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Este trabalho investiga as interações eletrônicas em algumas cetonas cíclicas, substituídas em α por um átomo de enxofre, pela comparação com os compostos substituídos correspondentes. Os compostos estudados eram: ciclopentanona (I), 2-mercaptociclopentanona (II), 2-metiltiociclopentanona (III), 2-etiltiociclopentanona (IV), 2-n-propilciclopentanona (V), cânfora (VI), 2-etilcânfora (VII), 2-metiltiocânfora (VIII), ciclohexanona (IX), 2 -metilciclohexanona (X), 2-etiltiociclohexanona (XI), 2-hexanona (XII), etiltioacetona (XIII), 3-tiaciclopentanona (XIV), 3-tiaciclohexanona (XV), 2-ciclopentenona (XVI), 2-etiltio-2-ciclopentenona (XVII), l-etiltiociclopenteno (XVIII), ciclopenteno (XIX), ciclopentanotiol (XX) e etiltiociclopentano (XXI) (ver arquivo). São apresentadas as revisões bibliográficas sobre interações eletrônicas em compostos carbonílicos β-tia-substituídos e em vinil- e aril-tioéteres. São descritas as sínteses de compostos (II)-(V), (VII), (XVI)-(XVIII), (XX) e (XXI) por nós efetuadas. São apresentadas as constantes de basicidade de cetonas (I)-(XVII) e as medidas no ultravioleta de compostos (I-III), (XVI)-(XXI). Os dados experimentais indicam que: 1 - Todos os compostos carbonílicos contendo enxofre apresentam basicidade menor em relação aos compostos correspondentes não sulfurados. Entretanto, a grandeza desta diminuição não é a mesma para todos os compostos estudados. 2 - As bandas η → π* e π → π* do espectro no ultravio1eta de 2-etiltio-2-ciclopentenona (XVII) sofrem deslocamentos batocrômicos em comparação com as ciclanonas saturadas e ciclopentenos, respectivamente. Entretanto, a banda ηs → σ* é semelhante a de tioéteres e tióis. É apresentada uma discussão dos resultados obtidos, na qual sugere-se que: A diminuição da basicidade depende da posição da ligação C-S em relação ao grupo carbonila, sendo maior quando o ângulo de projeção Φ se aproxima de 0 ou 180°. A diminuição de basicidade é devida a interação no espaço e/ou através das ligações entre os pares de elétrons do enxofre e oxigênio carbonílico. A pequena diminuição de basicidade observada em 2-eti1tio-2-ciclopentenona de conformação plana é proveniente do cancelamento parcial do efeito da interação pelo efeito de campo que atua no sentido contrário. Na 2-etiltio-2-ciclopentenona ocorre uma estabilização adicional, por delocalização eletrônica, do orbital π*, quando os grupos SR e CO acham-se ligados conjuntamente à dupla ligação. / The present thesis investigates the electronic interactions in some cyclic ketones, α-sulphur substituted by comparison with the corresponding sulphur-free compounds. The compounds studied were: cyclopentanone (I), mercaptocyclopentanone (II), 2-methylthiocyclopentanone (III), 2-ethylthiocyclopentanone (IV), 2-n-propylcyclopentanone (V), camphor (VI), 2-ethylcamphor (VII), 2-methylthiocamphor (VIII), cyclohexanone (IX), 2-methylcyclohexanone (X), 2-ethylthiocyclohexanone (XI), 2-hexanone (XII), ethylthioacetone (XIII), 3-thiacyclopentanone (XIV), 3-thiacyclohexanone (XV), 2-cyclopentenone (XVI), 2-ethylthio-2-cyclopentenone (XVII), l-ethylthiocyclopentene (XVIII), cyclopentene (XIX), cyclopentanethiol (XX) and ethylthiocyclopentane (XXI) (ver arquivo). The literature reports are presented on electronic interactions in the β-thia-substituted carbonyl compounds and in the vinyl- and aryl-thioethers. The syntheses of the compounds (II)-(V), (VII) , (XVI)-(XVIII), (XX) and (XXI) are described. The basicity constants for ketones (I)-(XVII) and the ultraviolet spectra for compounds (I)-(III), (XVI)-(XXI) are reported. The experimental results indicate that: 1 - All sulphur substituted carbonyl compounds show a decrease in basicity in comparison with the corresponding unsubstituted compounds. However, the extent of this decrease is not the same for all compounds studied. 2 - The η → π* and π → π* absorption bands in the spectrum of the 2-ethylthio-2-cyclopentenone (XVII) undergo bathocromic shifts in comparison with the saturated cyclanones and cyclopentenes, respectively. However, the ηs → σ* band is similar to those for thioethers and thiols. The results suggest that: The decrease of basicity depends on the position of C-S bond towards carbonyl group, being of maximum value when the projected angle Φ approaches 0 or 180°. The decrease of basicity is due to through-space and/or through bond interaction between the lane pairs on sulphur and oxygen atoms. The decrease of basicity in the planar 2-ethylthio-2-cyclopentenone is partly cancelled by a field effect operating in the reversed direction. In the 2-ethylthio-2-cyclopentenone a additional stabilization takes place, wich is due to electronic delocalization of π* when the SR and CO groups are bonded to the double bond.

Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-15T12:16:24Z No. of bitstreams: 1 arquivototal.pdf: 5169144 bytes, checksum: 66d534e3f0c0c59bf5d35a45290fa390 (MD5) / Made available in DSpace on 2016-03-15T12:16:24Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 5169144 bytes, checksum: 66d534e3f0c0c59bf5d35a45290fa390 (MD5) Previous issue date: 2015-02-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis, we propose an experimental setup for the study of Landau quantization and associated effects in a two-dimensional ultracold atomic gas. Gauge fields can emerge in the equation of motion for the optically addressed ultracold atoms. To this end, spatially dependent dark states are necessary for the internal states of the atoms. A tripod level scheme yields two degenerate dark states which can leads to either an Abelian U(1) U(1) gauge field or a non-Abelian SU(2) gauge field. Using a suitable laser configuration, we obtain a uniform U(1) U(1) magnetic field which causes the atoms organize themselves in Landau levels. The strength of the effective magnetic field depends on the relative intensity of the lasers beams at the atomic cloud. We estimate the degeneracy of the energy levels for an atomic gas formed by atoms of 87Rb. In addition, we establish the experimental conditions to reach the lowest Landau level regime. In the zero-temperature limit, we realize the emergence of magnetic oscillations in the atomic energy and its derivative as function of the inverse of the effective magnetic field (de Haas van Alphen effect). The period of the de Haas van Alphen oscillation allow us to determine area of the Fermi circle for the atomic gas via an Onsager-like relation. We also show that detuning the a laser from the two-photon resonance we generate a parabolic scalar potential that laterally confines the atoms. As a consequence, the Landau levels degeneracy is removed, since the energy spectrum depends explicitly on the transverse atomic momentum. We show that the Landau levels presents a reminiscent degeneracy when the boundaries conditions are considered. The residual degeneracy occurs when different energy levels overlap. We map the residual degeneracy points as a function of the effective magnetic field. Finally, we present an experimental scheme for observing the spin Hall effect for ultracold atoms in a tripod configuration. / Nesta tese, propomos um arranjo experimental para o estudo da quantização de Landau e efeitos associados em um gás atômico ultrafrio bidimensional. Campos de calibre podem surgir na equação de movimento para átomos ultrafrios oticamente vestidos. Para que isto ocorra, estados escuros espacialmente dependentes são necessários a partir dos estados internos dos átomos. Átomos numa configuração de níveis de energia do tipo tripod produzem dois estados escuros degenerados, que podem levar a campos de calibre Abelianos U(1) U(1) ou não-Abelianos SU(2). Utilizando uma configuração adequada de lasers, mostramos que é possível se produzir um campo magnético sintético uniforme U(1) U(1) que atua nos átomos neutros fazendo-os se organizarem em níveis de Landau. A intensidade do campo efetivo depende da intensidade relativa dos feixes de luz na nuvem atômica. Estimamos a degenerescência dos níveis de energia para um gás atômico formado por átomos de 87Rb e estabelecemos as condições experimentais para que seja atingido o regime em que todos os átomos populam unicamente o nível de Landau menos energético. Considerando o limite de temperatura nula, verificamos o surgimento de oscilações magnéticas na energia e em sua derivada como uma função do inverso do campo magnético efetivo (efeito de Haas van Alphen). O período da oscilação magnética nos permite determinar a área do círculo de Fermi para o gás atômico através de uma expressão similar a de Onsager para sistemas eletrônicos. Mostramos também que dessintonizando um dos lasers em relação à ressonância de dois fótons geramos um potencial escalar parabólico que faz com os átomos sejam lateralmente confinados. Isto resulta na remoção da degenerescência dos níveis de Landau, uma vez que a energia depende explicitamente do momento atômico transverso. Demonstramos que, aplicando condições periódicas de contorno ao sistema, temos o surgimento de uma degenerescência residual. A degenerescência remanescente ocorre quando diferentes níveis de energia se superpõem. Mapeamos os pontos de degenerescência como uma função do campo magnético efetivo. Por fim, apresentamos um esquema experimental para a observação do efeito spin Hall para átomos ultrafrios em uma configuração tripod.

