<p>This thesis is divided into two parts. In the first part we study thermodynamics of the two-dimensional Heisenberg ferromagnet with dipolar interaction. This interaction breaks the conditions of the Mermin-Wagner theorem, resulting in a finite transition temperature. Our calculations are done within the framework of the self-consistent spin-wave theory (SSWT), which is modified in order to include the dipolar interaction. Both quantum and classical versions of the Heisenberg model are considered.</p><p>The second part of the thesis investigates the chemical bonding in solids from the first principles calculations. A new chemical bonding indicator called balanced crystal orbital overlap population (BCOOP) is developed. BCOOP is less basis set dependent than the earlier indicators and it can be used with full-potential density-functional theory (DFT) codes. We apply BCOOP formalism to the chemical bonding in the high-T_c superconductor MgB2 and the theoretically predicted MAX phase Nb3SiC2. We also study how the chemical bonding results in a repulsive hydrogen–hydrogen interaction in metal hydrides. The role of this interaction in the structural phase transition in Ti3SnHx is investigated.</p>

This thesis is divided into two parts. In the first part we study thermodynamics of the two-dimensional Heisenberg ferromagnet with dipolar interaction. This interaction breaks the conditions of the Mermin-Wagner theorem, resulting in a finite transition temperature. Our calculations are done within the framework of the self-consistent spin-wave theory (SSWT), which is modified in order to include the dipolar interaction. Both quantum and classical versions of the Heisenberg model are considered. The second part of the thesis investigates the chemical bonding in solids from the first principles calculations. A new chemical bonding indicator called balanced crystal orbital overlap population (BCOOP) is developed. BCOOP is less basis set dependent than the earlier indicators and it can be used with full-potential density-functional theory (DFT) codes. We apply BCOOP formalism to the chemical bonding in the high-T_c superconductor MgB2 and the theoretically predicted MAX phase Nb3SiC2. We also study how the chemical bonding results in a repulsive hydrogen–hydrogen interaction in metal hydrides. The role of this interaction in the structural phase transition in Ti3SnHx is investigated.

Dipolar couplings are one of the major source of structural information. Due to their dependence on the distance between the nuclei and the angle of orientation of the dipolar vector with respect to the magnetic field, they provide significant insight into the geometry and topology of molecules. As the dipolar interactions are in general present in the solid phase of the compounds, solid state NMR experiments have gained significant popularity and is widely used. Separated Local Field NMR spectroscopy based on cross-polarization technique has been used to measure the heteronuclear dipolar couplings in solid state. However, the technique undergoes many experimental challenges and requires further development. This thesis is concerned mainly with the development of techniques to measure the dipolar couplings accurately in oriented molecules. In this regard, a method for fast data acquisition is also proposed. The first chapter briefly introduces the basics of NMR spectroscopy, methodologies applied for obtaining a high resolution NMR spectrum in the solid state. An introduction to liquid crystals is presented and the nature of NMR interaction in the liquid crystalline phases is described. In chapter-2, a new pulse scheme has been proposed that includes the X-nucleus polarization in the SLF experiments and is shown to provide better sensitivity and resolution. A quantitative analysis with simulation and experimental results are also presented. In chapter-3, the performance of various homonuclear decoupling pulse schemes incorporated into SLF experiments tested on oriented systems are compared. The proposed pulse schemes are shown to provide high resolution spectrum with accurate dipolar coupling measurement for natural abundant samples and for uniformly labeled compounds as well. Theoretical description with simulation and experimental results shown here are found to provide optimum results under several technical complications seen with respect to the conventional methods used for SLF experiments. Chapter-4, an attempt is made to reconstruct 2D J-resolved and 2D- SLF spectra from several 1D experimental data. This is achieved with the help of projection reconstruction method and is shown to provide high resolution 2D spectrum with saving of experimental time by an order of two. Chapter-5, high resolution spectra from SLF experiments under phase alternating pulses and using amplitude and time averaged nutation techniques are shown for accurate dipolar coupling measurement with a dramatic reduction in rf power. This is important as the use of low rf power leads to low sample heating and can be applied suitably for the study of liquid crystals and salty biomolecules. Chapter-6, attempts are made to characterize two novel thiophene based liquid crystals using both solution and solid state NMR spectroscopy. C-H dipolar couplings measured from SLF experiments are mainly used to find the order parameters and geometry of the molecules.

