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The Mini-Numerical Electromagnetic Code (MININEC) program, a PC-Compatible version of the powerful NEC program, is used to design a new type of reduced-size antenna. The validity of the program to model simple well-known antennas, such as dipoles and monopoles, is first shown. More complex geometries such as folded dipoles, and meander dipole antennas are also analysed using the program. The final design geometry of a meander folded dipole is characterized with MININEC, yielding results that serve as the basis for the practical construction of the antenna. Finally, the laboratory work with a prototype antenna is described, and practical results are presented.

This thesis provides a summary of the laser system constructed in the Quantum Degenerate Gases Laboratory for laser cooling and trapping of 85/87Rband 6Li as well as of experiments that have been pursued in our lab to date. The first chapter provides an overview of the experimental focus of the QDG lab. The second and third chapters provide the fundamental theory behind laser cooling and trapping. The fourth chapter provides details of the laser system. The fifth chapter describes an experiment performed on the subject of dual-injection, performed in collaboration with Dr. James Booth of the British Columbia Institute of Technology (BCIT) involving the dual-injection of a single slave amplifier. The last chapter describes the progress made on the experimental setup needed for the study of Feshbach resonances between 85/87Rb and 6Li and the photoassociative formation of molecules. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Nitrogen-containing molecules are ubiquitous in both natural products and pharmaceutical drugs, thus an efficient method for the formation of these motifs is of great importance. Hydroamination, that is the addition of an N-H bond across an unsaturated carbon-carbon bond of an alkene or alkyne, stands out as a potential approach to obtain such molecules. To date, most research in this area relies on transition-metal catalysis to enable such reactivity. In efforts directed towards metal-free alternatives, we have developed a simple, metal-free hydroamination of alkenes using hydrazides. Further investigation into the corresponding reactivity of alkynes with hydrazides has provided access to novel azomethine imine products. In Chapter 2, expansion of the substrate scope with respect to the intramolecular hydroamination of alkenes using hydrazides, as well as studies directed towards elucidation of the mechanism of this reaction will be presented. The intramolecular hydroamination of alkynes using hydrazides and methods to access and isolate the azomethine imine products formed will be discussed in Chapter 3.

This thesis is a continuation of a study of molecular moments begun by Joseph T. Fielder. In his paper he discussed the theory and the equipment necessary for such a study. It is the purpose of this paper to set forth modifications of his equipment, to present data obtained with this modified equipment, and to interpret this data.

It is a well known fact that the visible universe is made almost entirely of baryonic matter. Yet, this is also one of the greatest puzzles that physicists are trying to solve: Where did all of this matter come from in the first place? The Standard Model (SM) of particle physics predicts a baryon asymmetry that is much smaller than what is observed in nature. In order to try and explain this discrepancy, Sakharov (1967) postulated three necessary conditions for baryogenesis in the early universe. One of these is the requirement that charge conjugation (C) and the product of C and parity (P) symmetries are violated. Because the SM fails to generate the observed baryon asymmetry, additional sources of CP violation are needed in order to help reconcile theory and observation. Thus, physicists have been looking for extensions to the SM in search of an answer. The presence of a neutron Electric Dipole Moment (nEDM) would signal a new source of CP violation. A non-vanishing nEDM would provide evidence for the breaking of both parity (P) and time-reversal symmetry (T). Because CPT symmetry is assumed to be conserved and has not been found to be broken, this would signal CP violation. To look for an nEDM, stored ultracold neutrons are placed in parallel and anti-parallel magnetic and electric fields and the Larmor precession frequency is carefully measured. A difference in the precession frequency of the neutrons in the two states of the fields would signal the existence of an nEDM. The current upper limit of the nEDM was set by the RAL-Sussex-ILL collaboration and stands at dn < 3.0x10-26 e cm (90% CL). Currently a new cryogenic apparatus is under construction at the Spallation Neutron Source (SNS) at the Oak Ridge National Laboratory (ORNL) which aims to reduce the current upper limit by two orders of magnitude. A central problem to all neutron EDM experiments is the generation of a highly uniform and stable magnetic field. Because the suppression of systematic effects that arise from magnetic field nonuniformities and temporal drifts is vital to the success of these experiments, it is important to have the ability to precisely control and monitor the magnetic field gradients inside of the experimental volume. However, it is not always possible to measure the field gradients within the region of interest directly. To remedy this issue in the SNS nEDM experiment, a field monitoring system has been designed and tested that will allow for the reconstruction of the field gradients inside of the fiducial volume using noninvasive measurements of the field components at discrete locations external to this volume. This document will outline the theoretical framework of our method and present the results of experimental and simulated studies performed and the engineering design for such a field monitoring system.