Initiated with the purpose of assigning the Fraunhofer lines in the solar spectrum to atomic transitions in the 18th century, the collaboration between spectroscopists and astrophysicists has remained fruitful, successful and ever fascinating. This collaboration has resulted in the unique detection of over 200 different molecular species in the interstellar medium (ISM). These interstellar molecular species play significant roles in diverse fields such as atmospheric chemistry, astrochemistry, prebiotic chemistry, astrophysics, astronomy, astrobiology, etc, and in our understanding of the solar system ''the world around us''. This Thesis work focuses on understanding of the different aspects of the chemistry of the various classes of these molecular species. Chapter one starts with an historical perspective of what is now regarded as Molecular Astrophysics or Astrochemistry and discusses the interstellar medium and its properties; interstellar molecular species and their importance; molecular spectroscopy as an indispensible tool in interstellar chemistry and the different formation routes of these molecular species. It also discusses hydrogen bonding which is one of the most important of all the intermolecular interactions. The chapter ends by setting the stage for the present investigations. The chapter two of the Thesis saddled with the task of describing the methodology employed in this Thesis begins by setting the stage on the importance of computational chemistry in interstellar chemistry. It discusses the Gaussian 09 suite of programs and the various theoretical methods used in all the quantum chemical calculations reported in this Thesis. The chapter ends with a brief summary on the homebuilt Pulsed Nozzle Fourier Transform Microwave (PN-FTMW) spectrometer used for the preliminary studies on Isoprene...Argon weakly bound complex reported in the appendix. After the introductory chapters, chapter three begins with what is unarguably one of the most important classes of interstellar molecular species - 'interstellar isomers'. In this chapter, the Energy, Stability and Abundance (ESA) relationship existing among interstellar molecular species has been firmly established using accurate thermochemical parameters obtained with the composite models and reported observational data. From the relationship, “Interstellar abundances of related species are directly proportional to their stabilities in the absence of the effect of interstellar hydrogen bonding”. The immediate consequences of the relationship in addressing some of the questions in interstellar chemistry such as: Where are Cyclic Interstellar Molecules? What are the possible candidates for astronomical observation? Why are more Interstellar Cyanides than isocyanides? among others are briefly discussed. Following the ESA relationship, other studies addressing some of the whys and wherefores in interstellar chemistry are discussed in details. From ESA relationship, though there has not been any successful astronomical observation of any heterocycle, the ones so far searched remain the best candidates for astronomical observation in their respective isomeric groups. The observation of the first branched chain molecule in ISM is in agreement with the ESA relationship and the C5H9N isomers have been shown to contain potential branched chain interstellar molecules. That molecules with the C-C-O backbone have less potential of formation in ISM as compared to their counterparts with the C-O-C backbone has been demonstrated not to be true following the ESA relationship. A detailed investigation on the relationship between molecular partition function and astronomical detection of isomeric species (or related molecules) shows that there is no direct correlation between the two rather there is a direct link between the thermodynamic stability of the isomeric species (or related molecules) and their interstellar abundances which influences the astronomical observation of some isomers at the expense of others. Chapter four presents an interesting and a fascinating phenomenon among the interstellar molecular species as it discusses for the first time, the existence and effects of Interstellar Hydrogen Bonding. This interstellar hydrogen bonding is shown to be responsible for the deviations from thermodynamically controlled processes, delayed observation of the most stable isomers, unsuccessful observations of amino acids among other happenings in interstellar chemistry and related areas. On the prediction that ketenes are the right candidates for astronomical searches among their respective isomers, a ketenyl radical; HCCO has recently been detected in line with this prediction. The deviation from the rule that the ratio of an interstellar sulphur molecule to its oxygen analogue is close to the cosmic S/O ratio is well accounted for on the basis of hydrogen bonding on the surface of