<p>An atom or ion can change quantum state, usually through emission or absorption of a photon. The photon has the same energy as the energy difference between the states of the transition. The states, or energy levels, of an atom are quantized and light emitted, or absorbed, from the atom is therefore of specific wavelengths, giving spectral lines. The spectrum of an atomic ion is unique and contains information of the structure and energy levels of the ion. The spectrum of an atom can be used as a fingerprint in determinations of the abundance of the element in different objects.</p><p>This thesis is focused on some weak effects observed by spectroscopy. Although the effects are weak, they turn out to be of great importance. According to quantum mechanics transitions between certain states are not allowed. Here the weak effects open the possibility for transitions. Spectral lines from forbidden transitions are very weak and difficult to observe under ordinary laboratorial conditions, but they are commonly observed from astrophysical objects and can be very useful for diagnostics of astrophysical plasmas. The first reported observation of forbidden lines was from an astrophysical object and at that time supposed to be from new, previous unknown, elements. If all possible decay channels from an energy level are forbidden, the energy level is metastable and has usually a lifetime 10$^8$ times longer than an ordinary excited state. Measurements of such long lifetimes are difficult since the ion need to be confined during the observation time. Confinement of ions can be achieved with a storage device, such as a storage ring or a trap, where the ions are stored without interacting with each other or the surroundings.</p><p>A laser probing technique has been developed at the storage ring CRYRING, for measurements of lifetimes of metastable states. The technique has now been improved for measurement of longer lifetimes. The technique has also been modified to fit when measuring on negative ions. Results of lifetime measurements are reported and the techniques and methods used are described.</p><p>Another weak effect is hyperfine interaction, which splits the energy levels of an atom or ion. Hyperfine splitting is very small and usually special spectral techniques are needed to resolve such structure. A laser can, in combination with an electromagnetic radio-frequency field, be used for accurate determination of hyperfine structures in atomic ions. Such measurements are also important for evaluation of astrophysical properties, since hyperfine structure can broaden the spectral lines. An experimental setup for such double resonance measurements has been developed and constructed. Results of experimental measurements are reported and the technique is described.</p>

An atom or ion can change quantum state, usually through emission or absorption of a photon. The photon has the same energy as the energy difference between the states of the transition. The states, or energy levels, of an atom are quantized and light emitted, or absorbed, from the atom is therefore of specific wavelengths, giving spectral lines. The spectrum of an atomic ion is unique and contains information of the structure and energy levels of the ion. The spectrum of an atom can be used as a fingerprint in determinations of the abundance of the element in different objects. This thesis is focused on some weak effects observed by spectroscopy. Although the effects are weak, they turn out to be of great importance. According to quantum mechanics transitions between certain states are not allowed. Here the weak effects open the possibility for transitions. Spectral lines from forbidden transitions are very weak and difficult to observe under ordinary laboratorial conditions, but they are commonly observed from astrophysical objects and can be very useful for diagnostics of astrophysical plasmas. The first reported observation of forbidden lines was from an astrophysical object and at that time supposed to be from new, previous unknown, elements. If all possible decay channels from an energy level are forbidden, the energy level is metastable and has usually a lifetime 10$^8$ times longer than an ordinary excited state. Measurements of such long lifetimes are difficult since the ion need to be confined during the observation time. Confinement of ions can be achieved with a storage device, such as a storage ring or a trap, where the ions are stored without interacting with each other or the surroundings. A laser probing technique has been developed at the storage ring CRYRING, for measurements of lifetimes of metastable states. The technique has now been improved for measurement of longer lifetimes. The technique has also been modified to fit when measuring on negative ions. Results of lifetime measurements are reported and the techniques and methods used are described. Another weak effect is hyperfine interaction, which splits the energy levels of an atom or ion. Hyperfine splitting is very small and usually special spectral techniques are needed to resolve such structure. A laser can, in combination with an electromagnetic radio-frequency field, be used for accurate determination of hyperfine structures in atomic ions. Such measurements are also important for evaluation of astrophysical properties, since hyperfine structure can broaden the spectral lines. An experimental setup for such double resonance measurements has been developed and constructed. Results of experimental measurements are reported and the technique is described.