L’objectif de cette thèse est l’étude des différents aspects de l’interaction à quelques corps entre des atomes de Rydberg froids. Cette thèse a été réalisée dans le cadre d’une cotutelle entre l’Université Paris-Saclay et l’Université de Pise en travaillant sur deux différents montages expérimentaux sur des atomes de Rydberg froids : respectivement sur le Cs au Laboratoire Aimé Cotton et sur le Rb au département de Physique de l’Université de Pise. Au Laboratoire Aimé Cotton nous avons démontré l’existence des nouvelles interactions à quelques corps dans un gas gelé d’atomes de Rydberg. Ces nouvelles résonances sont la généralisation des résonances de Förster bien connues dans le domaine des atomes de Rydberg. Ces résonances agissent sur les degrés de liberté interne des atomes de Rydberg et ont l’effet d’un transfert résonant d’énergie et de population comme dans le cas des FRET (Fluorescence Resonance Energy Transfer). Comme dans le cas de la résonance de Förster à deux corps, les résonances FRET à trois corps sont accordées à la résonance avec un champ électrique externe et peuvent être observées pour différents nombres quantique principaux. Les effets à trois corps sont observés en absence de tout effet à deux corps et sont qualifiés de Borroméens. La présence d’un champ externe peut générer d’autres résonances entre atomes de Rydberg qui sont interdites en absence de champ électrique. Ces résonances, qu’on peut qualifier des résonances quasi-interdites, sont dues à un couplage dipole-dipole de type Förster. Nous avons identifié toutes ces résonances liées au couplage entre les niveaux de multiplicité de n différents.Dans le montage expérimental à Pise on a étudié les effets mécaniques liés à la répulsion van der Waals entre atomes de Rydberg. Nous avons étudié l’expansion due à l’interaction van der Waals dans une chaîne 1D des atomes de Rydberg de Rb qui ont étés excités avec une excitation laser hors résonance. La comparaison entre les différents désaccords de l’excitation laser démontre le rôle central joué par l’interaction van der Waals. / The aim of this thesis is to investigate different aspects of few-body interactions in cold Rydberg atoms. It has been realized in a co-tutelle program between the University of Paris-Saclay and the University of Pisa working on two different experimental set ups: one at Laboratoire Aimé Cotton on cold Cs Rydberg atoms and a second at Physics Department of Pisa on cold Rb Rydberg atoms. In Laboratoire Aimé Cotton we demonstrated the existence of new few-body interactions we observed in a frozen Rydberg gas of Cs atoms. These new resonances are a generalization of already known two-body Förster resonances. They act on the internal degrees of freedom of the Rydberg atoms leading to a resonant energy transfer analogous to the one in FRET (Fluorescence Resonance Energy Transfer). In analogy with Förster resonance, three-body FRETs are tuned with an external electric field and can be observed for different principal quantum number. The three-body interaction appeared in the absence of any two-body ones and for this reasons it has a Borromean character. The presence of this external electric field leads to additional resonances between Rydberg atoms supposedly forbidden. These resonances, we call quasi-forbidden Förster resonances, are due to dipole-dipole interaction as in the case of Förster resonance. We investigated these resonances finding a large number close to the allowed two-body and three-body FRET. A precise study was necessary in order to identify and discriminate these resonances from the allowed ones.In the experiment in Pisa we instead focus our attention on the mechanical effect of van der Waals repulsion between Rydberg atoms. We studied the spatial expansion due to a van der Waals interaction in a 1D chain of Rb Rydberg atoms excited with an off-resonant laser excitation. The comparison of the spatial expansion for different detuning of the laser excitation reveals the central role of the van der Waals interaction whose strength is equal to the detuning of the laser excitation.