the dust grains. Detecting weakly bound complexes in ISM has not been a major interest in the field so far but the detectability of weakly bound complexes in ISM is very possible as discussed in this chapter. Following the conditions in which these complexes are observed in the terrestrial laboratory as compared to the ISM conditions; it suffices to say that weakly bound complexes are present and are detectable in ISM. They could even account for some of the 'U' lines. Chapter five of the Thesis discusses the Linear Interstellar Carbon Chains which are the dominant theme in interstellar chemistry accounting for over 20% of all the known interstellar and circumstellar molecular species. Accurate spectroscopic parameters within experimental accuracy of few kHz which are the indispensable tools for the astronomical observation of these molecular species; are obtained for over 200 different species from the various chains using an inexpensive combined experimental and theoretical approach. With the availability of the spectroscopic parameters; thermodynamics is utilized in accounting for the known systems and in examining the right candidates for astronomical searches. These molecular species are shown to also obey the ESA relationship observed for the isomeric species discussed in chapter three of this work. The effect of kinetics on the formation processes of these molecular species is well controlled by thermodynamics as discussed in this chapter. Finally, the application of these studies in reducing the 'U' lines and probing new molecular species has been briefly summarized. Chapter six discusses Interstellar Ions and Isotopologues which are two unique classes of interstellar molecular species. Different studies on interstellar ions and isotopologues are presented. From the studies on interstellar protonated species with over 100 molecular species; protonated species resulting from a high proton affinity prefers to remain protonated rather than transferring a proton and returning to its neutral form as compared to its analogue that gives rise to a lower proton affinity from the same neutral species. The studies on detectable interstellar anions account for the known interstellar anions and predict members of the C2nO-, C2nS-, C2n-1Si-, HC2nN-, CnP-, and C2n chains as outstanding candidates for astronomical observation including the higher members of the C2nH- and C2n-1N- groups whose lower members have been observed. From high level ab initio quantum chemical calculations; ZPE and Boltzmann factor have been used to explain the observed deuterium enhancement and the possibility of detecting more deuterated species in ISM. Though all the heterocycles that have so far been searched for in ISM have been shown to be the right candidates for astronomical observation as discussed in the ESA relationship, they have also been shown to be strongly bonded to the surface of the interstellar dust grains thereby reducing their abundances, thus, contributing to their unsuccessful detection except for furan which is less affected by hydrogen bonding. The D-analogues of the heterocycles are shown from the computed Boltzmann factor to be formed under the dense molecular cloud conditions where major deuterium fractionation dominates implying very high D/H ratio above the cosmic D/H ratio which suggests the detectability of these deuterated species. Chapter seven examines the isomerization of the most stable isomer (which is probably the most abundant) to the less stable isomer(s) as one of the plausible formation routes for interstellar molecular species. An extensive investigation on the isomerization enthalpies of 243 molecular species from 64 isomeric groups is reported. From the results, the high abundances of the most stable isomers coupled with the energy sources in interstellar medium drive the isomerization process even for relative enthalpy difference as high as 67.4 kcal/mol. Specifically, the cyanides and their corresponding isocyanides pairs appear to be effectively synthesized via this process. The following potential interstellar molecules; CNC, NCCP, c-C5H, methylene ketene, methyl Ketene, CH3SCH3, C5O, 1,1-ethanediol, propanoic acid, propan-2-ol and propanol are identified and discussed. In all the isomeric groups, isomerization appears to be an effective route for the formation of the less stable isomers (which are probably less abundant) from the most stable ones. Chapter eight summarizes the conclusions drawn from the different studies presented in this Thesis and also highlights some of the future directions of these studies. The first appendix presents the preliminary study on Isoprene...Ar weakly bound complex while the second appendix contains a study on interstellar C3S describing the importance of accurate dipole moment in calculating interstellar abundances of molecular species and in astrophysical and astronomical models.

