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.

Neste trabalho, apresentamos um amplo estudo das interações de longo alcance entre átomos de Rydberg frios na presença de campos elétricos estáticos. Nós observamos a transferência de população do estado quase molecular nD + nD para o estado (n+2)P após excitação pulsada na região de 29 ≤ n ≤ 41 em uma amostra de Rb aprisionada em uma armadilha magneto-óptica. A taxa de transferência pode ser manipulada com a presença de campo elétrico estático. Para explicar tais observações um modelo teórico multiníveis foi utilizado. O estudo de evolução temporal da população em (n+2)P mostrou que a dinâmica do processo é condizente com a interpretação clássica de uma transição diabática no domínio temporal. Utilizando um laser de excitação contínuo, realizamos experimentos envolvendo estados nD + nD, para 37 ≤ n ≤ 45, e estados nS + nS, para 39 ≤ n ≤ 47, onde foi possível estudarmos processos de transferência de população com resolução da estrutura fina. Também realizamos experimentos, tanto para estados nD quanto nS, para verificar a importância da estrutura hiperfina da estado fundamental no processo de transferência de população. / In this work, we present an extensive study of long-range interactions between cold Rydberg atoms in the presence of static electric fields. We have observed the population transfer from the quasi-molecular nD + nD state to the (n +2) P state after pulsed excitation for 29 ≤ n ≤ 41 in a sample of Rb trapped atoms in a magneto-optical trap. The transfer rate can be manipulated by the static electric field. To explain such observations, a multilevel theoretical model was used. The study of the time evolution of the population (n +2) P indicates that the dynamics of the process is consistent with a classical interpretation of a nonadiabatic transition in time domain. Using a CW laser excitation, experiments involving states nD + nD, for 37 ≤ n ≤ 45 states and nS + nS for 39 ≤ n ≤ 47, where performed with high spectral resolution. We also performed experiments for both states, nD and nS, to verify the importance of the hyperfine structure of the ground state in the process of population transfer.

Neste trabalho estudamos algumas interações entre átomos de Rydberg em uma armadilha ótica de dipolo do tipo QUEST. Com esta armadilha obtemos uma amostra de 1,2 × 106 átomos de 85Rb no estado fundamental, à uma densidade de ∼ 1012 átomos/cm3 e temperatura média de 60 µK. Os átomos de Rydberg foram preparados utilizando uma transição de dois fótons a partir do estado fundamental 5S1/2, passando pelo estado intermediário 5P3/2 e em seguida para o estado de Rydberg desejado. Estudamos a interação entre pares de átomos, em diferentes níveis energéticos, através de duas técnicas diferentes. Na primeira, monitoramos os efeitos de transferência de população em estados nD oriundas de uma ressonância Förster. Estudamos a ressonância nD5/2 + nD5/2 → (n+2)P3/2 + (n2)F7/2 onde 37 ≤ n ≤ 47, em função da densidade da amostra atômica; e para o estado 37D5/2 manipulamos a mesma ressonância com a aplicação de um campo elétrico externo. Os resultados mostraram que este é um processo binário, evidenciado pela dependência quadrática da população no estado produto com relação ao estado excitado. Num outro experimento, estudamos a interação entre estados nS através do monitoramento, e controle, do efeito de bloqueio de excitação. Aqui mostramos que é possível controlar as interações interatômicas em uma amostra quasi-unidimensional de átomos de Rydberg variando a orientação de um campo elétrico externo. Mostramos que ao polarizar uma amostra de átomos no estado 50S1/2 com um campo, esta passa a interagir de modo semelhante ao de dipolos elétricos clássicos, onde a interação pode ser controlada com a variação da orientação dos dipolos atômicos. Tal interação pode, inclusive, ser cancelada quando os dipolos elétricos são alinhados em um ângulo de 54,7° com relação ao eixo internuclear. / In this work we have studied some interactions between Rydberg-atoms in a QUEST type optical dipole trap. With this trap we obtained a sample of 1,2 × 106 85Rb atoms in the ground state, in a density of ∼ 1012 atoms/cm3 and average temperature of 60 µK. The Rydberg-atoms were prepared using a two-photon transition from the ground state 5S1/2, through an intermediate state 5P3/2 and then to the desired Rydberg state. We have studied interactions between pairs of atoms at several energy levels, using two different techniques. In the first one, we have monitored the effects of the population transfer in nD states derived from a Förster resonance. We have studied the resonance nD5/2 + nD5/2 → (n + 2)P3/2 + (n 2)F7/2 for states of 37 ≤ n ≤ 47 as a function of of the samples atomic density. For the 37D5/2 state we have also manipulated the same resonance with the application of an external electric field. Our results have shown that this is a binary process, indicated by the quadratic dependence of the transferred population in relation with the excited state. In another experiment, we have studied the interaction between nS1/2 states by monitoring, and controlling, the excitation blockade effect. Here we have shown that it is possible to control the inter-atomic interactions in a quasi-one-dimensional sample of Rydberg-atoms by varying the orientation of an external electric field. We have demonstrated that when polarizing a sample of atoms, in the 50S1/2 state with a field, it starts to interact in a similar way as classic electric-dipoles, where the interaction can be controlled by varying the orientation of the atomic dipoles. Such interaction may even be canceled when the electric dipoles are aligned at an angle of 54,7° related to the internuclear axis.