We consider the two-dimensional Navier-Stokes equation on the (possibly) asymmetric torus, D_δ = [0,2𝜋δ] × [0,2𝜋], both with and without stochastic forcing. Absent external force, the vorticity is known to reach a rest state of zero. There exists at least three so called "quasi-stationary states" which attract nearby solutions at rates faster than the global decay rate. The system evolves toward one of these three qualitatively different transient states for long times while the system overall tends toward the final rest state. We develop a finite-dimensional model of the associated deterministic vorticity equation to show how the selection of the dominant quasi-stationary state depends on the aspect ratio of the domain, given by δ. This is followed by formal analysis of the problem as a perturbation from the symmetric domain. Once the selection mechanism for the deterministic model is characterized, stochastic forcing is added to the reduced system. Numerical analysis shows the dominant quasi-stationary state is consistent with what is seen in the deterministic setting. Finally through multiscale averaging methods, the leading order dynamics of the stochastically forced finite-dimensional model for δ close to one is studied. As a result we formally obtain leading order asymptotics of statistics of interest, including the selection mechanism.

The search for physics beyond the Standard Model has been a main focus of the scientific community for several decades. Unknown physics in the form of new interactions violating the simultaneous reversal of charge and parity symmetries (CP) would, for example, provide a significant step towards understanding the baryon matter-antimatter asymmetry observed in the Universe. Such parameters are predicted to also manifest themselves in atomic and molecular systems in the form of both: permanent electric dipole moments and nuclear charge distribution asymmetries described by the nuclear Schiff moment. Both can be measured to a high degree of precision in modern experiments, allowing us to place stringent limits on parameters appearing in new fundamental theories. The Cold Molecule Nuclear Time Reversal Experiment (CeNTREX) is the latest approach to probing these effects. CeNTREX is a molecular beam experiment that uses thallium fluoride (²⁰⁵Tl⁹F) as its test species to measure energy shifts induced by the interaction of thallium's nuclear Schiff moment. It does so by performing nuclear magnetic resonance using a separate oscillatory fields technique. The precision of this measurement is dictated by the free precession time and the number of interrogated molecules, and is significantly enhanced by thallium fluoride's inherent properties. Employing novel methods, CeNTREX strives to achieve significant improvements to limits placed on the fundamental parameters. One such method is rotational cooling. It was thoroughly analyzed, simulated and experimentally confirmed - with the help of optical and microwave pumping, we collapsed the initial Boltzmann distribution of molecules amongst their rotational states into one chosen hyperfine state of the ground rotational state manifold. The efficiency of this process depends on multiple factors, the most crucial being the approach towards dark state destabilization and remixing. After careful investigation, we chose the most appropriate method and devised an efficient rotational cooling scheme. Experimental confirmation showed an enhancement factor of r𝑓23.70±1.13, very close to our theoretical predictions. This allows us to conclude that CeNTREX should provide a 2500-fold improvement over the current best measurements of the nuclear Schiff moment in thallium nucleus.

Density functional theory (DFT) calculations (using Becke's exchange in conjunction with Lee-Yang-Parr's correlation functional (BLYP) and Becke's three-parameter hybrid DFT/HF method using Lee-Yang-Parr's correlation functional (B3LYP)) have been carried out to investigate the structure, dipole moment, and vibrational spectrum of azulene. Structural parameters obtained by both BLYP/6-31G* and B3LYP/6-31G* geometry optimization are in good agreement with available experimental data and show clearly the aromatic nature (bond equalization), a property the Hartree-Fock theory fails to describe correctly. The BLYP/6-31G* and B3LYP/6-31G* dipole moments are within experimental uncertainty and are in good agreement with results obtained from the much more expensive MP2 and MR-SDCI calculations. Most of the BLYP/6-31G* vibrational frequencies are in excellent agreement with available experimental assignments. On the basis of the calculated results, assignments of some missing frequencies in the experimental studies are proposed.