The subject of this thesis is the study of coherent interaction of light with matter (atoms) to improve the precision measurements and techniques. Special attention is drawn to get the narrow subnatural electromagnetically induced transmission (EIT), electromagnetically induced absorption (EIA) and nonlinear magneto-optic rotation (NMOR) caused by alkali atoms contained in a vapor cell. Subnatural polarization rotation introduces by a strong circularly polarized light in the absence of any external magnetic field was also studied. A detailed theoretical treatment, given in this dissertation, allows to associate each of the features of the spectra with a special physical mechanism. Many quantum phenomena related to interferences, coherences, optical pumping etc. experiments are studied using home-built diode lasers. This thesis also describes laser cooling and trapping of rubidium atoms using two techniques. Deflection of cold atoms horizontally from MOT using pushing beams are discussed in close consideration for the improvements in the precision measurements. This thesis is organized as follows. In Chapter 1, an introduction to the importance of sub-natural narrow resonance and simplified technique in the precision measurement will be discussed. In Chapter 2, an introduction to EIT, EIA and NMOR resonance are discussed. This chapter will provide a basic theoretical background of atom-field interactions, especially for Λ-type and N -type systems and its steady state solution using density matrix analysis and experimental tools. The most important notion of laser cooling of atoms, ions or molecule i.e., exchange of momentum between light and atoms combining with the Doppler effect will be discussed. In Chapter 3, the observation of subnatural EIT and subnatural EIA in closed and open degenerate two-level system using room temperature vapor cell filled with Rb will be presented. Physical mechanisms that contribute to EIT and EIA, and the contrast of our results from the coherent population trapping (CPT)–type resonances are discussed in detail in appendix A.2 according to our experimental results. In Chapter 4, the narrowing of subnatural EIT and subnatural EIA linewidth in closed and open systems again in degenerate two level transition, using the “Laguerre-Gaussian” control beam instead of generally studied Gaussian beam, will be discussed in detail. In Chapter 5, the conversion between subnatural EIT to subnatural EIA in a degenerate Λ system will be discussed. The physical mechanism created by the introduction of a coherent counter propagating control laser to the co-propagating probe and the control laser are studied. The effect of polarization and axial velocity Doppler averaging will also be studied. In Chapter 6, we will discuss the sensitive technique for precise measurement of small magnetic fields using the NMOR, by chopping the resonant laser beam. We will study the sensitivity and the potential application of this technique in the measurement of an atomic electric-dipole moment. In Chapter 7, we will be studying about the induced optical rotation by a circularly polarized control laser on the linearly polarized probe laser. The effect of the intensity of the control laser beam on the higher order optical rotation will also be studied. In Chapter 8, we will be studying about the cooling and trapping of 87Rb in magneto-optic trap. We will be studying two techniques of trapping of atoms in MOT. The cold cloud of atoms from the MOT are deflected horizontally by using different configuration of pushing beam are studied. A brief summary and outlook of my thesis work will be discussed at Chapter 9.

This thesis deals with time-frequency analysis of electrograms measured on isolated guinea pig hearts perfused according to Langendorff. Time-frequency analysis is based on algorithms Matching Pursuit and Wigner-Ville Distribution. The theoretical part describes the basics of electrocardiography, measurement on isolated hearts, the theory of approximation method Matching Pursuit and its combination with the Wigner-Ville distribution spectrum showing the energy density of the signal. Also other common approaches of time-frequency analysis are presented including the theory of continuous wavelet transform. The presented algorithms were tested on a set of electrograms, on which were induced ischemia within measurement followed by reperfusion. The proposed method allows for the fast detection of ischemia without any a priori knowledge of the signal, and also serves as a tool for measurement of EG important points and intervals. In the conclusion efficacy of the method was presented and its possible uses has been discussed.

