal degree of freedom of the charge excitation introduces strong dispersive hopping channels encaving ladder-like features. Finally, we discuss how the choice of the coupling scheme to calculate multiplet structure can affect the theoretical calculation of angle-resolved photoemission spectroscopy and scanning tunnelling spectroscopy spectral functions.

Spin-orbit coupling (SOC) reduces the spatial symmetry of ferromagnetic solids. That is, the physical properties of ferromagnetic materials are anisotropic, depending on the magnetization direction. In this thesis, by means of numerical calculations with full-relativistic density functional theory, we studied two kinds of physical properties: surface magnetic anisotropy energy (MAE) and anisotropic thermoelectric power due to Lifshitz transitions. After a short introduction to the full-relativistic density functional theory in Chapter 2, the MAE of ferromagnetic thin films is studied in Chapter 3. For such systems, separation of different contributions, such as bulk magnetocrystalline anisotropy (MCA) energy, shape anisotropy energy, and surface/interface anisotropy energy, is crucial to gain better understanding of experiments. By fitting our calculating results for thick slabs to a phenomenological model, reliable surface MAE could be obtained. Following this idea, we have studied the MAE of Co slabs with different geometries, focusing on the effects of orbital polarization correction (OPC). We found that the surface anisotropy is mainly determined by the geometry. While OPC gives better results of orbital moments, it overestimates the MAE. In the second part of Chapter3, the effects of electric fields on the MAE of L10 ferromagnetic thin films are studied. Using a simple model to simulate the electric field, our calculations are in good agreement with previous experimental results. We predicted that for CoPt, even larger effects exist. Moreover, we found that it is the amount of screening charge that determines the magnetoelectric coupling effects. This gives us some clue about how to achieve electric field control of magnetization direction. In Chapter 4, Lifshitz transitions in L10 FePt caused by a canted magnetic field are studied. We found several Lifshitz transitions in ordered FePt with tiny features in DOS. Using a two-band model, it is demonstrated that at such transitions, the singular behaviour of kinetic properties is due to the interband scattering, and the singularity itself is proportional to the derivative of the singular DOS. For FePt, such singularity will be smeared into anomaly by chemical disorder. Using CPA, we studied the effects of energy level broadening for the critical bands in FePt. We found that for experimentally available FePt thin films, Lifshitz transitions would induce up to a 3% increase of thermopower as the magnetization is rotated from the easy axis to the hard axis. / Spin-Bahn-Kopplung reduziert die Symmetrie ferromagnetischer Festkörper. Das bedeutet, dass die physikalischen Eigenschaften ferromagnetischer Stoffe anisotrop bezüglich der Magnetisierungsrichtung sind. In dieser Dissertation werden mittels numerischer voll-relativistischer Dichtefunktional-Rechnungen zwei Arten physikalischer Eigenschaften untersucht: magnetische Oberflächen-Anisotropieenergie (MAE) und anisotrope Thermokraft durch Lifshitz-Übergänge. Nach einer kurzen Einführung in die relativistische Dichtefunktional-Theorie in Kapitel 2 wird in Kapitel 3 die MAE ferromagnetischer dünner Filme untersucht. In diesen Systemen ist es für ein Verständnis experimenteller Ergebnisse wichtig, verschiedene Beiträge zu separieren: Volumenanteil der magnetokristallinen Anisotropie (MCA), Formanistropie und Oberflächen bzw. Grenzflächenanisotropie. Durch Anpassen berechneter Daten für dicke Schichten an ein phänomenologisches Modell konnten verlässliche Oberflächen Anisotropien erhalten werden. In dieser Weise wurde die MAE von Co- Schichten mit unterschiedlichen Geometrien untersucht, wobei der Einfluss von Orbitalpolarisations-Korrekturen (OPC) im Vordergrund stand. Es wurde gefunden, dass die Oberflächenanisotropie hauptsächlich von der Geometrie bestimmt wird. Während OPC bessere Ergebnisse für die Orbitalmomente liefert, wird die MAE überschätzt. Im zweiten Teil von Kapitel 3 wird der Einfluss elektrischer Felder auf die MAE von dünnen ferromagnetischen Filmen mit L10-Struktur untersucht. Unter Verwendung eines einfachen Modells zur Simulation des elektrischen Feldes liefern die Rechnungen gute Übereinstimmung mit vorliegenden experimentellen Ergebnissen. Es wird vorhergesagt, dass für CoPt ein noch größerer Effekt existiert. Weiterhin wurde gefunden, dass die magnetoelektrische Kopplung von der Größe der Abschirmladung bestimmt wird. Dies ist eine wichtige Einsicht, um die Magnetisierungsrichtung durch ein elektrisches Feld kontrollieren zu können. In Kapitel 4 werden Lifshitz-Übergänge untersucht, die ein gekantetes Magnetfeld hervorruft. Es wurden mehrere Lifshitz-Übergänge in geordnetem FePt gefunden, welche kleine Anomalien in der Zustandsdichte hervorrufen. Mit Hilfe eines Zweiband-Modells wird gezeigt, dass an solchen Übergängen das singuläre Verhalten kinetischer Eigenschaften durch Interband- Streuung verursacht wird und dass die Singularität proportional zur Ableitung der singulären Zustandsdichte ist. In FePt wird durch chemische Unordnung diese Singularität zu einer Anomalie verschmiert. Der Einfluss einer Verbreiterung der Energieniveaus der kritischen Bänder in FePt wurde mittels CPA untersucht. Es wurde gefunden, dass in experimentell verfügbaren dünnen FePt-Filmen Lifshitz-Übergänge bis zu 3% Erhöhung der Thermokraft erzeugen, wenn die Magnetisierung von der leichten in die harte Richtung gedreht wird.