The progess in NMRQIP can be outlined in to four parts.1) Implementation of theoretical protocols on small number of qubits. 2) Demonstration of QIP on various NMR systems. 3) Designing and implementing the algorithms for mixed initial states. 4) Developing the techniques for coherent and decoherent control on higher number(up to 15) of qubits. This thesis contains some efforts in the direction of first three points. Quantum-state discrimination has important applications in the context of quantum communication and quantum cryptography. One of the characteristic features of quantum mechanics is that it is impossible to devise a measurement that can distinguish nonorthogonal states perfectly. However, one can distinguish them with a finite probability by an appropriate measurement strategy. In Chapter 2, we describe the implementation of a theoretical protocol of programmable quantum-state discriminator, on a two-qubit NMR System. The projective measurement is simulated by adding two experiments. This device does the unambiguous discrimination of a pair of states of the data qubit that are symmetrically located about a fixed state. The device is used to discriminate both linearly polarized states and eillipitically polarized states. The maximum probability of successful discrimination is achieved by suitably preparing the ancilla quubit. The last step of any QIP protocol is the readout. In NMR-QIP the readout is done by using density matrix tomography. It was first proposed by Ernst and co-workers that a two-dimensional method can be used to correlate input and output states. This method uses an extra (aniclla) qubit, whose transitions indicate the quantum states of the remaining qubits. The 2D spectrum of ancilla qubit represent the input and output states along F1 and F2 dimensions respectively. However the 2D method requires several t1 increments to achieve the required spectral width and resolution in the indirect dimension, hence leads to large experimental time. In chapter 3, the conventional 2D NMRQIP method is speeded-up by using Hadamard spectroscopy. The Hadamard method is used to implement various two-, three-qubit gates and qutrit gates. We also use Hadamard spectroscopy for information storage under spatial encoding and to implement a parallel search algorithm. Various slices of water sample can be spatially encoded by using a multi-frequency pulse under the field gradient. Thus the information of each slice is projected to the frequency space. Each slice represents a classical bit, where excitation and no excitation corresponds to the binary values 0 and 1 respectively. However one has to do the experiment for each binary information, by synthesizing a suitable multi-frequency pulse. In this work we show that by recording the data obtained by various Hadamard encoded multi-frequency pulses, one can suitably decode it to obtain any birnary information, without doing further experiments. Geometric phases depend only on the geometry of the path executed in the projective Hilbert space, and are therefore resilient to certain types of errors. This leads to the possibility of an intrinsically fault-tolerant quantum computation. In liquid state NMRQIP. Controlled phase shift gates are achieved by using qubit selective pulses and J evolutions, and also by using geometir phases. In order to achieve higher number of qubits in NMR, one explores dipolar couplings which are larger in magnitude, yielding strongly coupled spectra. In such systems since the Hamiltonian consists of terms, it is difficult to apply qubit selective pulses. However such systems have been used for NMRQIP by considering 2n eigen states as basis states of an n-qubit system. In chapter 4, it is shown that non-adiabatic geometric phases can be used to implement controlled phase shift gates in strongly dipolar coupled systems. A detailed theoretical explanation of non-adiabatic geometric phases in NMR is given, by using single transition operators. Using such controlled phase shift gates, the implementation of Deutsch-Jozsa and parity algorithms are demonstrated. Search algorithms play an important role in the filed of information processing. Grovers quantum search algorithm achieves polynomial speed-up over the classical search algorithm. Bruschweiler proposed a Liouville space search algorithm which achieve polymonial speed-up. This algorithm requires a weakly coupled system with a mixed initial state. In chapter 5 we modified the Bruschweiler’s algorithm, so that it can be implemented on a weakly as well as strongly coupled system. The experiments are performed on a strongly dipolar coupled four-qubit system. The experiments from four spin-1/2 nuclei of a molecule oriented in a liquid crystal matrix. Chapter 6 describes the implementation of controlled phase shift gates on a quadrupolar spin-7/2 nucleus, using non-adiabatic geometric phases. The eight energy levels of spin-7/2 nucleus, form a three qubit system. A general procedure is given, for implementing a controlled phase shift gate on a system consisting of any number of energy levels. Finally Collin’s version of three-qubit DJ algorithm using multi-frequency pulses, is implemented in the spin-7/2 system.