Les systèmes en interaction à longue portée sont connus pour avoir des propriétés statistiques et dynamiques particulières. Pour décrire leur évolution dynamique, on utilise des équations cinétiques décrivant leur densité dans l'espace des phases. Ce manuscrit est divisé en deux parties indépendantes. La première traite de notre collaboration avec une équipe expérimentale sur un Piège Magnéto-Optique. Ce dispositif à grand nombre d'atomes présente des interactions coulombiennes effectives provenant de la rediffusion des photons. Nous avons proposé des tests expérimentaux pour mettre en évidence l'analogue d'une longueur de Debye, et son influence sur la réponse du système. Les expériences réalisées ne permettent pour l'instant pas de conclure de façon définitive. Dans la deuxième partie, nous avons analysé les modèles cinétiques de Vlasov et de Kuramoto. Pour étudier leur dynamique de dimension infinie, nous avons examiné les bifurcations autour des états stationnaires instables, l'objectif étant d'obtenir des équations réduites décrivant la dynamique de ces états. Nous avons réalisé des développements en variété instable sur cinq systèmes différents. Ces réductions sont parsemées de singularités, mais prédisent correctement la nature de la bifurcation, que nous avons testée numériquement. Nous avons conjecturé une réduction exacte (obtenue via la forme normale Triple Zero) autour des états inhomogènes de l'équation de Vlasov. Ces résultats génériques pourraient être pertinents dans un contexte astrophysique. Les autres résultats s'appliquent aux phénomènes de synchronisation du modèle de Kuramoto pour les oscillateurs avec inertie et/ou interactions retardées. / Long-range interacting systems are known to display particular statistical and dynamical properties.To describe their dynamical evolution, we can use kinetic equations describing their density in the phase space. This PhD thesis is divided into two distinct parts. The first part concerns our collaboration with an experimental team on a Magneto-Optical Trap. The physics of this widely-used device, operating with a large number of atoms, is supposed to display effective Coulomb interactions coming from photon rescattering. We have proposed experimental tests to highlight the analog of a Debye length, and its influence on the system response. The experimental realizations do not allow yet a definitive conclusion. In the second part, we analyzed the Vlasov and Kuramoto kinetic models. To study their infinite dimensional dynamics, we looked at bifurcations around unstable steady states. The goal was to obtain reduced equations describing the dynamical evolution. We performed unstable manifold expansions on five different kinetic systems. These reductions are in general not exact and plagued by singularities, yet they predict correctly the nature and scaling of the bifurcation, which we tested numerically. We conjectured an exact dimensional reduction (obtained using the Triple Zero normal form) around the inhomogeneous states of the Vlasov equation. These results are expected to be very generic and could be relevant in an astrophysical context. Other results apply to synchronization phenomena through the Kuramoto model for oscillators with inertia and/or delayed interactions.

