Die Arbeit beschäftigt sich mit der Dynamik von Gasen aus hoch angeregten Atomen. Es wird sowohl die Erzeugung von Rydberggasen, als auch ihre Dynamik nach der Laser-Anregung betrachtet. Zur Beschreibung des Anregungsprozesses wird ein quasi-klassischer Zugang verwendet. Er basiert auf der adiabatischen Eliminierung von Kohärenzen aus der vollen Quanten-Beschreibung und führt auf eine klassische Mastergleichung. Diese Näherung ist gerade für typische experimentelle Situationen durchführbar. Die klassische Mastergleichung kann durch ein simples Monte-Carlo-Verfahren für Systeme aus zehntausenden von Teilchen unter voller Berücksichtigung der Rydberg-Rydberg-Wechselwirkung gelöst werden. Mit Hilfe des Monte-Carlo-Verfahrens wird die Anregung von Rydbergatomen in einem ultrakalten Gas untersucht. Die in Experimenten gefundene Anregungsblockade wird durch die Methode gut beschrieben. Bei der Anregung von Rydbergatomen aus einem optischen Gitter wird sogar eine Anregungsverstärkung - eine Antiblockade - vorhergesagt. Die Antiblockade in einem Gitter erlaubt eine Charakterisierung räumlicher Korrelationen der Rydbergatome allein durch die Messung ihrer Dichte. Sie ist robust gegenüber Gitterfehlstellen und sollte mit heutigen experimentellen Techniken nachweisbar sein. Für die Anregung im ungeordneten Gas wird gezeigt, dass sich die räumlichen Korrelationen der Rydbergatome indirekt in den Momenten der Häufigkeitsverteilung angeregter Atome widerspiegeln. Durch die Untersuchung der Fluktuationen in der Zahl angeregter Atome lassen sich die Unterschiede in den Paarkorrelationsfunktionen bei Blockade und Antiblockade im Gas messen. Ein Vergleich mit experimentellen Daten zeigt eine qualitativ gute Übereinstimmung. Für die Dynamik des Rydberggases nach dem Abschalten der Anregungslaser ist der Fall besonders interessant, dass Atome in unterschiedlichen Rydbergzuständen resonant ihre Anregungsenergie austauschen können. In der Arbeit wird argumentiert, dass sich der räumliche Transfer von Anregungsenergie in Rydbergsystemen ohne störende Umgebungseinflüsse gezielt untersuchen lässt. Mit Hilfe der Frenkelschen Exziton-Theorie wird der Energietransfer entlang einer eindimensionalen Anordnung von Rydbergatomen untersucht. Zusätzlich wird dargelegt, dass die exzitonische Anregung auch mechanische Kräfte auf die Rydbergatome induziert. Diese werden mit Hilfe einer quanten-klassischen Methode analysiert. Der Zusammenhang der auftretenden Kräfte mit den Symmetrien der exzitonischen Eigenfunktionen wird aufgezeigt. In einer eindimensionalen Anordnung von Rydbergatomen wird ein adiabatischer Energietransfer vorhergesagt, der an die Bewegung der Atome gebunden ist. Er läuft vollständig auf einer einzigen adiabatischen Potentialfläche ab. Dieser Transport ist langsam genug, um mit heutigen experimentellen Methoden im Prinzip orts- und zeitaufgelöst abgebildet zu werden.