Pantothenate synthetase (PS), which catalyzes the last step in the pantothenate (vitamin B5) biosynthesis, is a dimeric enzyme present in bacteria, fungi and plants. The enzymatic properties of PS from Escherichia Coli, Mycobacterium tuberculosi, Fusarium Oxysporum, Lotus japonicus, Oryza sativum, Brassica napus and Arabidopsis thaliana have been characterized. The chemical reaction and the proposed mechanism of reaction are identical for PS, irrespective of the source. However, from an enzyme mechanistic point of view, plant PS’s are dissimilar to their bacterial counterparts, in that they exhibit “allosteric behavior”, a property that has not been observed in the bacterial enzyme. The behavior is quite remarkable when one takes into consideration the fact that plant PS’s share a high degree of sequence identity (~ 40%) with the bacterial enzymes. Even more intriguing is the structural mechanism proposed to explain the observed differences in structure between the PS’s from E.Coli and M.tb, which share a 42% sequence identity. Till date there is no structural information available on the plant PS’s and of the substrate bound conformation of E.coli PS. This thesis aims to provide an understanding on some aspects of the structure – function relationship of this physiologically important enzyme. Specifically, the solution properties of E. coli PS have been examined using high-resolution multinuclear, multidimensional NMR methods. Given the large size of the full-length protein (~ 63 KDa), the structurally distinct N and C-terminal domains were cloned and expressed as individual proteins and their properties investigated. Towards this end, the tertiary fold of the 40 kDa dimeric amino-terminal domain of E. coli pantothenate synthetase has been determined using multidimensional multinuclear nuclear magnetic resonance (NMR) methods (PDB entry 2k6c). Sequence specific resonance assignments for backbone HN, 15N, 13Cα, 13C', sidechain 13Cβ and aliphatic 13CH3 (of isoleucine, leucine and valine residues) were obtained using perdeuterated ILV-methyl protonated samples (BMRB entry 6940). Secondary structure of nPS was determined from 13C secondary chemical shifts and from short and medium range NOEs. Global fold of the 40 kDa homo-dimeric nPS has been determined using a total of 1012 NOEs, 696 dihedral angles, 260 RDCs, 155 hydrogen bonds, radius of gyration potential, non-crystallographic symmetry potential and database derived potential based upon the Ramachandran map. The calculated structures, which show that the N-terminal domain forms a homo-dimer in solution, is of high stereochemical quality as judged by the Ramachandran statistics (70% of the residues have backbone dihedral angles in the allowed region, 25.5% in the additionally allowed region, 4.0% in generously allowed region, and only 0.5% in disallowed region). Dynamics of nPS, which has rotational correlation time τc of 17.3 ns, was investigated by 15N relaxometry measurements. Results of these studies indicate that the E. coli protein exhibits dynamic nature at the dimer interface. These structural and dynamic features of the protein were found to be of interest when correlated with NMR based substrate binding studies. Interaction of homo-dimeric amino-terminal domain (nPS) of E. coli pantothenate synthetase (PS; encoded by the gene panC; E.C. 6.3.2.1) with the substrates pantoate, β-alanine, ATP and the product pantothenate has been studied using isotopically edited solution NMR methods. Addition of pantoate prior to ATP has led to the interesting observation that pantoate binds each monomer of nPS at two sites. ATP displaces a molecule of pantoate from the ATP binding site. β-alanine and pantothenate do not bind the protein under the condition studied. Binding of pantoate and ATP also manifests as changes in residual dipolar couplings (RDCs) of backbone 1H-15N pairs in nPS when compared to the free form of the protein. Structures of homo-dimeric nPS bound to two molecules of pantoate (PDB entry 2k6e) as well as to pantoate + ATP (PDB entry 2k6f) were calculated by inclusion of hydrogen bonds between the ligands and backbone 1H-15N pairs of nPS in addition to other NMR derived restraints. The ligand bound structures have been compared to the similar forms of the M. tb PS. Structure of each monomer of nPS bound to pantoate and ATP shows the substrates in a favorable orientation for the intermediate pantoyl adenylate to form. Moreover, at all stages of substrate binding the symmetry of the dimer was preserved. A single set of resonances was observed for all protein-ligand complexes implying symmetric binding with full-occupancy of the ligands bound to the protein. In an effort to understand the structural basis of the observed enzymatic properties of plant PS’s, a structural model of the Arabidopsis PS was constructed. The results of these structural and substrate binding studies strongly suggest that 1 Substrate binding to PS occurs only at the active site. 2 There are no additional substrate binding sites which could potentially participate as regulatory sites. 3 Pantoate does not bind at the dimer interface to induce the observed homotropic effects. 4 The structural results presented on the substrate bound forms of nPS have direct implication for the development of novel antibacterial and herbicidal agents. Recently a great deal of interest has been evinced on the effects of molecular crowding on protein folding / unfolding pathways. Nuclear magnetic resonance is the only method by which high resolution structural information can be obtained on partially denatured states of a protein under equilibrium condition. Recent methodological advances have enabled the determination of high resolution structures using information embedded in the residual dipolar couplings. Molecular crowding using confinement may thus reveal important details about chaperone mediated protein folding. We have attempted to develop a protocol to study the effects of molecular confinement by sequestering proteins in poly-acrylamide gels and then subjecting these protein molecules to denaturation and then characterize these states by nuclear magnetic resonance. The preliminary results of these studies are described here.