Title: Theoretical study of spin-orbit coupling on spectra and photophysics of rhenium complexes Author: RNDr. Radka Heydová Department: Physical and Macromolecular Chemistry Supervisor: Ing. Stanislav Záliš, CSc., JHI AS CR, v.v.i. Supervisor's e-mail address: stanislav.zalis@jh.inst-cas.cz Abstract: Relativistic effects, especially spin-orbit coupling (SOC), play an essential role in transition metal chemistry and SOC treatment is indispensable for a correct theoretical description. To demonstrate the importance of SOC, the energies and oscillator strengths of vertical transitions for a series of [ReX(CO)3(2,2'-bipyridine)] (X = Cl, Br, I) and [Re(imidazole)(CO)3(1,10-phenanthroline)]+ complexes were calculated in the spin-free (SF) and spin-orbit (SO) conceptual frameworks. Two different computational approaches were adopted: SO-MS-CASPT2 where SOC was added a posteriori using a configuration interaction model (SO-RASSI), and the approximate perturbative SO-TD-DFT method. Relativistic effects were included via the two-component Douglas-Kroll-Hess transformation and the zeroth-order regular approximation in the former and the latter technique, respectively. The SF (i.e. accounting only for the scalar relativistic effects) and SO results from both methods were compared with each other and to available...

No description available.

Topological insulators (TIs) are semiconductors with protected electronic surface states that allow dissipation-free transport. TIs are envisioned as ideal materials for spintronics and quantum computing. In Bi14Rh3I9, the first weak 3D TI, topology presumably arises from stacking of the intermetallic [(Bi4Rh)3I]2þ layers, which are predicted to be 2D TIs and to possess protected edge-states, separated by topologically trivial [Bi2I8]2+ octahedra chains. In the new layered salt Bi12Rh3Cu2I5, the same intermetallic layers are separated by planar, i.e., only one atom thick, [Cu2I4]2- anions. Density functional theory (DFT)-based calculations show that the compound is a weak 3D TI, characterized by Z2 ¼ ð0; 0001Þ, and that the topological gap is generated by strong spin–orbit coupling (Eg,calc.~ 10 meV). According to a bonding analysis, the copper cations prevent strong coupling between the TI layers. The calculated surface spectral function for a finite-slab geometry shows distinct characteristics for the two terminations of the main crystal faces 〈001〉, viz., [(Bi4Rh)3I]2þ and [Cu2I4]2-. Photoelectron spectroscopy data confirm the calculated band structure. In situ four-point probe measurements indicate a highly anisotropic bulk semiconductor (Eg,exp.¼ 28 meV) with pathindependent metallic conductivity restricted to the surface as well as temperatureindependent conductivity below 60 K.

