Superatomic crystals (SACs) with tunable physical properties offer a new approach to the design of inorganic nanomaterials. Very little is known about how these systems function, or how their properties can be transformed. Here I describe work that helps to develop an understanding of how functional properties behave in SACs, and how they can be altered through superatomic intercalation or with phase transitions. Chapter 1 describes work characterizing the thermal transport behavior of SACs. We find that heat transfer is dominated by coherent inter-cluster phonons with vibrational frequencies determined by the periodicity of the SAC superstructure. We also demonstrate a transformation from amorphous to crystalline thermal transport behavior through manipulation of the vibrational landscape and orientational order of the superatoms. Chapters 2 and 3 describe the intercalation of a porous superatomic host, [Co6Te8(PnPr3)6][C60]3. We find that guests can be inserted into the superstructure through single-crystal-to-single-crystal transformations, dramatically transforming the electronic properties of the SAC. Using electronic absorption spectroscopy, electrical transport measurements and electronic structure calculations, we demonstrate that the intercalation is driven by the exchange of charge between the host, establishing an exciting design space for the preparation of superatomic materials. Chapter 4 describes a hierarchical solid, [Co6Te8(PEt3)6][C70]2, in which the delicate balance of interactions between constituent building blocks produces two separate phase transitions: one affecting thermal transport properties, the other transforming the electronic and magnetic behavior of the SAC. We use a wide range of structural and spectroscopic characterization tools to understand the mechanism of each transformation. This work establishes a new ability to program functional phase transitions into cluster-assembled materials. In a completely different area of study, chapter 5 describes a new covalent organic framework (COF) whose unique structure enables a post-synthetic topochemical polymerization of the framework’s linker fragments. The polymerization of the 1-3 butadiyne into a polydiacetylene backbone covalently crosslinks the material without compromising its original crystallinity. This work not only enables the preparation of more structurally resilient COFs, but also diversifies the design space for this emerging class of materials.

Quasicrystals are long-range ordered and yet non-periodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, self-similarity, and the presence of non-trivial structure on all scales. The concept of aperiodic order has been extensively studied in mathematics and geometry, exemplified by the celebrated Penrose tiling. However, the understanding of physical quasicrystals (the vast majority of them are intermetallic compounds) is still incomplete owing to their complexity, regarding both growth processes and stability. Ultracold atoms in optical lattices offer an ideal, yet untested environment for investigating quasicrystals. Optical lattices, i.e. standing waves of light, allow the defect-free formation of a large variety of potential landscapes, including quasiperiodic geometries. In recent years, optical lattices have become one of the most successful tools in the large-scale quantum simulation of condensed-matter problems. This study presents the first experimental realisation of a two-dimensional quasicrystalline potential for ultracold atoms, based on an eightfold symmetric optical lattice. It is aimed at bringing together the fields of ultracold atoms and quasicrystals - and the more general concept of aperiodic order. The first part of this thesis introduces the theoretical aspects of aperiodic order and quasicrystalline structure. The second part comprises a detailed account of the newly designed apparatus that has been used to produce quantum-degenerate gases in quasicrystalline lattices. The third and final part summarises the matter-wave diffraction experiments that have been performed in various lattice geometries. These include one- and two-dimensional simple cubic lattices, one-dimensional quasiperiodic lattices, as well as two-dimensional quasicrystalline lattices. The striking self-similarity of this quasicrystalline structure has been directly observed, in close analogy to Shechtman's very first discovery of quasicrystals using electron diffraction. In addition, an in-depth study of the diffraction dynamics reveals the fundamental differences between periodic and quasicrystalline lattices, in excellent agreement with ab initio theory. The diffraction dynamics on short timescales constitutes a continuous-time quantum walk on a homogeneous four-dimensional tight-binding lattice. On the one hand, these measurements establish a novel experimental platform for investigating quasicrystals proper. On the other hand, ultracold atoms in quasicrystalline optical lattices are worth studying in their own right: Possible avenues include the observation many-body localisation and Bose glasses, as well as the creation of topologically non-trivial systems in higher dimensions.