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Nous étudions dans cette thèse des problèmes d’optimisation avec applications dans les réseaux optiques. Les problèmes étudiés sont liés à la tolérance aux pannes et à l’utilisation efficace des ressources. Les résultats obtenus portent principalement sur la complexité de calcul de ces problèmes. La première partie de cette thèse est consacrée aux problèmes de trouver des chemins et des chemins disjoints. La recherche d’un chemin est essentielle dans tout type de réseaux afin d’y établir des connexions et la recherche de chemins disjoints est souvent utilisée pour garantir un certain niveau de protection contre les pannes dans les réseaux. Nous étudions ces problèmes dans des contextes différents. Nous traitons d’abord les problèmes de trouver un chemin et des chemins lien ou nœud- disjoints dans des réseaux avec nœuds asymétriques, c’est-à-dire des nœuds avec restrictions sur leur connectivité interne. Ensuite, nous considérons les réseaux avec des groupes de liens partageant un risque (SRLG) en étoile : ensembles de liens qui peuvent tomber en panne en même temps suite à un événement local. Dans ce type de réseaux, nous examinons le problème de recherche des chemins SRLG-disjoints. La deuxième partie de cette thèse est consacrée au problème de routage et d’allocation de spectre (RSA) dans les réseaux optiques élastiques (EONs). Les EONs sont proposés comme la nouvelle génération des réseaux optiques et ils visent une utilisation plus efficace et flexible des ressources optiques. Le problème RSA est central dans les EONs. Il concerne l’allocation de ressources aux requêtes sous plusieurs contraintes. / We study in this thesis optimization problems with application in optical networks. The problems we consider are related to fault-tolerance and efficient resource allocation and the results we obtain are mainly related to the computational complexity of these problems. The first part of this thesis is devoted to finding paths and disjoint paths. Finding a path is crucial in all types of networks in order to set up connections and finding disjoint paths is a common approach used to provide some degree of protection against failures in networks. We study these problems under different settings. We first focus on finding paths and node or link-disjoint paths in networks with asymmetric nodes, which are nodes with restrictions on their internal connectivity. Afterwards, we consider networks with star Shared Risk Link Groups (SRLGs) which are groups of links that might fail simultaneously due to a localized event. In these networks, we investigate the problem of finding SRLG-disjoint paths. The second part of this thesis focuses on the problem of Routing and Spectrum Assignment (RSA) in Elastic Optical Networks (EONs). EONs are proposed as the new generation of optical networks and they aim at an efficient and flexible use of the optical resources. RSA is the key problem in EONs and it deals with allocating resources to requests under multiple constraints. We first study the static version of RSA in tree networks. Afterwards, we examine a dynamic version of RSA in which a non-disruptive spectrum defragmentation technique is used. Finally, we present in the appendix another problem that has been studied during this thesis.

Cette thèse étudie les aspects combinatoires, algorithmiques et la complexité de problèmes de théorie des graphes, et tout spécialement de problèmes liés aux notions de marches, de transitions et de distance dans les graphes. Nous nous intéressons d’abord au problème de traffic monitoring, qui consiste à placer aussi peu de capteurs que possible sur les arcs d’un graphe de façon à pouvoir reconstituer des marches d’objets. La caractérisation d’instances intéressantes dans la pratique nous amène à la notion de transitions interdites, qui renforce le modèle de graphe. Notre travail sur les graphes à transitions interdites comprend aussi l’étude de la notion d’ensemble de transitions connectant, que l’on peut voir comme l’analogue en terme de transitions de la notion d’arbre couvrant. Une partie importante de cette thèse porte sur les graphes géométriques, qui sont des graphes dont les sommets sont des points de l’espace réel et dont les arêtes sont déterminées par les distances géométriques entre les sommets. Ces graphes sont au coeur du célèbre problème de Hadwiger-Nelson et nous sont d’une grande aide dans notre étude de la densité des ensembles qui évitent la distance 1 dans plusieurs types d’espaces normés. Nous développons des outils pour étudier ces problèmes et les utilisons pour prouver la conjecture de Bachoc-Robins sur plusieurs paralléloèdres. Nous nous penchons aussi sur le cas du plan euclidien et améliorons les bornes sur la densité des ensembles évitant la distance 1 et sur son nombre chromatique fractionnaire. Enfin, nous étudions la complexité de problèmes d’homomorphismes de graphes et établissons des théorèmes de dichotomie sur la complexité des homomorphismes localement injectifs vers les tournois réflexifs. / This thesis studies combinatorial, algorithmic and complexity aspects of graph theory problems, and especially of problems related to the notions of walks, transitions and distances in graphs. We first study the problem of traffic monitoring, in which we have to place as few censors as possible on the arcs of a graph to be able to retrace walks of objects. The characterization of instances of practical interests brings us to the notion of forbidden transitions, which strengthens the model of graphs. Our work on forbidden-transition graphs also includes the study of connecting transition sets, which can be seen as a translation to forbidden-transition graphs of the notion of spanning trees. A large part of this thesis focuses on geometric graphs, which are graphs whose vertices are points of the real space and whose edges are determined by geometric distance between the vertices. This graphs are at the core of the famous Hadwiger- Nelson problem and are of great help in our study of the density of sets avoiding distance 1 in various normed spaces. We develop new tools to study these problems and use them to prove the Bachoc-Robins conjecture on several parallelohedra. We also investigate the case of the Euclidean plane and improve the bounds on the density of sets avoiding distance 1 and on its fractional chromatic number. Finally, we study the complexity of graph homomorphism problems and establish dichotomy theorems for the complexity of locally-injective homomorphisms to reflexive tournaments.