Les photons apparaissent comme des vecteurs d'information fiables, car ils interagissent peu avec leur environnement. Malheureusement, ils interagissent si faiblement entre eux que la réalisation directe de portes logiques optiques à deux qubits est impossible. La propagation à travers des milieux atomiques non-linéaires permet néanmoins d'engendrer des interactions photon-photon effectives. L'utilisation du phénomène de transparence électromagnétiquement induite (EIT) permet d'induire une forte non-linearité résonante -- néanmoins pas encore détectable dans le domaine quantique, sur une transition d'un système à trois niveaux en “échelle”. Pour augmenter les effets non-linéaires et atteindre le régime quantique, il a récemment été proposé de combiner l'approche EIT au blocage d'excitation induit par les fortes interactions dipôle-dipôle entre atomes de Rydberg. En plaçant le milieu en cavité, on impose à la lumière des passages multiples et on accroît encore la non-linéarité optique. Ce type de dispositif a été étudié théoriquement et expérimentalement dans le régime dispersif et pour une non-linéarité faible, pour lequel un traitement classique du champ est adapté. Dans le présent mémoire, nous nous intéressons aux effets optiques non-linéaires induits par un milieu Rydberg dans le régime quantique.Dans le chapitre 1, nous présentons notre système d'étude, ses équations dynamiques et rappelons la définition et les principales propriétés de la fonction de corrélation d'intensité g^{2}que nous utilisons pour caractériser l'action de la non-linéarité sur le champ incident. Dans le chapitre 2, nous considérons le régime dispersif, i.e. lorsque l'état intermediaire est très désaccordé et peut être éliminé adiabatiquement. Nous utilisons l'approximation des bulles Rydberg selon laquelle le système peut être effectivement ramené à un ensemble de superatomes à deux niveaux couplés au mode de la cavité, décrit par le modèle de Tavis-Cummings forcé. Nous calculons analytiquement et numériquement la fonction g^{2}pour la lumière transmise, qui, selon les paramètres de la cavité, peut être “groupée” ou “dégroupée”. Dans le chapitre 3, nous présentons un traitement alternatif du système, qui nous permet d'étudier le régime résonant. Dans la limite d'un champ incident faible, nous dérivons analytiquement la fonction de corrélation g^{2} pour les lumières transmise et réfléchie, grâce à la factorisation des moyennes de produits d'opérateurs à l'ordre le plus bas de la théorie de perturbation. Nous proposons ensuite un modèle effectif non-linéaire à trois bosons pour le système couplé atomes-cavité. Enfin, nous étudions le régime résonant et observons de nouvelles caractéristiques de la fonction de corrélation g^{2}qui attestent la relation entre les conditions d'adaptation d'impédance de la cavité pour les différentes composantes du champ et les interactions dipôle-dipôle entre les atomes. Dans le chapitre 4, nous analysons le système dans le formalisme de Schwinger-Keldysh. En appliquant le théorème de Wick, nous développons perturbativement les fonctions de corrélation par rapport au Hamiltonien d'alimentation de la cavité et au Hamiltonien d'interaction dipôle-dipôle et effectuons une resommation complète par rapport à ce dernier. Nous retrouvons par cette méthode les résultats du Chapitre 3, sous une forme analytique. Nous allons aussi au-delà et derivons des expressions analytiques pour les composantes élastique et inélastique du spectre en transmission de la cavité. Nous identifions une structure de résonance polaritonique, jusque-là inconnue, que nous interprétons physiquement. Dans le chapitre 5, nous décrivons un protocole de porte photonique de phase de haute fidélité fondé sur le blocage Rydberg dans un ensemble atomique placé dans une cavité optique. Ce protocole peut être réalisé avec des cavités de finesse modérée et permet en principe un traitement efficace de l'information quantique codée dans des photons. / Photons appear as reliable information messengers since they interact very weakly with their environment. Unfortunately, they interact so weakly with each other that the direct implementation of optical two-qubit gates is impossible. The propagation through atomic nonlinear media however allows one to achieve effective photon-photon interactions. The technique of electromagnetically induced transparency (EIT) allows one to induce a strong resonant non-linearity -- not strong enough to be noticeable in the quantum domain though, on one of the transitions of a three-level ladder system. To enhance the nonlinear effects and reach the quantum regime, it was recently proposed to combine the EIT approach with the excitation blockade induced by the strong dipole-dipole interactions