Dans le premier chapitre de la thèse, nous étudions la possibilité d’améliorer le couplage opto- mechanique photon-phonon entre le mode de résonance d’une cavité Fabry-Pérot de haute finesse et les vibrations mécaniques des éléments diélectriques (membranes) à l’intérieur de la cavité. En introduisant un défaut quadratique dans la disposition des membranes, nous montrons que le deux couplages (linéaire et quadratique) augmentent. Enfin, nous proposons un modèle très simple avec lequel on cherche à simuler un cristal photonique quasipériodique. Dans le deuxième chapitre de cette thèse, nous présentons nos résultats de recherche sur le transport d’excitons à travers une cavité visant à augmenter l’efficacité du transport. Le modèle que l’on étudie est une chaîne unidimensionnelle d’atomes froids comprenant chacun deux niveaux énergétiques. Grâce au couplage entre exciton et photon, ces deux quanta s’hybrident et forment deux branches de polariton à l’intérieur de la cavité. Nous avons observé qu’à résonance avec un des deux modes de polariton, on peut transmettre l’exciton via le mode polaritonique dans un temps très court. En outre, le désordre n’affecte la propagation excitonique que de façon algébrique. Dans le troisième chapitre de cette thèse, nous présentons nos résultats de recherche sur la réalisa- tion d’interactions entre photons grâce à la médiation d’atomes ultrafroids piégés dans un réseaux optique unidimensionnelle et placés à l’intérieur d’une fibre à cristaux photoniques. Nous avons détecté un régime dans lequel on peut réaliser le “bunching” photon-photon.Dans le quatrième et dernière chapitre de cette thèse, nous étendons les résultats du chapitre précédent aux atomes de Rydberg. / In the first chapter of this thesis, we study a quasiperiodic array of dielectric membranes inside a high-finesse Fabry-Pérot cavity. We work within the framework of the transfer matrix formal- ism. We show that, in a transmissive regime, the introduction of a quadratic spatial defect in the membrane positions enhances both the linear and quadratic optomechanical couplings between optical and mechanical degrees of freedom. Finally, we propose a theoretical model to simulate a one-dimensional quasiperiodic photonic crystal. In the second chapter of this thesis, we consider the problem of the transport of an exciton through a one-dimensional chain of two-level systems. We embed the chain of emitters in a transverse optical cavity and we show that, in the strong coupling regime, a ultrafast ballistic transport of the exciton is possible via the polaritonic modes rather than ordinary hopping. Due to the hybrid nature of polaritons, the transport efficiency is particularly robust against disorder and imperfections in the system. In the third chapter of this thesis, we consider an ordered array of cold atoms trapped in an optical lattice inside a hollow-core photonic crystal fiber. We study photon-photon interactions mediated by hard-core repulsion between excitons. We show that, in spite of underlying repulsive interac- tion, photons in the scattering states demonstrate bunching, which can be controlled by tuning the interatomic separation. We interpret this bunching as the result of scattering due to the mismatch of the quantization volumes for excitons and photons, and discuss the dependence of the effect on experimentally relevant parameters. In the fourth chapter of the thesis, we extend the results of the previous chapter to Rydberg atoms.

