This thesis outlines the fabrication of two atom chips for the study of interactions between ⁸⁷Rb Rydberg atoms and a Au surface. Atom chips yield tightly confined, cold samples of an atomic species by generating magnetic fields with high gradients using microfabricated current-carrying wires. These ground state atoms may in turn be excited to Rydberg states. The trapping wires of Chip 1 are fabricated using thermally evaporated Cr/Au and patterned using lift-off photolithography. Chip 2 uses a Ti/Pd/Au tri-layer, instead of Cr/Au, to minimize interdiffusion. The chip has a thermally evaporated Au surface layer for Rydberg atom-surface interactions, which is separated from the underlying trapping wires by a planarizing polyimide dielectric. The polyimide was patterned using reactive ion etching. Special attention was paid to the edge roughness and electrical properties of the trapping wires, the planarization of the polyimide, and the grain structure of the Au surface.

This thesis outlines the fabrication of two atom chips for the study of interactions between ⁸⁷Rb Rydberg atoms and a Au surface. Atom chips yield tightly confined, cold samples of an atomic species by generating magnetic fields with high gradients using microfabricated current-carrying wires. These ground state atoms may in turn be excited to Rydberg states. The trapping wires of Chip 1 are fabricated using thermally evaporated Cr/Au and patterned using lift-off photolithography. Chip 2 uses a Ti/Pd/Au tri-layer, instead of Cr/Au, to minimize interdiffusion. The chip has a thermally evaporated Au surface layer for Rydberg atom-surface interactions, which is separated from the underlying trapping wires by a planarizing polyimide dielectric. The polyimide was patterned using reactive ion etching. Special attention was paid to the edge roughness and electrical properties of the trapping wires, the planarization of the polyimide, and the grain structure of the Au surface.

The properties of a Rydberg atom immersed in an ultracold environment were investigated. Two scenarios were considered, one of which involves the neighbouring ground-state atoms arranged in a spatially structured configuration, while the other involves them distributed randomly in space. To calculate the influence of the multiple ground-state atoms on the Rydberg atom, Fermi-pseudopotential was used, which simplified greatly the numerical effort. In many cases, the few-body interaction can be written down analytically which reveals the symmetry properties of the system. In the structured case, we report the first prediction of the formation of ``Rydberg Borromean trimers''. The few-body interactions and the dynamics of the linear A-B-A trimer, where A is the ground-state atom and B is the Rydberg atom, were investigated in the framework of normal mode analysis. This exotic ultralong-range triatomic bound state exists despite that the Rydberg-ground-state interaction is repulsive. Their lifetimes were estimated using both quantum scattering calculations and semi-classical approximations which are found to be typically sub-microseconds. In the disordered case, the Rydberg-excitation spectra of a frozen-gas were simulated, where the nuclear degrees of freedom can be ignored. The systematic change of the spectral shape with respect to the density of the gas and the excitation of the Rydberg atom were found and studied. Some parts of the spectral shape can be described by simple scaling laws with exponents given by the basic properties of the atomic species such as the polarizability and the zero-energy electron-atom scattering length.

My dissertation treats the physics of ultracold gases, in particular of Bose-Einstein condensates with long-ranged interactions induced by admixing a small fraction of a Rydberg state to the atomic ground state. The resulting interaction leads to the emergence of supersolid states and to the self-trapping of a Bose-Einstein condensate.

The properties of a Rydberg atom immersed in an ultracold environment were investigated. Two scenarios were considered, one of which involves the neighbouring ground-state atoms arranged in a spatially structured configuration, while the other involves them distributed randomly in space. To calculate the influence of the multiple ground-state atoms on the Rydberg atom, Fermi-pseudopotential was used, which simplified greatly the numerical effort. In many cases, the few-body interaction can be written down analytically which reveals the symmetry properties of the system. In the structured case, we report the first prediction of the formation of ``Rydberg Borromean trimers''. The few-body interactions and the dynamics of the linear A-B-A trimer, where A is the ground-state atom and B is the Rydberg atom, were investigated in the framework of normal mode analysis. This exotic ultralong-range triatomic bound state exists despite that the Rydberg-ground-state interaction is repulsive. Their lifetimes were estimated using both quantum scattering calculations and semi-classical approximations which are found to be typically sub-microseconds. In the disordered case, the Rydberg-excitation spectra of a frozen-gas were simulated, where the nuclear degrees of freedom can be ignored. The systematic change of the spectral shape with respect to the density of the gas and the excitation of the Rydberg atom were found and studied. Some parts of the spectral shape can be described by simple scaling laws with exponents given by the basic properties of the atomic species such as the polarizability and the zero-energy electron-atom scattering length.

My dissertation treats the physics of ultracold gases, in particular of Bose-Einstein condensates with long-ranged interactions induced by admixing a small fraction of a Rydberg state to the atomic ground state. The resulting interaction leads to the emergence of supersolid states and to the self-trapping of a Bose-Einstein condensate.