between Rydberg atoms. By putting the medium in a cavity, one imposes multiple passes to the light therefore increasing the optical nonlinearity. This kind of setup was studied both theoretically and experimentally in the dispersive regime and for a relatively weak nonlinearity, for which a classical treatment of the field is still valid. In this dissertation, we investigate the optical nonlinear effects induced by a Rydberg medium in the quantum regime.In chapter 1, we present our system, its dynamical equations and recall the definition and basic properties of the intensity correlation function g^{left(2right)}that we use to characterize the action of nonlinearity on the photonic field. In chapter 2, we consider the so-called dispersive regime, i.e. when the intermediate state is far detuned and can be adiabatically eliminated. We employ the Rydberg bubble approximation in which the system effectively consists in an ensemble of two-level superatoms coupled to the cavity mode, described by the driven Tavis-Cummings model. We compute analytically and numerically the g^{left(2right)}function of the transmitted light, which, depending on the cavity parameters, is shown to be either bunched or antibunched. In chapter 3, we present an alternative treatment of the system, which allows us to investigate the resonant regime. In the low-feeding limit, we analytically derive the correlation function g^{left(2right)}left(tauright)for the transmitted and reflected lights, based on the factorization of the lowest perturbative order of operator product averages. We then propose an effective non-linear three-boson model for the coupled atom-cavity system. Finally, we investigate the resonant regime and observe novel features of the correlation function g^{left(2right)}showing the interplay of impedance matching conditions and dipole-dipole interactions. In chapter 4, we analyze the system in the Schwinger-Keldysh formalism. Applying Wick's theorem, we perturbatively expand correlation functions with respect to both, feeding and dipole-dipole interactions Hamiltonians and perform a complete resummation with respect to the latter. By this method we recover the results of Chap. 3 in an analytic form. We also go beyond and derive analytic expressions for the elastic and inelastic components of the cavity transmission spectrum. We identify a polaritonic resonance structure in this spectrum, to our knowledge unreported so far, that we physically interpret. In chapter 5, we describe a novel scheme for high fidelity photonic controlled-phase gates using Rydberg blockade in an ensemble of atoms in an optical cavity. This protocol can be implemented with cavities of moderate finesse allowing for highly efficient processing of quantum information encoded in photons.

The coupling of light to ensembles of strongly interacting Rydberg atoms via electromagnetically induced transparency (EIT) has emerged as a particularly promising approach towards quantum nonlinear optics, allowing freely propagating photons to acquire long-ranged effective interactions of unprecedented strength. This thesis explores different photon interaction mechanisms enabled by this general approach, and examines how these can be utilized for various different practical applications. Considering dissipative photon interactions, we first examine the effect of blockade-induced photon scattering on the spatial coherence of collective Rydberg excitations stored in an atomic medium, and how this influences the efficiency of photon storage and retrieval. Based on this developed understanding, we examine the performance of single-photon switching capabilities enabled by dissipative scattering and establish optimized switching protocols over a range of parameters. We then generalize this to consider the many-body decoherence of multiple stored excitations. Here we identify a correlated coherence protection mechanism in which photon scattering from one excitation can preserve the spatial coherence of all others in the medium, and consider the utility of this effect for implementing robust single-photon subtraction. We then outline a new approach towards coherent quantum nonlinear optics via Rydberg-EIT, in which the emergent photon interaction features intrinsically suppressed photon losses. The underlying idea exploits Rydberg blockade to modify rather than break EIT conditions for multiple photons in close proximity, the effect of which alters the underlying dispersion relation of light propagation in a coherent fashion. We devise a specific implementation of this general mechanism fostering a reflective optical nonlinearity and discuss how this can enable efficient single-photon routing with a multitude of unique practical applications.