Intermédiaire essentiel au dialogue entre théorie et vérification expérimentale, la mesure n'a de sens que si la précision des résultats est élevée. La métrologie en laboratoire s'attache à augmenter autant que possible la précision avec laquelle l'expérimentateur a accès à la valeur d'un paramètre. Le bruit quantique affectant la mesure impose une limite sur la précision maximale accessible à partir d'états quasi-classiques: la limite quantique standard (SQL). La métrologie quantique cherche à utiliser les caractéristiques propres à la mécanique quantique pour la dépasser et se rapprocher le plus possible de la limite ultime, physiquement non franchissable, appelée limite de Heisenberg. Dans ce mémoire, nous avons développé une stratégie de mesure d'un champ électromagnétique contenant moins d'un photon basée sur l'utilisation de corrélations atome-champ dans une expérience d'électrodynamique quantique en cavité. L'idée est de mesurer l'amplitude de ce petit champ en sondant la perturbation qu'il introduit sur un état intriqué atome-champ mésoscopique déjà présent dans une cavité supraconductrice. Nous avons pu démontrer que le choix de notre mesure est, en principe, optimal grâce aux outils que sont l'information de Fisher (dépendant du processus de mesure) et l'information de Fisher dite quantique (qui elle n'en dépend pas), liées à la précision sur la mesure par des inégalités de type Cramér-Rao. Expérimentalement, nous avons très largement dépassé la précision obtenue sur l'amplitude du champ électromagnétique par une mesure classique et nous nous sommes rapprochés de la limite de Heisenberg autant que les imperfections expérimentales nous le permettaient. / As an essential intermediary between theories and their experimental proofs, measurement is meaningfull if the precision of its results is high. The main emphasis of metrology in laboratories is therefore on increasing as much as possible the precision of the experimental evaluation of a parameter. Quantum noise that affects the measurement establishes a quantitative limit on the maximal precision that can be achieved with classical states: the standard quantum limit (SQL). Quantum metrology aims at using quantum features to beat this limit and to approach the physically ultimate limit called Heisenberg limit. This thesis presents a measurement strategy for an electromagnetic field containing less than one photon, which is based on the use of atom-field correlations in a cavity quantum electrodynamics experiment. The idea is to measure the amplitude of the small field by probing the disturbance caused on an entangled mesoscopic state that is already stored in the superconducting cavity. We demonstrated that our measurement strategy is in principle optimal thanks to two tools: the Fisher information (that depends on the measurement process) and the quantum Fisher information (that does not), which define the precision tanks to Cramér-Rao like equations. The measurement signal subsequently largely exceeded the level of accuracy obtained with classical states and we got as closed to the Heisenberg limit as the experimental imperfections allowed us.

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.

Dans cette thèse, nous mesurons la dynamique cohérente et les corrélations spatiales des excitations Rydberg dans des matrices 2D d’atomes uniques.Nous utilisons un modulateur spatial de lumière pour façonner la phase spatiale d'un faisceau laser de piégeage optique avant de le focaliser avec une lentille asphérique de grande ouverture numérique. En imprimant une phase appropriée sur le faisceau laser, nous pouvons créer des matrices 2D de pièges optiques, de forme arbitraire et facilement reconfigurables, avec jusqu'à 100 pièges séparées de quelques micromètres. Les pièges sont chargés à partir d'un nuage d'atomes froids de 87Rb, et due aux collisions assistées par la lumière, au plus un seul atome peut être présent dans chaque piège en même temps. Une caméra CCD sensible permet en temps réel l'imagerie de la fluorescence atomique émanant des pièges, ce qui nous permet de détecter individuellement la présence d'un atome dans chaque piège avec une précision presque parfaite.Pour créer des interactions importantes entre les atomes uniques, nous les excitons vers des états de Rydberg, qui sont des états électroniques avec un nombre quantique principal élevé.Un faisceau supplémentaire d'adressage permet la manipulation individuelle d'un atome sélectionné dans la matrice.La connaissance précise, de la fois de la matrice des atomes préparé et des positions des excitations Rydberg, nous a permis de mesurer l’augmentation collective de la couplage optique dans le régime de blocage Rydberg, où une seule excitation est partagée de façon symétrique entre tous les atomes de la matrice.Dans le régime où l'interaction ne s’étend que sur quelques sites, nous avons mesuré la dynamique et les corrélations spatiales des excitations Rydberg, dans des matrices d’atomes à une et deux dimensions. La comparaison à une simulation numérique d'un modèle d'Ising quantique d'un système de spin-1/2 montre un accord exceptionnel pour les matrices où l'effet de l'anisotropie de l’interaction Rydberg-Rydberg est faible. Les résultats obtenus démontrent que les atomes Rydberg uniques sont une plate-forme bien adaptée pour la simulation quantique des systèmes de spin. / In this thesis, we measure the coherent dynamics and the pair correlations of Rydberg excitations in two-dimensional arrays of single atoms.We use a spatial light modulator to shape the spatial phase of a single optical dipole trap beam before focusing it with a high numerical-aperture aspheric lens. By imprinting an appropriate phase pattern on the trap beam, we can create arbitrarily shaped and easily reconfigurable 2D arrays of high-quality single-atom traps, with trap-spacings of a few micrometers for up to 100 traps. The traps are loaded from a cloud of cold 87Rb atoms, and due to fast light-assisted collisions of atoms inside the traps, at most one atom can be present in each trap at the same time. A sensitive CCD camera allows the real-time, site-resolved imaging of the atomic fluorescence from the traps, enabling us to detect the presence of an atom in each individual trap with almost perfect accuracy.In order to induce strong, tunable interactions between the atoms in the array, we coherently laser-excite them to Rydberg states, which are electronic states with a high principal quantum number.An additional addressing beam allows the individual manipulation of an atom at a selected site in the array.The precise knowledge of both the prepared atom array and the positions of the Rydberg excitations allowed us to measure the collective enhancement of the optical coupling strength in the regime of full Rydberg blockade, where one single excitation is shared symmetrically among all atoms in the array.In the regime where the strong interaction only extends over a few sites, we measured the dynamics and the spatial pair-correlations of Rydberg excitations, in one- and two-dimensional atom arrays. The comparison to a numerical simulation of a quantum Ising model of a spin-1/2 system shows an exceptional agreement for trap geometries where the effect of the anisotropy of the Rydberg-Rydberg interaction is small. The obtained results demonstrate that single Rydberg atoms are a suitable platform for the quantum simulation of spin systems.

