Depuis l’avènement de la mécanique quantique, l’étude des interactions lumière-matière à l’échelle quantique s’est énormément développée en tant que domaine de recherche. Par exemple, grâce à des prédictions théoriques surprenantes, des interactions d’une force sans précédant ont été démontrées entre de la matière et des radiations terahertz et microonde. Ces résultats correspondent à un régime dit de couplage ultrafort, atteint lorsque l’énergie d’interaction devient comparable aux énergies propres de la lumière et de la matière lorsque celles-ci n’interagissent pas. Dans ce régime, des propriétés intrigantes peuvent subsister telles que la présence de photons même lors qu’aucune énergie n’est fournie au système. Cependant, ces photons ne peuvent, a priori, être émis du système vers l’extérieur de manière à pouvoir être mesurés et par conséquent démontrer ces propriétés.Dans cette thèse, nous avons étudié ces propriétés intrigantes et proposé plusieurs moyens permettant d’y accéder expérimentalement. Nous nous sommes appuyés sur plusieurs plate-formes physiques qui sont de bon candidats pour ces études, et pour chacun de ces systèmes nous avons mis au point un modèle mettant en évidence ces propriétés d’une manière ou d’une autre. De cette façon, nous avons exploré le lien entre le régime de couplage ultrafort et la génération d’états non-classiques de la lumière. En outre, dans une étude plus ouverte nous avons montré que les interactions lumière- matière dans l’une de ces plate-formes peuvent être utilisés pour concevoir des protocols de communication quantique. En plus de montrer un intérêt fondamental, nos résultats s’inscrivent dans une optique de développement d’applications pour les technologies quantiques en utilisant différents systèmes expérimentaux disponibles actuellement / Since the advent of quantum mechanics, the study of light-matter interactions at thequantum level has been greatly developed as a research field. For instance, surprisingtheoretical predictions gave rise to experiments with unprecedented interactionstrengths between matter, and terahertz and microwave radiations. These results correspondto the so-called ultrastrong coupling regime, that is reached when the interactionenergy becomes comparable to the typical energies of the light and matter when they arenot interacting. In this regime, intriguing properties can be found such as the presenceof photons even when no energy is given to the system. However, these photons cannot,a priori, be emitted from the system to the outside world in order to be measured andtherefore demonstrate these properties. In this thesis, we studied these intriguing properties and proposed several means toaccess them experimentally. We relied on several physical platforms which are goodcandidates for such studies, and for each one of these systems we devised a model thatcan evidence these properties one way or another. By doing so, we explored the linkbetween the ultrastrong coupling regime and the generation of nonclassical states oflight. Additionally, as an outlook we showed that the light-matter interactions in oneof these platforms could be used to design quantum communication protocols. On topof showing fundamental interest, our results fit in the line of developing applications forquantum technologies using different experimentally available systems.

The quantum properties of matter waves, in particular quantum correlations and entanglement are an important frontier in atom optics with applications in quantum metrology and quantum information. In this thesis, we report the first observation of sub-Poissonian fluctuations in the magnetization of a spinor 87Rb condensate. The fluctuations in the magnetization are reduced up to 10 dB below the classical shot noise limit. This relative number squeezing is indicative of the predicted pair-correlations in a spinor condensate and lay the foundation for future experiments involving spin-squeezing and entanglement measurements. We have investigated the limits of the imaging techniques used in our lab, absorption and fluorescence imaging, and have developed the capability to measure atoms numbers with an uncertainly < 10 atoms. Condensates as small as ≈ 10 atoms were imaged and the measured fluctuations agree well with the theoretical predictions. Furthermore, we implement a reliable calibration method of our imaging system based on quantum projection noise measurements. We have resolved the individual lattice sites of a standing-wave potential created by a CO2 laser, which has a lattice spacing of 5.3 µm. Using microwaves, we site-selectively address and manipulate the condensate and therefore demonstrate the ability to perturb the lattice condensate of a local level. Interference between condensates in adjacent lattice sites and lattice sites separated by a lattice site are observed.