Neste trabalho apresentamos os primeiros resultados sobre medida do tempo de vida de estados de Rydberg utilizando átomos frios confinados em uma armadilha magneto-optica de 85Rb. Medidas de tempo de vida de estados altamente excitados são importantes para o teste de teorias modernas sobre interação átomo-vácuo; desta forma medidas precisas são necessárias. A utilização de átomos frios apresenta várias vantagens quando comparadas com técnicas convencionais. Entre elas podemos citar a possibilidade de observação do sistema atômico por longos períodos (>100 &#181;s), e o controle da densidade de forma eficiente para evitar a manifestação de efeitos indesejáveis (colisões, superradiância) que limitam a precisão da medida. Apresentamos a medida do tempo de vida do estado 27D e 38S e comparamos os resultados experimentais com previsões teóricas de diferentes modelos. Algumas discrepâncias são observadas, o que reforça a necessidade da obtenção de um conjunto maior de medidas incluindo outros níveis para indicar qual modelo teórico é mais próximo da realidade. / In this work we present our first results on lifetime measurement of Rydberg states using cold atoms held in a magneto-optical trap of 85Rb. Lifetime measurements of highly excited states are important for testing modern theories on atom-vaccum interaction, therefore precise measurements are required. The use of cold atoms presents some advantage when compared with conventional techniques. Among them we cam point out the possibility of atomic observation for long periods of time (<100 &#181;s), the atomic density control in order to avoid undesired effects (such collisions and superradiance) which can limit the measurement precision. We present the lifetime measurement of 27D and 38S states and compared the experimental results with theoretical prediction using different models. Some discrepancies are observed, which indicates the need of a large set of measurement for other states in order to indicate the best model.

O entendimento das interações de ultralongo alcance envolvendo átomos de Ryberg frios é o ponto principal para o uso deste sistema em computação quântica. Neste trabalho estudamos tais interações envolvendo estados nD+nD em um novo aparato experimental, o qual permite o controle de campo elétrico de uma forma mais eficiente. Mais especificamente estudamos o processo colisional $nD + nD$ $ightarrow$ $(n+2)P + (n-2)F$ na presença de campo elétrico estático fixo. Este processo é importante porque pode levar a decoerência da amostra. Os resultados obtidos indicam a existência de uma ressonância molecular que é sensível ao efeito Stark. Além disso, investigamos se o movimento atômico é importante para popular tais estados. Por fim, proporemos novos experimentos que podem ser úteis para controlar e suprimir tais processos colisionais e assim permitir avanços na área de computação quântica com tais sistemas. / The understanding of ultralong-range interaction involving cold Rydberg atoms is the main step for use this system in quantum computation. In this work, we have studied interaction involving $nD$ states in a new experimental setup, which allows us to control the electric field in a more efficient way. More specifically, we have studied the collision process $nD + nD ightarrow (n+2)P + (n-2)F$ in the presence of a static electric field. This process is important because it can lead to a decoherence of the sample. The observed results show the existence of a molecular resonance which is dependent of Stark effect. Moreover, the atomic motion is perhaps also important to populate such states. Finally, we propose new experiments that can be useful to control and to suppress theses colisional processes and in this way allows us to move on in quantum computing area with such systems.