Arrays of free-standing metallic nanorods are promising candidates for sensors, switches and spectroscopy. They have structure sizes much smaller than the wavelength of visible light, feature a long-axis surface plasmonic resonance (LSPR) and show metamaterial-like properties. This thesis provides a detailed investigation of their linear optical properties and highlights some nonlinear optical aspects. By means of graded structures having a tunable LSPR and three different theoretical models -- a numerical multiple-multipole method (MMP) model, a semi-analytic collective surface plasmon (CSP) model and an analytic dipolar interaction model (DIM) -- the optical properties were analyzed. Using the DIM, the experimentally observed blueshift of the LSPR in comparison to a single nanorod is confirmed and a physical explanation is provided. The LSPR strongly depends on the angle of incidence and the rod diameter. However, for a varying length the changes are small with the long-axis mode showing a lower energy limit. The detailed arrangement of the nanorods and the azimuthal angle of the incoming light plays only a minor role for small nanorod separations. Similarly, the dependence on the metal is the same as for single particles, whereas the sensitivity to the surrounding dielectric is much stronger than in the single-particle case. For longer nanorods made of silver, angle-dependent higher-order modes are observed and reproduced using MMP. The CSP model is applied and Fabry-Pérot-like oscillations of the CSPs are found. The propagating nature of these modes leads to the discovery that the p component of the transmitted light experiences a phase jump and to the observation of polarization conversion inside the structures. Negative refraction is found in nanorod arrays; it is revealed that a negative energy flux occurs only within a bandwidth given by the LSPR of a single nanorod and the array resonance. For smaller wavelengths, the in-plane component of the Poynting vector reverses, leading to an (extraordinary) positive flux. At the LSPR itself, the flux parallel to the surface is found to be zero. The negative refraction is also exploited to mimic a nanolens with structure parameters that are infact technical realizable. In the visible regime the nanolens shows a NA of 1.06 and superlens-like features such as identical rotation and linear translation of image and object. The nonlinear measurements on graded structures are conducted using femtosecond pump-probe spectroscopy resulting in kinetics showing either an increased transmission or absorption with signal changes of up to 40%. By converting them to transient spectra and by comparison with the literature, electron distribution changes at the Fermi edge and hot electrons/phonons are identified as the main reasons for the changes. Probing at the inflection points of the LSPR reveals ultrafast signals. Using transient spectra they are traced back to a short blueshift of the LSPR. / Strukturen aus frei stehenden metallischen Nanostäbchen versprechen interessante An­wendungen als Sensoren, Schalter und in der Spektroskopie. Da ihre Strukturgrößen kleiner als die Wellenlänge des sichtbaren Lichtes sind, besitzen sie eine langachsige Oberflächen­plasmonenresonanz (LSPR) und weisen metamaterialartige Eigenschaften auf. In dieser Dissertation werden die linearen und nichtlinearen optischen Eigenschaften solcher Struk­turen im Detail untersucht. Mit Hilfe von Gradientenstrukturen, die eine durchstimmbare LSPR besitzen, und dreier theoretischer Modelle – eines numerischen Modells basierend auf der Methode der mul­tiplen Multipole (MMP), eines semianalytischen Modells kollektiver Oberflächenplasmonen (CSP) sowie eines analytischen dipolaren Interaktionsmodells (DIMs) – werden die op­tischen Eigenschaften analysiert. Unter Verwendung des DIMs wird die experimentell beobachtete Blauverschiebung der LSPR im Vergleich zur Resonanz