Les atomes de Rydberg sont des états très excités, dans lesquels un électron est placé sur une orbite éloignée du noyau. Leur grand dipôle électrique les rend très sensibles à leur environnement électromagnétique. En utilisant des champs microondes et radiofréquences, nous préparons des états quantiques non-classiques spécialement conçus pour exploiter au mieux cette sensibilité et mesurer des champs électriques et magnétiques avec une grande précision. Dans la première partie, nous préparons des états chats de Schrödinger, superpositions d'orbitales de polarisabilités très différentes, qui nous permettent de mesurer de petites variations du champ électrique statique avec une sensibilité bien supérieure à la limite quantique standard et proche de la limite Heisenberg fondamentale. Nous atteignons une sensibilité par atome de 30mV/m pour un temps d'interrogation de 200ns, faisant de notre système l'un des électromètres les plus sensibles à ce jour. Nous implémentons ensuite des manipulations plus complexes de l'atome. Grâce à une technique d'écho de spin qui exploite la richesse de la multiplicité Rydberg, nous mesurons les corrélations temporelles du champ électrique avec une bande passante de l'ordre du MHz. Dans la partie finale, nous préparons une superposition quantique de deux états circulaires de nombres quantiques magnétiques opposés. Cet état très non-classique correspond à un électron tournant à la fois dans des directions opposées sur la même orbite. La grande différence de moment magnétique entre les deux composantes de la superposition, de l'ordre de 100muB, ouvre la voie à la mesure de petites variations du champ magnétique avec une grande bande passante. / Rydberg atoms are highly excited states, in which the electron is orbiting far from the nucleus. Their large electric dipole makes them very sensitive to their electromagnetic environment. Using a combination of microwave and radio-frequency fields, we engineer non-classical quantum states specifically designed to exploit at best this sensitivity for electric and magnetic field metrology. In the first part, we prepare non-classical states, similar to Schrödinger cat states, superpositions of two orbitals with very different polarizabilities, that allow us to measure small variations of the static electric field with a sensitivity well beyond the standard quantum limit and close to the fundamental Heisenberg limit. We reach a single atom sensitivity of 30mV/m for a 200ns interrogation time. It makes our system one of the most sensitive electrometers to date. We then implement more complex manipulations of the atom. Using a spin-echo technique taking advantage of the full extent of the Rydberg manifold, we perform a correlation function measurement of the electric field with a MHz bandwidth.In the final part, we prepare a quantum superposition of two circular states with opposite magnetic quantum numbers. It corresponds to an electron rotating at the same time in opposite directions on the same orbit, a rather non-classical situation. The huge difference of magnetic moment between the two components of the superposition, in the order of 100muB, opens the way to the measurement of small variations of the magnetic field with a high bandwidth.

No description available.

Many problems in applied mathematics and physics are formulated most naturally in terms of matrices, and can be solved by computing functions of these matrices. For example, in quantum mechanics, the coherent dynamics of physical systems is described by the matrix exponential of their Hamiltonian. In state of the art experiments, one can now observe such unitary evolution of many-body systems, which is of fundamental interest in the study of many-body quantum phenomena. On the other hand the theoretical simulation of such non-equilibrium many-body dynamics is very challenging. In this thesis, we develop a symbolic approach to matrix functions and quantum dynamics based on a novel algebraic structure we identify for sets of walks on graphs. We begin by establishing the graph theoretic equivalent to the fundamental theorem of arithmetic: all the walks on any finite digraph uniquely factorise into products of prime elements. These are the simple paths and simple cycles, walks forbidden from visiting any vertex more than once. We give an algorithm that efficiently factorises individual walks and obtain a recursive formula to factorise sets of walks. This yields a universal continued fraction representation for the formal series of all walks on digraphs. It only involves simple paths and simple cycles and is thus called a path-sum. In the second part, we recast matrix functions into path-sums. We present explicit results for a matrix raised to a complex power, the matrix exponential, matrix inverse, and matrix logarithm. We introduce generalised matrix powers which extend desirable properties of the Drazin inverse to all powers of a matrix. In the third part, we derive an intermediary form of path-sum, called walk-sum, relying solely on physical considerations. Walk-sum describes the dynamics of a quantum system as resulting from the coherent superposition of its histories, a discrete analogue to the Feynman path-integrals. Using walk-sum we simulate the dynamics of quantum random walks and of Rydberg-excited Mott insulators. Using path-sum, we demonstrate many-body Anderson localisation in an interacting disordered spin system. We give two observable signatures of this phenomenon: localisation of the system magnetisation and of the linear magnetic response function. Lastly we return to the study of sets of walks. We show that one can construct as many representations of series of walks as there are ways to define a walk product such that the factorisation of a walk always exist and is unique. Illustrating this result we briefly present three further methods to evaluate functions of matrices. Regardless of the method used, we show that graphs are uniquely characterised, up to an isomorphism, by the prime walks they sustain.