Neste trabalho, estudamos colisões entre átomos de Rydberg ultrafrios em uma amostra atômica de alta densidade aprisionada em uma armadilha óptica de dipolo (AOD) tipo QUEST (Quasi Electrostatic Trap). Nossos objetivos incluíam testar a manifestação de fenômenos de muitos corpos bem como estudar efeitos de anisotropia nos processos colisionais envolvendo dois corpos. Para isso, escolhemos o processo colisional descrito por 5/2+5/2(+2)3/2+(2)7/2 no intervalo de 37 &le; &le;47. O processo foi estudado na ausência e presença de campo elétrico estático, originando as ressonâncias Förster. Os resultados mostram que mesmo em alta densidade atômica o processo de dois corpos domina a interação, apesar da clara manifestação do bloqueio dipolar. Após modificações na montagem experimental, estudamos um dos picos da ressonância Förster 375/2+375/2393/2+357/2 em função da direção e amplitude em relação ao eixo longitudinal da AOD. Discutimos os resultados e os desafios futuros do experimento. / In this paper, we study collisions between ultracold Rydberg atoms in a high density atomic sample trapped in an optical dipole trap (ODT), type QUEST (Quasi Electrostatic Trap). Our goals included testing the manifestation of many-body phenomena and to study anisotropy effects in collisional processes involving two Rydberg atoms. In order to do this, we have chosen the collision process described by 5/2+5/2(+2)3/2+(2)7/2 in the range of 37 &le; &le;47. The process was studied in the presence and absence of a dc static electric field, also known as Förster resonances. The results show that even at high atomic density, two-body interaction dominates de process, despite the clear manifestation of Rydberg blockade. After several improvements in our experimental setup, we have studied also a Förster resonance peak 375/2+375/2393/2+357/2 as a function of the magnitude of the dc static electric field as well as the angle between this field and the longitudinal axis of the ODT. We discuss the results and future challenges of the experiment.

Neste trabalho, descrevemos a construção de uma armadilha óptica de dipolo, tipo Quest, para átomos de Rydberg utilizando um laser de CO2 de alta potência. A amostra aprisionada apresenta aproximadamente 3 &times; 106 átomos de 85Rb numa densidade 4 &times; 1011 átomos/cm3, em temperaturas da ordem 30 &micro;K. O tempo de vida da armadilha é da ordem de 200 ms. Neste sistema, observamos a fotoionização dos estados de Rydberg devido ao laser de CO2 em 10, 6 &micro;m, contudo fomos incapazes de quantificá-lo. Além disso, medimos o tempo de vida do estado 37D do Rb na armadilha de dipolo, o resultado foi compatível ao encontrado na literatura. Em suma, o sistema esta operante para experimentos mais complexos. / In this work, we describe the implementation of a QUEST dipole trap for Rydberg atoms using a CO2 high power laser. The trapped atomic sample has approximately 3 &times; 106 85Rb atoms, at a density of 4 &times; 1011 atoms/cm3 and a temperature of about 30 &micro;K. The trap lifetime is about 200 ms. We observed photoionization of the Rydberg states due to the CO2 laser at 10, 6 &micro;K, however we were unable to quantify it. Furthermore, we measured the 37D state lifetime of the Rb in the dipole trap, the experimental result was in agreement with the literature. In summary, the system is fully operating for more complex experiments.

In the last decade, ultracold plasmas have been created in the laboratory by photo-ionizing laser-cooled atoms. To understand the overall dynamics of ultracold plasmas, one needs to understand Rydberg collisional processes at ultracold temperatures. The two kinds of problems addressed in this thesis are: study of Rydberg atomic processes at ultracold temperatures, and a study of the overall dynamics of the ultracold plasmas. Theoretical methods based on quantal-classical correspondence is used to understand Rydberg atomic processes such as radiative cascade, and radiative recombination. A simulation method suitable for ultracold collisions is developed and tested. This method is then applied to study collisional-Stark mixing in Rydberg atoms. To study the dynamics of the ultracold plasmas, a King model for the electrons in plasmas is proposed. The King model is a stationary, finite sized electron distribution for the electrons in a cloud of fixed ions with a Gaussian distribution. A Monte-Carlo method is developed to simulate the overall dynamics of the King distribution.