eines Einzelstäbchens bestätigt und eine physikalische Erklärung dafür geliefert. Die LSPR ist stark vom Einfallswinkel und vom Stäbchendurch­messer abhängig. Im Unterschied dazu sind die Änderungen bei einer Längenvariation klein, wobei die langachsige Mode ein unteres Energielimit aufweist. Weiterhin haben die genaue Anordnung der Stäbchen und der azimutale Winkel des einfallenden Lichtes nur einen untergeordneten Einfluss. Die Abhängigkeit vom verwendeten Metall ist analog zu einem Einzelstäbchen, während die Empfindlichkeit in Bezug auf das Umgebungsmedium wesentlich stärker ist. Längere Nanostäbchen aus Silber zeigen winkelabhängige Moden höherer Ordnung, welche mittels MMP reproduziert werden können. Das CSP-Modell wird ebenfalls darauf ange­wendet, wobei Fabry-Pérot-artige Oszillationen der CSPs entdeckt werden. Die propa­gierende Natur der CSPs führt zur Entdeckung eines Phasensprungs der p‑Komponente des transmittierten Lichtes sowie zur Beobachtung von Polarisationskonversion in den Strukturen. Nanostäbchen-Arrays weisen außerdem negative Brechung auf. Es wird gezeigt, dass ein negativer Energiefluss nur in dem Wellenlängenbereich zwischen der LSPR der Einzelstäb­chen und der Arrayresonanz auftritt. Für kleinere Wellenlängen kehrt sich die in der Ebene befindende Poynting-Vektor-Komponente um, was zu einer (außerordentlichen) positiven Brechung führt. An der LSPR selbst ist der zur Strukturebene parallele Fluss Null. Die negative Brechung wird ferner ausgenutzt, um eine Nanolinse mit realistischen Struktur­parametern zu simulieren. Im sichtbaren Bereich zeigt sie eine NA von 1,06 und super­linsenartige Eigenschaften, wie eine identische Rotation und eine lineare Translation von Bild und Objekt. Die nichtlinearen Messungen an Gradientenstrukturen werden mittels Femtosekunden-Pump-Probe-Spektroskopie durchgeführt und liefern Kinetiken, welche entweder eine ver­stärkte Transmission oder eine verstärkte Absorption mit Signalstärken von bis zu 40% aufweisen. Durch Konvertierung in transiente Spektren und Vergleich mit der Literatur werden eine veränderte Elektronverteilung an der Fermi-Kante und heiße Elektronen/Pho­nonen als Ursache für die Änderungen gefunden. Das Abtasten mit dem Probe-Puls an den Wendepunkten der Resonanz offenbart ultraschnelle Signale. Mit Hilfe der transienten Spektren wird dies auf eine kurzzeitige Blauverschiebung der LSPR zurückgeführt.

In der vorliegenden Arbeit wird über 1,3-dipolare Cycloadditionen mit Lachgas (N2O) unter milden Reaktionstemperaturen (≈ RT) berichtet. N2O ist ein sehr unreaktives 1,3-dipolares Reagenz. Bisher in der Literatur durchgeführte 1,3-dipolare Cycloadditionen mit N2O benötigten immer sehr drastische und gefährliche Reaktionsbedingungen (bis zu 300°C und 500 atm.). Dabei entstanden nach einer (postulierten) einleitenden 1,3-dipolaren Cycloaddition von N2O an Olefine oder Alkine immer nur stickstofffreie Reaktionsprodukte. Durch den Einsatz von hochreaktiven Cycloalkinen als 1,3-Dipolarophile konnten erstmals 1,3-dipolare Cycloadditionen mit N2O bei deutlich milderen Bedingungen (–25°C bis +60°C) als den bisher bekannten durchgeführt werden. Dabei war es mit Cyclooctin und Cycloocten-5-in erstmals möglich, stabile und vollständig charakterisierbare Reaktionsprodukte zu erhalten, die alle drei Atome des addierten N2O-Moleküls enthalten. Mit 4,5-Didehydro-2,3,6,7-tetrahydro-3,3,6,6-tetramethylthiepin konnte sogar erstmals ein alpha-Diazoketon durch 1,3-dipolare Cycloaddition von N2O erhalten und dieses bei –25°C NMR-spektroskopisch untersucht werden. Diese alpha-Diazoketone entstehen aus der elektrocyclischen Ringöffnung der entsprechenden 1,2,3-Oxadiazole welche aus der Cycloaddition von N2O und dem eingesetzten Cycloalkin stammen. Mit alpha-substituierten Cyclooctinen konnten auch 1,3-dipolare Cycloadditionen mit N2O bei milden Temperaturen durchgeführt werden, um stickstofffreie Reaktionsprodukte zu erhalten.