Neste trabalho reportamos a produção da primeira armadilha magneto-ótica que confina simultaneamente duas espécies atômicas distintas: Sódio e Potássio. Para podermos realizar este aprisionamento, foi necessário vencer algumas dificuldades técnicas que justificam, inclusive, a escolha dos elementos utilizados. Nossa armadilha também foi utilizada para realizar o primeiro estudo de colisões frias entre átomos de espécies diferentes. Experimentalmente, as informações sobre essas colisões são obtidas através da medida da dinâmica de perdas da armadilha de S6dio em presença e ausência de átomos frios de Potássio. Observamos que o efeito de colisões heteronucleares e dez vezes menor do que as homonucleares. Esta diferença já era esperada devido ao menor alcance dos potenciais de interação entre átomos no caso de espécies distintas. Nossos resultados são comparados a uma teoria semi-clássica simples e se encontram em bom acordo com as previsões. Introduzimos uma nova técnica que consiste em mudar repentinamente a intensidade do laser aprisionador e observar a variação do número de átomos aprisionados. Medimos a taxa de perdas por colisão entre átomos de Potássio frios como função da intensidade do laser aprisionador. Essa técnica nos permite alcançar o regime de baixas intensidades, inclusive abaixo da intensidade de saturação, sem as limitações da técnica tradicional. Aplicamos essa técnica ao aprisionamento simultâneo e medimos a taxa de perdas por colisão do sódio na presença e ausência de potássio. Com essa medida somos capazes de estimar a seção e choque entre sódio e potássio ambos no estado fundamental / In this thesis we report the production of the first magneto-optical trap that confines simultaneously two atomic species, sodium and potassium. In order to realize this experiment we had to overcome some technical difficulties that justified our choice of these two elements. This trap was used to study cold collisions between two different species. The information about these collisions is obtained experimentally from the dynamics of the sodium trap loss process in the presence and absence of potassium atoms. We observed that the heteronuclear effect is ten times smaller than the homonuclear one. This difference is explained by the smaller range of the interaction potentials between different species. Our results are compared with the theoretical predictions of the semi-classical theory and show a good agreement with the predictions. We have introduced a new technique which consists of a sudden decrease of the laser intensity, after which we observe the temporal variation in the number of trapped atoms. We have measured the loss rate coefficient between cold potassium atoms as a function of light intensity of the trapping laser. This technique allowed us to reach the very low intensity regime, as low as 30% of the saturation intensity, without compromising the loading process. We applied this technique to the simultaneous trapping and measured the loss rate coefficient between cold sodium atoms in the presence and absence of cold potassium atoms. With this measurement we can estimate the value of the cross section between sodium and potassium in the ground state

Estudamos, de uma maneira sistemática, o campo hiperfino de contacto em átomos livres a fim de analisar a qualidade das funções de onda obtidas a partir da aproximação do operador de massa, da teoria de muitos corpos. 0 campo de contacto depende diretamente da função de onda dos eléctrons na origem e a aproximação utilizada para calculá-lo leva em conta tanto a dependência do exchange com a energia cinética do elétron quanto a inclusão da correlação coulombiana eletrônica, sem necessidade de parâmetros ajustáveis. Observamos que os resultados encontrados para tais campos, como esquema proposto, são competitivos com os de Hartree-Fock e por ser um esquema mais simples pode substituí-lo na obtenção de grandezas físicas relacionadas com as funções de onda dos sistemas a serem estudados. / The hyperfine contact field for free atoms has been calculated within the framework of the mass operator approximation for various atoms, in order to analyze the quality of the electronic wave functions. The mass operator approximation takes into account the electron-correlation effects as well as the dependence of the exchange with the velocity of the electrons. We found that the mass operator approximation to the exchange correlation effects yields values for the hyperfine contact field in good agreement with those obtained through the Hartree-Fock scheme. However, the mass operator approximation is simpler than the Hartree-Fock operator.

Let R be an integral domain. An atom is a nonzero nonunit x of R where x = yz implies that either y or z is a unit. We say that R is an atomic domain if each nonzero nonunit is a finite product of atoms. An atomic domain with only finitely many nonassociate atoms is called a Cohen-Kaplansky (CK) domain. We will investigate atoms in integral domains R with a unique maximal ideal M. Of particular interest will be atoms that are not in M^2. After studying the atoms in integral domains, we will narrow our focus to CK domains with a unique maximal ideal M. In this pursuit, we investigate atoms in M^2 for these CK domains. We will show that the minimal number of atoms needed to have an atom in M^2 is exactly eight. This disproves a conjecture given by Cohen and Kaplansky in 1946 that the minimal number would be ten. We then classify complete local CK domains with exactly three atoms.