Mon travail porte sur la construction d'une expérience d'électrodynamique quantique en cavité visant à réaliser un long temps d'interaction entre des atomes, portés dans des états de Rydberg circulaires, et des photons confinés dans une cavité micro-onde supraconductrice. Une source d'atomes froids génère un jet vertical d'atomes lents, traversant le mode de la cavité, avec une vitesse moyenne de 12 m.s$^{-1}$. Ainsi, nous obtenons un temps d'interaction atome-champ de l'ordre de la milliseconde. Il devrait permettre, en particulier, l'implémentation de l'effet Zénon quantique dynamique (QZD) sur le champ. Cette dynamique non-classique est un outil puissant, permettant la manipulation cohérente de l'état du champ et la synthèse de superpositions arbitraires d'états quasi-classiques de Glauber. Sa mise en oeuvre nécessite une perturbation, faisant office de mesure, affectant seulement la cavité quand elle contient un nombre de photons $n_{0}$ choisi. Nous mettrons à profit le long temps d'interaction dont nous disposons afin de résoudre le spectre des états de l'atome habillés par le champ. L'anharmonicité du spectre vis-à-vis du nombre de photons permet une mesure sélective sur l'état de Fock $n_{0}$. Nous décrivons dans ce travail les premiers résultats expérimentaux attestant notre capacité à obtenir un long temps d'interaction. Nous présentons des données spectroscopiques résolvant les transitions associées aux états habillés correspondant à des nombres de photons allant de zéro à quatre et ce pour divers états du champ. Nous quantifions la sélection du nombre de photons obtenue à partir de telles mesures. Ces résultats ouvrent la voie à l'implémentation de la dynamique de Zénon. / The subject of my thesis was the construction of a new cavity quantum electrodynamics (CQED) setup. This setup allowed us to achieve a long interaction time between circular Rydberg states and a few photons confined inside a high-finesse supraconductor cavity. A cold atoms source produces a slow atomic beam of atoms with a mean velocity of about 12 m.s$^{-1}$ wich cross the cavity. With a few milisecond interaction time we are able to perform quantum Zeno dynamics (QZD) on the field. This evidently non-classical dynamics constitute an elegant tool to manipulate and synthetize arbitrary superpositions of quasi-classical Glauber states. Thanks to the anaharmonisity of the spectrum this can be achieved $via$ a probe pulse used for measurement, providing in a binary way the complete information to decide if there are $n_{0}$ photons in the cavity or not. Thanks to our long interaction time we are able to resolve the dressed states. In this work we describe the first results attesting our abily to achieve a long interaction time. Particularly, we report a long Rabi vacuum oscillation and the spectrum of the dressed states for different cavity fields. Finaly we characterize the efficiency with wich we can select a Fock state using the interaction with only one atom. This thesis paves the way to study QZD on the cavity field.

Neste trabalho apresentamos os primeiros resultados sobre medida do tempo de vida de estados de Rydberg utilizando átomos frios confinados em uma armadilha magneto-optica de 85Rb. Medidas de tempo de vida de estados altamente excitados são importantes para o teste de teorias modernas sobre interação átomo-vácuo; desta forma medidas precisas são necessárias. A utilização de átomos frios apresenta várias vantagens quando comparadas com técnicas convencionais. Entre elas podemos citar a possibilidade de observação do sistema atômico por longos períodos (>100 &#181;s), e o controle da densidade de forma eficiente para evitar a manifestação de efeitos indesejáveis (colisões, superradiância) que limitam a precisão da medida. Apresentamos a medida do tempo de vida do estado 27D e 38S e comparamos os resultados experimentais com previsões teóricas de diferentes modelos. Algumas discrepâncias são observadas, o que reforça a necessidade da obtenção de um conjunto maior de medidas incluindo outros níveis para indicar qual modelo teórico é mais próximo da realidade. / In this work we present our first results on lifetime measurement of Rydberg states using cold atoms held in a magneto-optical trap of 85Rb. Lifetime measurements of highly excited states are important for testing modern theories on atom-vaccum interaction, therefore precise measurements are required. The use of cold atoms presents some advantage when compared with conventional techniques. Among them we cam point out the possibility of atomic observation for long periods of time (<100 &#181;s), the atomic density control in order to avoid undesired effects (such collisions and superradiance) which can limit the measurement precision. We present the lifetime measurement of 27D and 38S states and compared the experimental results with theoretical prediction using different models. Some discrepancies are observed, which indicates the need of a large set of measurement for other states in order to indicate the best model.