La réalisation de condensats de Bose-Einstein et de gaz de Fermi dégénérés ont déclenché d'énormes progrès dans les méthodes théoriques ainsi que dans la mise en place de nouvelles techniques expérimentales. Parmi celles-ci, de fascinantes possibilités viennent de l'implémentation de réseaux optiques : potentiels périodiques pour atomes neutres créés à travers l'interférence de rayons laser. Un gaz dégénéré dans un réseau optique peut être forcé dans des pièges fortement anisotropes, jusqu'à réduire la dimensionnalité du système physique. Du point de vue fondamental, le comportement des ondes de matière en dimensions réduites éclaircit les propriétés intrinsèques des interactions entre particules. En outre, ces systèmes à dimensionnalité réduite peuvent être manipulés afin de créer des simulateurs quantiques de la matière condensée, comme par exemple des réseaux à deux dimensions, dans un environnement pur et contrôlable. Motivés par les passionnantes perspectives de ce domaine, on a consacré cette Thèse à l'étude théorique de deux systèmes dans lesquels une onde de matière se propage en dimensions réduites. L'interaction dipôle-dipôle, à longue portée et anisotrope, affecte fortement le comportement des gaz quantiques. Les progrès expérimentaux dans ce domaine florissant permettront bientôt de piéger dans des réseaux optiques un gaz dégénéré de dipôles. Dans la première partie de cette thèse, on considère l'apparition d'une seule résonance dipolaire dans l'interaction entre deux particules pour différents systèmes quasi-unidimensionnels. On propose une approche à deux canaux qui décrit cette résonance dans un piège harmonique fortement allongé “en forme de cigare”, qui représente l'approximation d'un site d'un réseau optique quasi-unidimensionnel. A` ce stade, on développe un nouveau modèle étendu de Bose-Hubbard atome-dimère, qui est valable pour des bosons dipolaires dans un réseau optique quasi-unidimensionnel. On étudie donc le diagramme de phase du modèle pour T =0 par la diagonalisation exacte de systèmes de petite taille, en soulignant les effets de la résonance dipolaire sur la physique à plusieurs corps dans le réseau. Dans la seconde partie de la thèse, on propose un modèle pour réaliser des simulateurs quantiques de cristaux bidimensionnels avec des atomes froids, basé sur le piégeage indépendant de deux espèces atomiques. La première constitue une onde de matière bidimensionnelle qui interagit exclusivement avec les atomes de la seconde espèce, piégés aux nœuds d'un réseau optique bidimensionnel. En introduisant une approche théorique générale, on examine les propriétés de transport de l'onde de matière. On propose des exemples d'application pour réseaux soit de Bravais (carré, triangulaire), soit de non-Bravais (graphène, kagomé), en étudiant soit des systèmes périodiques idéaux, soit des systèmes de taille expérimentale et désordonnés. Les caractéristiques d'un réseau atomique artificiel dépendent de l'intensité de l'interaction entre les deux espèces, qu'on montre être largement réglable grâce à des résonances à dimensionnalité mixte de type 0D-2D. / The experimental achievement of Bose-Einstein condensation and Fermi degeneracy with ultracold gases boosted tremendous progresses both in theoretical methods and in the development of new experimental tools. Among them, intriguing possibilities have been opened by the implementation of optical lattices: periodic potentials for neutral atoms created by interfering laser beams. Degenerate gases in optical lattices can be forced in highly anisotropic traps, reducing the effective dimensionality of the system. From a fundamental point of view, the behavior of matter waves in reduced dimensions sheds light on the intimate properties of interparticle interactions. Furthermore, such reduced-dimensional systems can be engineered to quantum-simulate fascinating solid state systems, like bidimensional crystals, in a clean and controllable environment. Motivated by the exciting perspectives of this field, we devote this Thesis to the theoretical study of two systems where matter waves propagate in reduced dimensions.The long-range and anisotropic character of the dipole-dipole interaction critically affects the behavior of dipolar quantum gases. The continuous experimental progresses in this flourishing field might lead very soon to the creation of degenerate dipolar gases in optical potentials. In the first part of this Thesis, we investigate the emergence of a single dipolar-induced resonance in the two-body scattering process in quasi-one dimensional geometries. We develop a two-channel approach to describe such a resonance in a highly elongated cigar-shaped harmonic trap, which approximates the single site of a quasi-one- dimensional optical lattice. At this stage, we develop a novel atom-dimer extended Bose- Hubbard model for dipolar bosons in this quasi-one-dimensional optical lattice. Hence we investigate the T=0 phase diagram of the model by exact diagonalization of a small- sized system, highlighting the effects of the dipolar-induced resonance on the many-body behavior in the lattice.In the second part of the Thesis, we present a general scheme to realize cold-atom quantum simulators of bidimensional atomic crystals, based on the possibility to independently trap two different atomic species. The first one constitutes a two-dimensional matter wave which interacts only with the atoms of the second species, deeply trapped around the nodes of a two-dimensional optical lattice. By introducing a general analytic approach, we investigate the matter-wave transport properties. We propose some illustrative appli- cations to both Bravais (square, triangular) and non-Bravais (graphene, kagomé) lattices, studying both ideal periodic systems and experimental-sized, eventually disordered, ones. The features of the artificial atomic crystal critically depend on the two-body interspecies interaction strength, which is shown to be widely tunable via 0D-2D mixed-dimensional resonances.