No description available.

Long-term storage of quantum information has diverse applications in quantum information science. This work presents an experimental realization of quantum memories with lifetimes greater then 0.1 s. The memories are based on cold rubidium atoms confined in one-dimensional optical lattices. First realization of lattice-based quantum memory and entanglement between a light field and a spin wave is presented in Chapter II. Chapter III describes two different methods (two-photon and magnetic) of compensation for inhomogeneous differential light shifts between the memory levels due to optical trapping potentials, and demonstration of entanglement between a telecom-band light field and a light-shift compensated memory qubit. Highly excited Rydberg atoms present a unique platform for study of strongly correlated systems and quantum information, because of their enormous dipole moments and consequent strong, long-range interactions. In the experiment described in Chapter IV single collective Rydberg excitations are created in a cold atomic gas. After a variable storage period the excitations are converted into light. As the principal quantum number n of the Rydberg level is increased beyond ~ 70, no more than a single excitation is retrieved from the entire mesoscopic ensemble of atoms. In Chapter V, by spatially selective conversion of the spin wave into a light field, we demonstrate that Rydberg-level interactions create long-range correlations of collective atomic excitations. These results hold promise for studies of dynamics and disorder in many-body systems with tunable interactions and for scalable quantum information networks. Chapter VI presents initial observations of coherent many-body Rabi oscillations between the ground level and a Rydberg level using several hundred cold rubidium atoms. The strongly pronounced oscillations indicate a nearly complete excitation blockade of the entire mesoscopic ensemble by a single excited atom.

The energy levels of a hydrogen Rydberg atom approaching a metallic structure are perturbed by the image-charge interaction with the surface. At small atom-surface separations surface ionisation of the Rydberg electron can occur, whereby the electron is transferred to a metal-localised state. In previous studies investigating surface ionisation at bulk metallic surfaces, this state has been part of a conduction band; however this thesis focuses on metallic and structured surfaces where the Rydberg electron transfers into a discrete image-state or hybrid 'well-image state'. The surface ionisation of hydrogen Rydberg atoms at a Cu(100) projected band-gap surface is investigated experimentally and theoretically. Experimentally, the surface ionisation of an incident beam of hydrogen Rydberg atoms is measured by extraction of the resulting ions. Resonance-enhanced charge transfer is seen for hydrogen Rydberg states that are degenerate with copper-localised image-states. A wavepacket propagation study shows that for on-resonance states the maximum in the surface-ionisation probability is shifted away from the surface by decreasing the collisional velocity. The discrete hybrid 'well-image states' localised along the surface normal of a thin-film change energy with thin-film thickness. The interaction of hydrogen Rydberg atoms with iron thin films deposited on an insulating substrate is investigated. The preference for electron penetration along the surface normal is seen by the resonance-enhancement of charge transfer at energies where the Rydberg state and well-image state are degenerate. By changing the thickness of the thin film, by in situ depositions, the energies of the well-image state are altered and the Rydberg n-values at which resonances occur, change. At a thickness of 30-monolayer the energetic spacings between the well-image states and the Rydberg states become comparable, and the single well-image state resolution is lost. A wavepacket-propagation study investigates the interaction of a nanoparticle and low-n hydrogen Rydberg atoms. The nanoparticle has a fully confined potential which at small radii yields well-spaced, fully discrete well-image states. Resonance-enhanced charge transfer occurs when the Rydberg state and the nanoparticle well-image state energy levels are degenerate. However, when there is poor energy matching between the nanoparticle well-image state and the Rydberg atom, no charge transfer is seen i.e. surface ionisation does not occur. Overall, the work presented here demonstrates the capability of Rydberg-surface studies to identify discrete, high-lying energy levels at specific surfaces.