<p>Bose-Einstein condensates (BECs) in light-induced synthetic gauge fields and spaces can provide a highly-tunable platform for quantum simulations. Chapter 1 presents a short introduction to the concepts of BECs and our BEC machine. Chapter 2 introduces some basic ideas of how to use light-matter interactions to create synthetic gauge fields and spaces for neutral atoms. Three main research topics of the thesis are summarized below.</p> <p>Chapter 3: Recently, using bosonic quasiparticles (including their condensates) as spin carriers in spintronics has become promising for coherent spin transport over macroscopic distances. However, understanding the effects of spin-orbit (SO) coupling and many-body interactions on such a spin transport is barely explored. We study the effects of synthetic SO coupling (which can be turned on and off, not allowed in usual materials) and atomic interactions on the spin transport in an atomic BEC.</p> <p>Chapter 4: Interplay between matter and fields in physical spaces with nontrivial geometries can lead to phenomena unattainable in planar spaces. However, realizing such spaces is often impeded by experimental challenges. We synthesize real and curved synthetic dimensions into a Hall cylinder for a BEC, which develops symmetry-protected topological states absent in the planar counterpart. Our work opens the door to engineering synthetic gauge fields in spaces with a wide range of geometries and observing novel phenomena inherent to such spaces.</p> <p>Chapter 5: Rotational properties of a BEC are important to study its superfluidity. Recent studies have found that SO coupling can change a BEC's rotational and superfluid properties, but this topic is barely explored experimentally. We study rotational dynamics of a SO-coupled BEC in an effective rotating frame induced by a synthetic magnetic field. Our work may allow for studying how SO coupling modify a BEC's rotational and superfluid properties.</p> <p>Chapter 6 presents some possible future directions.</p>

Le travail théorique présenté dans cette thèse concerne la formation de molécules ultra-froides bialcalines et le contrôle de leurs degrés de liberté externes et internes. Cette étude est motivée par les nombreuses expériences en cours visant à l'obtention d'un gaz quantique dégénéré de molécules dans leur état fondamental absolu. Le schéma de formation étudié repose sur le processus de transfert adiabatique stimulé (STIRAP) réalisé en présence d'un potentiel optique de piégeage (réseau optique) des atomes et des molécules.Nous avons déterminé les paramètres du réseau optique (intensité et fréquence du champ laser) qui permettent de piéger efficacement des dimères d'alcalins en évaluant la polarisabilité dynamique acquise par les molécules soumises à un champ externe. Ces calculs reposent en particulier sur la connaissance détaillée de la structure électronique des molécules. Nous avons identifié des plages de longueur d'ondes dites « magiques » où la polarisabilité est la même pour chaque niveau peuplé au cours du transfert adiabatique, permettant ainsi un transfert optimal. Ce formalisme nous a également permis d'obtenir les coefficients Van der Waals de l'interaction à longue portée nécessaires pour étudier les taux de collisions entre molécules.Nous avons réalisé une étude plus détaillée de la molécule RbCs. En étudiant précisément la probabilité de transition de la molécule vers un niveau excité, nous avons proposé un schéma STIRAP pour transférer des molécules de RbCs, initialement dans un niveau vibrationnel excité, vers leur état rovibrationnel fondamental.Ces travaux ont montré l'importance de la connaissance précise de la structure hyperfine de l'état électronique moléculaire excité pour réaliser un gaz dégénéré de molécules dans un état quantique bien défini. Un modèle asymptotique nous a permis d'obtenir une première estimation de la structure hyperfine des courbes d'énergies potentielles des premiers états moléculaires excités des molécules Cs2 et RbCs. / The theoretical work presented in this thesis is focused on the formation of ultracold bialcaline molecules and on the control of their external and internal degrees of freedom. This study is motivated by the increasing number of experiments aiming at obtaining a quantum degenerate gas of molecules in their absolute ground state. The formation scheme we worked on is based on the Stimulated Raman Adiabatic Passage (STIRAP) technique operated while molecules are trapped inside an optical lattice.We have determined the parameters of the optical lattice (intensity and wavelength of the laser) that allow for an efficient trapping of the alkali dimers by evaluating the dynamic polarizability of molecules in the presence of an external field. Such calculations require the accurate knowledge of the electronic structure of the molecules. We have identified the so-called ``magic'' wavelength for which all levels populated during the STIRAP sequence have the same polarizability, thus ensuring an optimal transfer. The same approach has also been used to compute the strength of the long-range interaction between polar bialkali molecules needed to evaluate collision rates.The particular case of the RbCs molecule has been investigated. We have selected a radiative transition allowing for an efficient STIRAP scheme yielding molecules in their rovibrational ground state. These works have raised the need for the precise knowledge of the hyperfine structure of the excited electronic molecular state involved in the STIRAP scheme. We have developed an asymptotic model to obtain a first estimate of the hyperfine structure for the potential curves of the lowest excited states of Cs2 and RbCs.