Elastic and inelastic interactions are studied in tunnel junctions of a superconducting nanoelectromechanical setup and in response to resent experimental superconducting scanning tunneling microscope findings on a paramagnetic molecule. In addition, the electron density of molecular graphene is modeled by a scattering theory approach in very good agreement with experiment. All studies where conducted through the use of model Hamiltonians and a Green function formalism. The nanoelectromechanical system comprise two fixed superconducting leads in-between which a cantilever suspended superconducting island oscillates in an asymmetric fashion with respect to both fixed leads. The Josephson current is found to modulate the island motion which in turn affects the current, such that parameter regions of periodic, quasi periodic and chaotic behavior arise. Our modeled STM setup reproduces the experimentally obtained spin excitations of the paramagnetic molecule and we show a probable cause for the increased uniaxial anisotropy observed when closing the gap distance of tip and substrate. A wider parameter space is also investigated including effects of external magnetic fields, temperature and transverse anisotropy. Molecular graphene turns out to be well described by our adopted scattering theory, producing results that are in good agreement with experiment. Several point like scattering centers are therefore well suited to describe a continuously decaying potential and effects of impurities are easily calculated.

Dans ce travail de thèse, je présente la construction d’une nouvelle expérience pour la production de gaz ultra froids de dysprosium. En tirant parti de la structure électronique à couche incomplète de ces atomes, nous visons à la réalisation de champs de jauge synthétiques, qui pourront conduire à l’observation de nouvelles phases (topologiques) de la matière. Le couplage du spin atomique avec le champ lumineux, plus efficace que pour des atomes alcalins, permettra d’atteindre des régimes d’interactions fortes qui restent, jusqu’à présent, hors de portée expérimentale. J’adapte des protocoles existants pour la réalisation de champs de jauge dans le cas de Dysprosium, en tenant compte de son grand spin électronique (J = 8 dans l’état fondamental). En outre, le dysprosium a le plus grand moment magnétique parmi les éléments stables, et il est donc le meilleur candidat pour l’étude des gaz dipolaires. Je détaille le dispositif expérimental que nous avons construit et comment nous effectuons le piégeage et le refroidissement du dysprosium. Nous étudions en détail le comportement du piège magnéto-optique, qui est réalisé sur la transition d’intercombinaison ¹S₀ ↔ ³P₁. La raie étroite et le grand spin rendent l’opération du piège très complexe. Néanmoins, je montre que sa compréhension devient assez simple dans le régime où le nuage se polarise spontanément en conséquence de la combinaison des forces optiques et gravitationnelles. Enfin, je décris les dernières étapes du transport optique et de l’évaporation, ce qui conduira à la production d’un gaz dégénéré. / In this thesis I present the construction of a new experiment producing ultra cold gases of Dysprosium. Using the favourable electronic structure of open-shell lanthanide atoms, we aim at the realisation of laser-induced synthetic gauge fields, which could lead to the observation of novel (topological) phases of matter. The coupling of the atomic spin with the light field, improved with respect to alkali atoms, opens the possibility to explore strongly interacting regimes that were up to now out of experimental reach. I adapt existing protocols for the implementation of gauge fields to the case of Dysprosium, taking into account its large electronic spin (J = 8 in the ground state). Moreover, Dysprosium has the largest magnetic moment among the stable elements, and is the best candidate for the study of dipolar gases. I describe the experimental setup that we built and how we perform the trapping and cooling of Dysprosium. We study in detail the behaviour of the magneto-optical trap, which is performed on the ¹S₀ ↔ ³P₁ intercombination line. The narrow linewidth and the large spin make the trap operation quite challenging. Nevertheless, I show that its understanding becomes quite simple in the regime where the cloud spontaneously polarises due to the interplay of optical and gravitational forces. Finally, I describe the last steps of optical transport and evaporation, which will lead to the production of a degenerate gas.

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The discoveries in applications of chirality in various areas of science seem to never cease to emerge. Chirality, being the property that some objects are geometrically distinguishable from their mirror image, is a tiny difference of vast importance. The fact that multiple biological structures are chiral is what permits life on Earth and its discovery had a severe impact on medical development. When the concept of quantum chirality was introduced, the connection between the chiral symmetry and the quantum states and operators that characterize quantum chirality was not particularly clear. It was shown that closed spin chains of an odd number of spins naturally had chiral states as eigenstates of a Hamiltonian describing Heisenberg and Dzyaloshinsky-Moriya (DM) interactions, and the symmetry of the system in direct relation to the chiral symmetry of the eigenstates quickly became of interest. The aim of this thesis is therefore to explore how quantum chirality is a chiral symmetry and to develop a scheme to create chiral states from systems that lack the required symmetry. The investigation showed that discretized probability current gives a good explanation to why the chiral states follow a chiral nature, but further examination is required in order to generalize a deeper connection between the probability current and the chiral states of spin chains. The results also indicated that it was possible to force open spin chains into purely chiral states, and into superpositions thereof, by time evolution. The scheme is still in its early stage and physical implementation and applications are yet to be explored. / Upptäckterna av tillämpningar av kiralitet inom ett flertal områden verkar ständigt öka i omfattning. Kiralitet är fenomenet att vissa objekt geometriskt kan särskiljas från sin spegelbild, vilket är en ringa skillnad men med väsentlig innebörd. Det faktum att flertalet biologiska strukturer är kirala är en förutsättning för liv på jorden och upptäckten av detta har haft en omfattande betydelse för medicinsk utveckling. När konceptet kvantkiralitet introducerades, var kopplingen mellan den kirala symmetrin och de kvantmekaniska tillstånden och operatorerna som utgör kvantkiralitet, inte trivial. Tidigare studier har visat att stängda spinnkedjor av ett udda antal spinn naturligt har kirala tillstånd som egentillstånd till en Hamiltonian beskrivande Heisenberg- och Dzyaloshinsky-Moriyainteraktioner. Att systemets symmetri stod i direkt relation till den kirala symmetrin av egentillstånden blev tidigt av intresse att undersöka. Syftet med denna kandidatuppsats är således att utforska en djupare förståelse till hur kvantkiralitet är en kiral symmetri samt utveckla en metod för hur kirala tillstånd kan drivas till att uppstå ur system som saknar den nödvändiga symmetrin. Resultaten visade att den diskretiserade sannolikhetsströmmen ger en god förklaring till varför de kirala tillstånden följer en kiral natur, men vidare efterforskning behövs för att kunna generalisera en djupare koppling mellan sannolikhetsströmmen och de kirala tillstånden hos spinnkedjor. Undersökningen indikerade också att det var möjligt att forcera en öppen spinnkedja till ett kiralt tillstånd, och till superpositioner därav, genom tidsutveckling. Metoden är fortfarande i sin tidiga utveckling och fysisk implementering samt tillämpningar väntar ännu på att upptäckas.