This thesis presents the results of a series of experiments in which electrons are superelastically scattered from various laser excited states of sodium. The atoms, once in the optically prepared state, are forced to relax via the superelastic collision with an electron. The rate of detection of superelastically scattered electrons was measured as a function of the laser polarisation which enabled pseudo Stokes parameters to be determined. These pseudo Stokes parameters are functions of both optical pumping parameters and atomic collision parameters. The optical pumping parameters describe the laser-atom interaction and the atomic collision parameters describe the electron-atom collision process. Three different laser excitation mechanisms were used to optically pump the atoms into various excited states. The first of these used a single laser tuned to the 32S 112(F'=2 hyperfine state)-~32P312 transition. The excited atoms underwent a superelastic collision with an electron leaving the atom in the ground state and pseudo Stokes parameters were measured as a function of both scattering angle and incident electron energy. The second superelastic experiment, utilised a folded step excitation mechanism which employed two lasers tuned from the two hypethne states of the 32S112 ground state respectively to the 32P312 excited state. Power broadening effects in the single laser experiment cause the atoms to be optically pumped into the F= 1 hyperfine ground state. The laser powers used were not great enough to power broaden the hyperfine ground states and as such the F'= 1 sublevel effectively acted as a sink. The folded step excitation method enabled the excited state population to be increased so that data at larger scattering angles could be obtained. Stokes parameters from both of these experiments which had an incident energy range of 10eV to 30eV and an angular range of 5°-25° were compared to three current electron-atom scattering theories and previous experimental data. Overall, fair to good agreement was found between theory and experiments for the individual Stokes parameters. Losses of coherence was observed at small scattering angles (50.200) at 20eV and 25eV incident electron energies which were poorly modelled by the three different theories. The third superelastic experiment involved the use of two lasers of specified polarisation to stepwise excite the atoms to the 32D512 excited state. Superelastic collisions with incident electron energies of 20eV from the 32D512-*32P312~312 collision were studied at three different scattering angles and pseudo Stokes parameters for the case where the polarisations of the radiation from the lasers were parallel were measured. The single step and folded step laser-atom interactions for it excitation were modelled using a full quantum electrodynamical treatment so that the optical pumping parameters from the single and folded step experiments could be investigated. Equations of motion were derived in the Heisenberg picture and it is shown that for the single laser case 59 equations of motion are required to fully model the interaction and for the folded step ease 78 equations of motion are required. The results of calculations demonstrated that the optical pumping parameters were sensitive to laser intensity, laser detuning and the Doppler width of the atomic beam. The theoretical quantum electrodynamical calculation results were in good agreement with the experimental results.

Atom chips are devices used to magnetically trap and manipulate ultracold atoms and Bose-Einstein condensates near a surface. In particular, permanent magnetic film atom chips can allow very tight confinement and intricate magnetic field designs while circumventing technical current noise. Research described in this thesis is focused on the development of a magnetic film atom chip, the production of Bose-Einstein condensates near the film surface, the characterisation of the associated magnetic potentials using rf spectroscopy of ultracold atoms and the realisation of a precision sensor based on splitting Bose-Einstein condensates in a double-well potential. The atom chip itself combines the edge of a perpendicularly magnetised GdTbFeCo film with a machined silver wire structure. A mirror magneto-optical trap collects up to 5 x 108 87Rb atoms beneath the chip surface. The current-carrying wires are then used to transfer the cloud of atoms to the magnetic film microtrap and radio frequency evaporative cooling is applied to produce Bose-Einstein condensates consisting of 1 x 105 atoms. We have identified small spatial magnetic field variations near the film surface that fragment the ultracold atom cloud. These variations originate from inhomogeneity in the film magnetisation and are characterised using a novel technique based on spatially resolved radio frequency spectroscopy of the atoms to map the magnetic field landscape over a large area. The observations agree with an analytic model for the spatial decay of random magnetic fields from the film surface. Bose-Einstein condensates in our unique potential landscape have been used as a precision sensor for potential gradients. We transfer the atoms to the central region of the chip which produces a double-well potential. A single BEC is formed far from the surface and is then dynamically split in two by moving the trap closer to the surface. After splitting, the population of atoms in each well is extremely sensitive to the asymmetry of the potential and can be used to sense tiny magnetic field gradients or changes in gravity on a small spatial scale.