The thesis entitled "Pushing the Limits of NMR Sensitivity and Chiral Analysis: Design of New NMR Methods and Bio-molecular Tools" consists of six chapters. The research work reported in this thesis is focused on the development of novel chemical and NMR methodological approaches for enantiomeric analysis and mea- surement of residual dipolar couplings (RDCs), and the development of sensitivity enhanced slice selective NMR experiments for obtaining pure shift 1H spectra and the measurement of scalar couplings. The thesis is divided into two parts. The Part I comprises chapters 2-4, where the enantiomeric analysis is discussed, which includes newly developed chiral reagents, two new weak chiral aligning media and design of novel NMR techniques. Part II comprises chapters 5 and 6, which discusses new sensitivity enhanced slice selective NMR techniques. Chapter 1 gives a general introduction to NMR and the problems investigated in the remaining chapters of the thesis. The chapter starts with a brief discussion on the introduction, advancements and general applications of NMR, discussion is also given on the NMR approaches for enantiomeric analysis both in isotropic and anisotropic phases and the measurement of RDCs, including the benefits and limitations associated with each approach. The chapter sets the tone by discussing limitations of the existed NMR enantiomeric approaches and slice-selective techniques, and builds the bridge for the rest of the chapters by addressing these limitations. The chapter also introduces slice selective experiments, their benefits over other conventional methods and limitations. Additional introductory notes are also given on some related concepts. Part I : NMR Chiral analysis and RDCs measurements Chapter 2 discusses chiral sensing properties of RNA nucleosides and their utility as chiral derivatizing agents for the enantio-discrimination of 1o-amines using one dimensional 1H NMR. A three component protocol has been proposed for the complexation of nucleosides with amines, which is rapid, economical and provides maximum diastereomeric conversion. The chiral differentiating ability of nucleosides are examined for different amines based on the 1H NMR chemical shift differences between the diastereomers (∆δ R, S ). Enantiomeric differentiation has been observed at multiple chemically distinct proton sites. It is observed that adenosine and guanosine exhibit large chiral differentiation (∆δ R, S ) due to the presence of a purine ring. The comparison of the diastereomeric excess (de) measured by NMR with those of the gravimetrically prepared ratios are in excellent agreement with each other confirming the robustness of these RNA nucleosides in discriminating primary amines. Chapter 3 establishes the smooth connectivity with the chapter 2 by discussing the limitations of the enantiomeric discrimination using NMR in isotropic solutions. This chapter discusses two new water compatible aligning media that were developed based on self-assembling strategy of small bio-molecules. The self-assembled folic acid, and the binary mixture of 50-GMP and guanosine are introduced as two novel weak aligning media. The properties of these low ordered media have been systematically studied for their easy preparation, physical parameter dependent tunability of their degree of alignment, mesosphere sustainability over a broad range of temperature and the concentration of the ingredients, and the phase reproducibility. The applications of both these new media are demonstrated for chiral and pro-chiral discrimination and also for the measurement of RDCs. Both these liquid crystalline media could be tuned to very low degree of alignment (order parameter of the order of 10−4), which provides simple first order spectra of molecules aligned in them, the analysis provide order dependent NMR spectral parameters. The 50-GMP:guanosine orienting medium can be prepared in less than 1 hour, and has been demonstrated to be an ideal medium for the determination of RDCs that are used as restraints in the structure calculations of small molecules. Chapter 4 describes 1H NMR spectral complexity in isotropic and anisotropic phases and its consequences on enantiomeric analysis. In circumventing such problems, new NMR techniques have been developed and the spin dynamics involved in the designed sequences are discussed. The newly developed 2D 1H NMR experimental method termed as RES-TOCSY, and its applicability for resolving R and S enantiomeric or diastereomeric peaks of all the coupled proton spins in isotropic phase is discussed. The utility of the developed method is demonstrated in diverse situations, such as, for suppressing impurities peaks, resolving the severely overlapped peaks and unraveling the peaks masked due to severe line broadening when metal complexes are used as chiral auxiliaries. The advantages and limitations of the method over other methods available in the literature are discussed and the significant advantage of the present method is illustrated by spectral comparison with J-resolved experiment. The appli- cation of the method for the accurate measurement of enantiomeric excess has also been demonstrated. The chapter also introduces another NMR experimental technique developed for resolving enantiomeric peaks and complete unraveling of R and S spectra in anisotropic phase. The developed 2D NMR method is cited in the literature as CH-RES-TOCSY. In addition