L’objectif principal de cette thèse est l’étude théorique de mélanges quantiques fortement interagissants à une dimension et soumis à un potentiel externe harmonique. De tels systèmes fortement corrélés peuvent être réalisés et testés dans des expériences d’atomes ultrafroids. Leurs propriétés de symétrie par permutation non triviales sont étudiées, ainsi que leurs effets sur les corrélations. Exploitant une solution exacte pour des interactions fortes, nous extrayons des propriétés générales des corrélations encodées dans la matrice densité à un corps et dans les distributions des impulsions associées, dans les mélanges fermioniques et de Bose-Fermi. En particulier, nous obtenons des résultats substantiels sur le comportement à courtes distances, et donc les queues à haute impulsions, qui suivent des lois en k^−4 typiques. Les poids de ces queues, dénotés contacts de Tan, sont liés à de nombreuses propriétés thermodynamiques des systèmes telles que les corrélations à deux corps, la dérivée de l’énergie par rapport à la longueur de diffusion unidimensionnelle, ou le facteur de structure statique. Nous montrons que ces contacts universels de Tan permettent également de caractériser la symétrie spatiale des systèmes, et constituent donc une connexion profonde entre les corrélations et les symétries. En outre, la symétrie d’échange est extraite en utilisant une méthode de théorie des groupes, à savoir la méthode de la somme des classes (class-sum method en anglais), qui provient à l’origine de la physique nucléaire. De plus, nous montrons que ces systèmes suivent une version généralisée du fameux théorème de Lieb-Mattis. Souhaitant rendre nos résultats aussi pertinents expérimentalement que possible, nous dérivons des lois d’échelle pour le contact de Tan en fonction de l’interaction, de la température et du confinement transverse. Ces lois présentent des effets intéressants liés aux fortes corrélations et à la dimensionnalité. / The main focus of this thesis is the theoretical study of strongly interacting quantum mixtures confined in one dimension and subjected to a harmonic external potential. Such strongly correlated systems can be realized and tested in ultracold atoms experiments. Their non-trivial permutational symmetry properties are investigated, as well as their interplay with correlations. Exploiting an exact solution at strong interactions, we extract general correlation properties encoded in the one-body density matrix and in the associated momentum distributions, in fermionic and Bose-Fermi mixtures. In particular, we obtain substantial results about the short-range behavior, and therefore the high-momentum tails, which display typical k^−4 laws. The weights of these tails, denoted as Tan’s contacts, are related to numerous thermodynamic properties of the systems such as the two-body correlations, the derivative of the energy with respect to the one-dimensional scattering length, or the static structure factor. We show that these universal Tan’s contacts also allow to characterize the spatial symmetry of the systems, and therefore is a deep connection between correlations and symmetries. Besides, the exchange symmetry is extracted using a group theory method, namely the class-sum method, which comes originally from nuclear physics. Moreover, we show that these systems follow a generalized version of the famous Lieb-Mattistheorem. Wishing to make our results as experimentally relevant as possible, we derive scaling laws for Tan’s contact as a function of the interaction, temperature and transverse confinement. These laws. Display displadisplay display interesting effects related to strong correlations and dimensionality.

Strong resonant dipole-dipole interactions in flexible Rydberg aggregates enable the formation of excitons, many-body states which collectively share excitation between atoms. Exciting the most energetic exciton of a linear Rydberg chain whose outer two atoms on one end are closely spaced causes the initiation of an exciton pulse for which electronic excitation and diatomic proximity propagate directed through the chain. The emerging transport of excitation is largely adiabatic and is enabled by the interplay between atomic motion and dynamical variation of the exciton. Here, we demonstrate the coherent splitting of such pulses into two modes, which induce strongly different atomic motion, leading to clear signatures of nonadiabatic effects in atomic density profiles. The mechanism exploits local nonadiabatic effects at a conical intersection, turning them from a decoherence source into an asset. The conical intersection is a consequence of the exciton pulses moving along a linear Rydberg chain and approaching an additional linear, perpendicularly aligned Rydberg chain. The intersection provides a sensitive knob controlling the propagation direction and coherence properties of exciton pulses. We demonstrate that this scenario can be exploited as an exciton switch, controlling direction and coherence properties of the joint pulse on the second of the chains. Initially, we demonstrate the pulse splitting on planar aggregates with atomic motion one-dimensionally constrained and employing isotropic interactions. Subsequently, we confirm the splitting mechanism for a fully realistic scenario in which all spatial restrictions are removed and the full anisotropy of the dipole-dipole interactions is taken into account. Our results enable the experimental observation of non-adiabatic electronic dynamics and entanglement transport with Rydberg atoms. The conical intersection crossings are clearly evident, both in atomic mean position information and excited state spectra of the Rydberg system. This suggests flexible Rydberg aggregates as a test-bench for quantum chemical effects in experiments on much inflated length scales. The fundamental ideas discussed here have general implications for excitons on a dynamic network.