Using a narrow-band resonant fluorescence spectra from a nano-cell with a thickness of L= [lambda]/2, and VSOP resonances formed at a thickness L =[lambda] ([lambda] is the wavelength of the resonant radiation), for the first time it was experimentally investigated the behaviour of the frequency and intensity (transition probabilities) of the atomic hyperfine structure transitions between the 85Rb, 87Rb, D1 and D2 lines Zeeman sublevels in external magnetic fields in range 5 - 7000G. The behaviour of tens of previously unstudied atomic transitions was analyzed and it is demonstrated that the intensities of these lines can both greatly increase, and decrease (tenfold). For the first time it is demonstrated that, in the case of partial pressure of neon buffer gas up to 6~torr into the nano-cell of thickness L = [lambda] filled with Rb, VSOP resonances are recorded confidently, while the addition of 0.1~torr neon buffer gas in a cell of a centimeter thickness leads to the complete disappearance of VSOP resonances formed with the help of the widely used technique of saturated absorption. It is demonstrated for the first time that the spectral width of the resonant fluorescence spectra of the rubidium nano-cell with thickness L= [lambda]/2, for all values of the neon buffer gas pressures is much narrower (6-8 times) compared with the resonant fluorescence spectra of an ordinary centimeter cell containing rubidium with the same pressures of neon

A l'aide d'un spectre de fluorescence de résonance à bande étroite obtenu avec une nano-cellule d'épaisseur L= [lambda]/2 et des résonances VSOP formées pour une épaisseur L =[lambda] ([lambda] est la longueur d'onde de la radiation résonnante), cette thèse présente pour la première fois une étude expérimentale du comportement en fréquence et en intensité (probabilités de transition) des transitions atomiques de la structure hyperfine entre sous-niveaux Zeeman des raies D1 and D2 pour le 85Rb et le 87Rb en présence de champs magnétiques extérieurs compris entre 5 et 7000 G. Le comportement d'une dizaine de transitions atomiques inétudiées à ce jour a été analysé et nous avons démontré que l'intensité de ces raies peut montrer alternativement de grandes variations : jusqu'à un facteur 10 de taux de croissance ou de décroissance. Pour la première fois, nous avons parfaitement enregistré des résonances VSOP dans le cas où un gaz tampon (néon de pression partielle 6 torr) est introduit dans la nano-cellule d'épaisseur L =[lambda], alors que l'addition d'un gaz tampon (néon) même à une pression partielle de 0,1 torr, dans une cellule d'épaisseur centimétrique conduit à une complète disparition de ces résonances VSOP obtenues par la méthode usuelle d'absorption saturée. Enfin, nous avons montré pour la première fois que la largeur spectrale d'un spectre de fluorescence de résonance d'une nano-cellule de rubidium d'épaisseur L= [lambda]/2, quelques soient les pressions du gaz tampon (néon), est beaucoup plus étroite (6 à 8 fois) que celle obtenue avec une cellule centimétrique de rubidium pour les mêmes valeurs de pressions / Using a narrow-band resonant fluorescence spectra from a nano-cell with a thickness of L= [lambda]/2, and VSOP resonances formed at a thickness L =[lambda] ([lambda] is the wavelength of the resonant radiation), for the first time it was experimentally investigated the behaviour of the frequency and intensity (transition probabilities) of the atomic hyperfine structure transitions between the 85Rb, 87Rb, D1 and D2 lines Zeeman sublevels in external magnetic fields in range 5 - 7000G. The behaviour of tens of previously unstudied atomic transitions was analyzed and it is demonstrated that the intensities of these lines can both greatly increase, and decrease (tenfold). For the first time it is demonstrated that, in the case of partial pressure of neon buffer gas up to 6~torr into the nano-cell of thickness L = [lambda] filled with Rb, VSOP resonances are recorded confidently, while the addition of 0.1~torr neon buffer gas in a cell of a centimeter thickness leads to the complete disappearance of VSOP resonances formed with the help of the widely used technique of saturated absorption. It is demonstrated for the first time that the spectral width of the resonant fluorescence spectra of the rubidium nano-cell with thickness L= [lambda]/2, for all values of the neon buffer gas pressures is much narrower (6-8 times) compared with the resonant fluorescence spectra of an ordinary centimeter cell containing rubidium with the same pressures of neon