to spectroscopic visualization of R and S spectra, the method also yields C-H RDCs. The applicability of the new experiment has been demonstrated on a chosen example. The wide utility of the method has also been demonstrated for the assignment of symmetric cis- and trans- isomers. Part II : Sensitivity Enhancement of Slice selective NMR Experiments Chapter 5 describes applications of slice selective NMR experiments over conven tional NMR methods and their limitations as far as the sensitivity of signal detection is concerned, especially in low concentrated samples. The chapter introduces the implementation of Acceleration by Sharing Adjacent Polarization (ASAP) technique in slice selective experiments. It is convincingly demonstrated that ASAP helps in reducing inter scan relaxation delay and consequently permits acquisition of more number of scans in a given time, resulting in the gain in signal enhancement by a factor of two. The pulse sequences have been suitably designed for obtaining the pure shift 1H spectra and in G-SERF experiment for the measurement of 1H-1H couplings, both with significantly enhanced signal intensities. Chapter 6 describes new sensitivity enhanced slice selective NMR methods for mea- surement of scalar couplings. A new experiment has been developed which is named as Quick G-SERF (QG-SERF). It is a 1D NMR slice selective method developed based on real time spin manipulation technique. The method gives multiple scalar couplings of a selected spin with simplified multiplets, which is analogous to the 2D G-SERF but with considerable saving in instrument time by 1-2 orders of magnitude. The rapidness of the experiment arises due to reduced dimensionality. The spin dynamics involved in the pulse sequence and its working principle have been described. The application of the method is illustrated for the measurement of 1H-1H couplings. The sequence has been further improved to obtain the heteronuclear couplings between two abundant spins in an orchestrated manner and has been demonstrated for measurement of 1H-19F couplings. This sequence cited as HF-QG-SERF has been implemented on the molecules containing number of chemically non-equivalent fluorine atoms.

Le travail de thèse est consacré à l'étude numérique de nanoparticules (NPs) magnétiques core@shell Fe3O4@CoO présentant des propriétés d'échange bias (EB) en utilisant la méthode Monte Carlo (MC). En particulier, nous nous sommes concentrés sur l'étude de l'effet des réponses collectives (interactions inter-particules telles que les interactions dipolaires (ID)) sur les propriétés magnétiques de ces structures. Des résultats expérimentaux préliminaires, montrant l'existence d'une relation entre le décalage du cycle d'hystérésis et l'interaction entre NPs, ont motivé le travail numérique mené dans le cadre de cette thèse.La première partie de ce mémoire est une étude méthodologique visant à trouver les conditions optimales pour simuler les cycles d'hystérésis d'une façon correcte par MC.Les résultats révèlent une dépendance linéaire entre le champ coercitif Hc et la constante d'anisotropie effective pour des conditions non biaisées (algorithme libre, algorithme du cône, algorithme mixte). La deuxième partie est consacrée à l'étude, à l'échelle atomique, des nanostructures présentant l'EB dont nous avons reproduit les deux caractéristiques (un décalage du cycle d'hystérésis, une augmentation importante de Hc).Nous avons également proposé une méthode permettant l'évaluation de la valeur de l'anisotropie effective.En passant à l'échelle d'une assemblée de NPs, plusieurs modèles furent étudiés. Nous arrivons à interpréter les résultats expérimentaux selon le degré d'agrégation des NPs. Nous montrons que l'agrégation (interactions d'échanges entre les NPs) a un effet direct sur le champ d'échange bias, mais le rôle d'ID sur le champ d'échange mérite des études complémentaires. / This thesis is dedicated to the numerical study by means of Monte Carlo (MC) simulations of core@shell Fe3O4@CoO magnetic nanoparticles (NPs) presenting exchange bias properties (EB). In particular, we focused our study on the effect of collective responses (inter-particle interactions as dipolar interactions (DI)) on the magnetic properties of these structures. Our numerical work is motivated by some preliminary experimental results showing the existence of a relationship between the hysteresis loop shift (exchange bias field) and the interaction between NPs. The first part of this thesis is a methodological study to figure out the optimal conditions to simulate hysteresis loops correctly by MC. The results reveal that the coercive field Hc is linearly related to the effective anisotropy constant for non-biased conditions (free algorithm, cone algorithm, mixed algorithm). The second part is dedicated to the study of exchange-biased nanostructures at the atomic scale. We have been able to reproduce both characteristics of EB (hysteresis loop shift, significant increase in Hc). A method allowing the evaluation of the effective anisotropy has been proposed. Considering an assembly of nanoparticles, several models are studied. The experimental results are interpreted according to the degree of aggregation of NPs. It was shown that the aggregation (exchange interactions between NPs) has a direct effect on the exchange bias field, but the role of the ID on the exchange field requires complimentary calculations to be clarified.