Au début de mon travail de thèse dans l'équipe Atomes et Molécules Froides du Laboratoire Aimé Cotton, l'intérêt du groupe était, d'un côté, la préparation et la manipulation des molécules de Césium créées via photoassociation, et de l'autre, à la préparation d'un échantillon de Césium à basse température et de grande densité dans un piége dipolaire. Initialement, j'ai participé aux études de realization du piége dipolaire atomique, et ensuite aux études de préparation et de manipulation des molécules. Dans la période entre Novembre 2006 jusqu'a Octobre 2008 j'ai développé une série de techniques différentes pour le chargement d'un piége dipolaire à partir d'un réservoir atomique, réalisé soit par un piége magnétique, soit par un piége du type 'Dark-SPOT', soit par C-MOT (piége magnéto-optique comprimé) et un mêlasse optique. Au commencement du mon travail, un BEC de Césium a été rapporté un seule fois [Web03], après des années des efforts de plusieurs équipes [Sod98, Boir98, Thom04]. De plus, l'intérêt sur l'atome de Césium a augmenté à cause des expériences liées à la formation de trimères de Césium et des résonances du type 'Efimof' [Lee07, Knoo08]. La stratégie sur laquelle notre approche pour le chargement du piége dipolaire était basée, est discutée dans une publication rédigée avant mon intégration au sein d'équipe Atomes et Molécules Froides du Laboratoire Aimé Cotton [Comp06]. Il s'agit d'un chargement à partir d'un réservoir obtenu par un piége magnétique. L'objectif de cette proposition était la préparation d'un échantillon ultra froid avec un dispositif expérimental beaucoup plus simple que celui de la référence [Web03]. De plus, la proposition [Comp06] prédit la préparation d'un condensat de Césium en un temps beaucoup plus court que les temps de préparation rapportée dans la référence [Web03]. L'étude de la réalisation expérimentale de cette proposition théorique a déjà commencé, dans le cadre de la thèse de G.Stern [Stern08]. J'ai continué cette étude et j'ai réalisé plusieurs études avec différents types de réservoir (Dark-SPOT, C-MOT) et aussi de un type de chargement différent qui est basé sur le refroidissement par bandes latérales (Raman-Sideband Cooling). Toutes les piéges préparés par ces méthodes, avait une densité inférieure a celle nécessaire pour la réalisation d'un processus de refroidissement évaporatif, qui est nécessaire pour la réalisation d'un condensat. Les problèmes techniques que nous avons rencontrés vers Mai 2008 (destruction de vide), nous ont conduit d'arrêter les études de refroidissement des atomes, et de s'orienter vers les études de manipulation des molécules de Césium. Pendant cette période, l'équipe avait beaucoup progressé dans manipulation des molécules de Césium, et plus spécifiquement sur la réalisation du refroidissement du degré de liberté qui correspond à la vibration des molécules. La nouvelle technique que l'équipe avait introduit et qui est rapporté à la référence [Vit08], permet le refroidissement de la vibration des molécules de Césium par un laser femtoseconde faconné, avec un processus de pompage optique [Kast66]. Mon objectif dans la thématique de la manipulation des molécules froides, était d'étudier la généralisation de cette technique. Par example le transfert de la population moléculaire dans un seul état vibrationnel pré – sélectionné a été observé. Ce résultat est discuté dans la référence [Sof09]. Une autre généralisation est la réalisation du refroidissement vibrationnel et du transfert de la population moléculaire avec une source de lumière non cohérente, résultat qui est discuté dans la référence [Sof09b]. Une autre généralisation importante est le refroidissement de la rotation moléculaire. Cette étude théorique est discutée dans les articles de l'équipe auxquels j'ai participé [Vit09, Sof09, Sof09c], et les études expérimentales préliminaires dans la référence [Fio09]. Finalement, la généralisation de la technique pour le refroidissement vibrationnel des molécules heteronucleaires est discuté dans le dernière chapitre de ma thèse. Le document de ma thèse est donc divisé en deux parties, dans chacune d'elles je discute en détails ma contribution scientifique dans l'équipe Atomes et Molécules Froides du Laboratoire Aimé Cotton.

F. Bitter. / "February 1, 1962." "Reprinted from Applied Optics, vol.1, page 1, January 1962." / Army Signal Corps Contract No. W-36-039-sc-78108 Dept. of the Army Task 3-99-20-001 and Project 3-99-00-000.

This thesis reports experimental observations of electric fields using Rydberg atoms, including dc field measurements near the surface of an atom chip, and demonstration of measurement techniques for ac fields far from the surface. Associated theoretical results are also presented, including Monte Carlo simulations of the decoherence of Rydberg states in electric field noise as well as an analytical calculation of the statistics of dc electric field inhomogeneity near polycrystalline metal surfaces. DC electric fields were measured near the heterogeneous metal and dielectric surface of an atom chip using optical spectroscopy on cold atoms released from the trapping potential. The fields were attributed to charges accumulating in the dielectric gaps between the wires on the chip surface. The field magnitude and direction depend on the details of the dc biasing of the chip wires, suggesting that fields may be minimized with appropriate biasing. Techniques to measure ac electric fields were demonstrated far from the chip surface, using the decay of a coherent superposition of two Rydberg states of cold atoms. We have used the decay of coherent Rabi oscillations to place some bounds on the magnitude and frequency dependence of ac field noise. The rate of decoherence of a superposition of two Rydberg states was calculated with Monte Carlo simulations. The states were assumed to have quadratic Stark shifts and the power spectrum of the electric field noise was assumed to have a power-law dependence of the form 1/f^κ. The decay is exponential at long times for both free evolution of the superposition and and Hahn spin-echo sequences with a π refocusing pulse applied to eliminate the effects of low-frequency field noise. This decay time may be used to calculate the magnitude of the field noise if κ is known. The dc field inhomogeneity near polycrystalline metal surfaces due to patch potentials on the surface has been calculated, and the rms field scales with distance to the surface as 1/z^2. For typical evaporated metal surfaces the magnitude of the rms field is comparable to the image field of an elementary charge near the surface.