As redes ópticas estão passando por mudanças significativas, impulsionadas pelo crescimento exponencial do tráfego, principalmente advindo de serviços multimídia e armazenamento em nuvem. Esta demanda exigirá aumento da capacidade da taxa de transmissão para padrões como 400 Gb/s e 1 Tb/s. Nesse contexto, foi proposta uma arquitetura de rede com grade de frequências granular flexível chamada elastic optical network (EON). A EON divide o espectro de frequências em fatias (slots) de tamanho fixo e aloca grupos de slots contíguos estritamente de acordo com os requisitos de banda das demandas de conexão, implicando eficiência de uso do espectro. Com o aumento significativo da taxa de transmissão, acentuou-se a preocupação em manter a sobrevivência da rede, já que pouco tempo de queda no serviço pode acarretar uma imensa perda de dados. Neste trabalho, investigamos esquemas de proteção baseados em caminhos compartilhados (shared-path protection, SPP) e esquemas de restauração de tráfego. Avaliamos esquemas divulgados na literatura como o dynamic load balancing shared-path protection (DLBSPP) e esquemas de restauração como o traffic aware restoration (TAR) e bandwidth squeezed restoration (BSR). Avaliamos também uma heurística de alocação de slots chamada inverted dual stack (IDS). O DLBSPP utiliza balanceamento dinâmico de carga para computar os caminhos primários e de proteção compartilhados. O TAR executa a restauração dinâmica ordenando as conexões por granularidade de banda. O BSR utiliza a capacidade de contração de banda do EON para restaurar conexões por meio da política de melhor esforço ou de banda garantida, dependendo do acordo de níveis de serviço do cliente. O esquema IDS concentra o maior número possível de slots compartilhados em uma região do espectro. As medidas de desempenho dos algoritmos são avaliadas segundo as métricas: probabilidade de bloqueio, taxa de utilização do espectro, número médio de hops e taxa de restauração falha. As simulações computacionais mostram o bom desempenho da utilização do esquema IDS com DLBSPP. / Optical networks are undergoing significant changes driven by the exponentially growing traffic, especially coming from multimedia and cloud storage services. This demand will require increasing of the transmission rate capacity as high as 400 Gb/s and 1 Tb/s. Within this context, it was proposed the elastic optical network (EON), which is a network architecture with flexible granular frequency grid. EON divides the frequency spectrum into slices (slots) of fixed size and allocates groups of contiguous slots strictly according to the bandwidth requirement of the connection demands, providing high spectrum use efficiency. The significant increase in transmission rate put emphasis on the need to maintain the survival of the network, since the occurrence of faults in the network nodes or links can cause huge loss of data. In this work, we investigate protection schemes based on shared-path protection (SPP) and traffic restoration schemes. We evaluate schemes related in the literature, such as the dynamic load balancing shared-path protection (DLBSPP), and restoration schemes such as the traffic aware restoration (TAR) and the bandwidth squeezed restoration (BSR). The DLBP scheme uses dynamic load balancing to compute primary and shared protection paths. The TAR performs dynamic restoration ordering the connections based on band granularity. The BSR uses EON\'s band squeezing feature to restore connections by means of the best effort or guaranteed bandwidth strategy, depending on the customer\'s service level agreement. IDS scheme concentrates the maximum possible number of shared slots in a given region of the spectrum. Performance of the algorithms are evaluated according to metrics: blocking probability, spectrum utilization rate, average number of hops and failure restoration rate. Computer simulations show that the use of the IDS scheme improves the performance of the investigated algorithms.

Dans cette thèse, nous discutons de la dégénérescence et de la construction d’états cohérents généralisés dans les systèmes quantiques en deux dimensions d’espace. Nous développons un schéma pour obtenir des spectres non dégénérés et des combinaisons linéaires appropriées des états propres d’énergie correspondants. Lorsque la dégénérescence dans le spectre d’énergie est linéaire dans les nombres quantiques, nous définissons des opérateurs d’échelle général- isés qui conduisent à une chaîne d’états avec un ensemble naturel de coefficients. De plus, nous récupérons des relations de complétude pour les états généralisés. Lorsque le spectre d’énergie est quadratique dans les nombres quantiques, nous utilisons certains résultats de la théorie des nombres pour catégoriser la dégénérescence et, par conséquent, les combinaisons linéaires appropriées des états propres d’énergie associés. En particulier, nous étudions des oscillateurs harmoniques bidimensionnels isotropes et anisotropes ainsi que le potentiel Morse bidimensionnel et son partenaire supersymétrique non séparable. Dans tous les cas, nous construisons des états cohérents et discutons certains aspects de leur caractère non classique. On retrouve une certaine compression dans les quadratures conjuguées, une dépendance non triviale des variances des quadratures vis-à-vis des paramètres introduits lors de la définition des spectres non dégénérés, et un problème de localisation pour les fonctions d’onde. Comme application, nous étudions le problème de la quantification et de l’analyse semi-classique de l’espace des phases en deux dimensions en exploitant la complétude des familles généralisées d’états cohérents comprimés en deux dimensions. / In this thesis we discuss degeneracy and the construction of generalised coherent states in two-dimensional quantum systems. We develop a scheme for defining non-degenerate spectra and the corresponding averaged energy eigenstates. When the degeneracy in the spectrum is linear in the quantum numbers, we are able to define generalised ladder operators which lead to a chain of states with a natural set of coefficients. Additionally, we are able to recover completeness relations for the generalised states. On the other hand, when the spectrum is quadratic in the quantum numbers, we utilise some results from number theory to categorise the degeneracy and correspondingly the averaged energy eigenstates. In particular we study the two-dimensional isotropic and anisotropic oscillators as well the two-dimensional Morse potential and its non-separable supersymmetric partner. In all cases, we compute the coherent states and discuss certain aspects of their non-classicality. We find squeezing between conjugate quadratures, non-trivial dependence of the quadrature variances on the parameters introduced when defining the non-degenerate spectra, and non-localisation of wavefunctions. As an application, we study the problem of quantisation and semiclassical phase space analysis in two dimensions by exploiting the completeness of generalised families of two-dimensional squeezed coherent states.