Les plasmons de surface sont des modes non-radiatifs qui vivent à l'interface d'un diélectrique et d'un métal. Ils peuvent confiner la lumière à des échelles sub-longueur d'onde. Néanmoins, leur propagation reste limitée par les pertes inhérentes au métal qui entraînent une absorption rapide du mode. L'objet de cette thèse est l'étude du couplage des plasmons de surface dans des structures planes métallo-diélectriques. L'obtention des propriétés des différents modes nécessite le prolongement des solutions dans le plan complexe définissant la constante de propagation. La méthode mise en œuvre consiste à déterminer les pôles de la matrice de diffusion en utilisant les intégrales de Cauchy. Une première solution pour résoudre le problème de propagation des plasmons de surface consiste à coupler ces modes entre eux. Dans un milieu symétrique, lorsque l'épaisseur d'un film métallique devient suffisamment faible, le couplage entre les modes plasmons existants sur chaque surface devient possible. L'un des deux modes couplés ainsi créé, dit plasmon longue portée, a une longueur de propagation supérieure à celle du plasmon de surface usuel tandis que l'autre, dit plasmon à courte portée, se propage moins. Nous présentons une configuration permettant l'excitation du mode longue portée sans le mode courte portée grâce à une couche métallique déposée sur un substrat infiniment conducteur. Cette excitation peut alors être effectuée dans l'air et permettre des applications comme la détection et la caractérisation de molécules. Ensuite, nous présentons le couplage entre deux guides d'ondes diélectriques, et plus particulièrement la théorie des modes couplés, étendue au cas de la polarisation transverse magnétique. Nous considérons aussi le cas de la PT symétrie. La dernière partie de ce mémoire présente la démonstration du régime de couplage fort entre un plasmon de surface et un mode guidé. Nous mettons alors en évidence une augmentation de la longueur de propagation pour le mode hybride plasmon dont le confinement reste celui d'un mode de surface. Un gain linéaire est ensuite ajouté dans les différentes couches de la structure pour en étudier l'effet. L'ajout de gain dans la couche intermédiaire entre les deux modes couplés a pour conséquence l'exaltation de la longueur de propagation des modes et plus particulièrement du mode hybride plasmon qui peut alors se propager au-delà du millimètre. / Surface plasmon polaritons are non radiative modes which exist at the interface between a dielectric and a metal. They can confine light at sub-wavelength scales. However, their propagation is restricted by the intrinsic losses of the metal which imply a rapid absorption of the mode. The aim of this thesis is the study of the coupling of surface plasmons in metallo-dielectric planar structures. Obtaining the properties of the modes implies the extension of the solutions to the complex plane of propagation constants. The method used consists in determining the poles of the scattering matrix by means of Cauchy's integrals. The first solution to solve the problem of propagation of the surface plasmons consists in coupling these modes to one another. In a symmetric medium, when the thickness of the metallic film becomes thin enough, the coupling between the plasmon modes which exist on each side becomes possible. One of the coupled modes which is created, the so-called long range surface plasmon, has a bigger propagation length than the usual plasmon whereas the other coupled mode, named short range surface plasmon, has a smaller propagation length. We present a configuration which allows the excitation of the long range surface plasmon without the short range mode with a metallic layer deposited on a perfect electric conductor substrate. This excitation can be done in air and allows applications, such as the detection and the characterisation of molecules. Then, we present the coupling between dielectric waveguides, and, in particular, the coupled-mode theory in the case of the transverse magnetic polarisation. We consider also the case of PT symmetric structure. The last part of this work presents the demonstration of the strong coupling regime between a surface plasmon and a guided mode. We demonstrate an increase of the propagation length of the hybrid surface plasmon, which still has the confinement of a surface mode. A linear gain is added in the different layers of the structure. When the gain is added in the layer between both coupled modes allows an enhancement of the propagation lengths of the modes, and more precisely of the hybrid surface plasmon mode, which can propagate at the millimeter scale.

Pour améliorer la conception des turbomachines, les industriels doivent appréhender des phénomènes aéroélastiques complexes présents dans les compresseurs comme les cycles limites d’interaction fluide-structure des fans. La compréhension et la modélisation de ces phénomènes impliquent de développer des modèles numériques complexes intégrant des phénomènes multi-physique et de valider ces modèles à l’aide de bancs d’essais. Le banc d’essai du compresseur CREATE est instrumenté pour étudier des instabilités aérodynamiques couplées à des vibrations, notamment sur le rotor du premier étage, et permet de valider des modèles numériques. La modélisation de l’écoulement en amont du premier étage du compresseur à l’aide du logiciel Turb’Flow, développé pour l’étude des écoulements dans les compresseurs aéronautiques, a permis de mettre en évidence l’importance des conditions limites d’entrée pour l’obtention de résultats précis. En particulier, il a été possible de modéliser correctement l’ingestion d’une alimentation non-homogène en entrée de la roue directrice d’entrée. Ce phénomène peut se produire en amont des fans et interagir avec un mode de la structure. Une stratégie de couplage partitionné fort explicite dans le domaine temporel a été introduite dans le logiciel Turb’Flow. Comme cette méthode présente un risque de décalage temporel à l’interface fluide-structure, une attention particulière a été portée à la modélisation de la conservation de l’énergie à cette interface. La conservation de l’énergie à l’interface est cruciale quand les déplacements sont importants et quand un comportement non-linéaire fort apparaît entre le fluide et la structure (onde de choc et amortissement structurel nonlinéaire). Parallèlement au développement du module aéroélastique, le schéma implicite de Runge- Kutta d’ordre 3 en temps (RKI-3) a été développé et évalué sur un cas de dynamique (vibration d’une aube de turbine transsonique) et sur un cas de propagation d’onde de choc. L’utilisation du schéma RKI-3 permet d’augmenter, à iso-précision, d’un ordre le pas de temps par rapport aux schémas de Gear et de Newmark. S’il apporte un gain en temps CPU pour l’étude de la dynamique des structures, il est pénalisant dans le cadre de simulation URANS. Cependant, le schéma RKI-3 est utilisable dans le cadre de simulations couplées fluide-structure. / To increase turbomachinery design, manufacturers have to comprehend complex aeroelastic phenomena involving compressors like fluid-structure interaction limit cycles of fans. The understanding and the modeling of these phenomena involve developing complex solvers coupling techniques and validating these techniques with bench tests. The bench test of the CREATE compressor is instrumented to study the coupling between aerodynamic instabilities and structure vibration, in particular on the first stage rotor, and allows to validate numerical techniques. The flow modeling upstream to the first stage with the Turb’Flow flow solver (targeting turbomachinery applications) shows that, to have accurate results, inlet limit conditions must take into account. The ingestion of non-homogeneous flow upstream to the inlet guide vane is accurately modeled. This phenomenon can appear upstream to fans and interact with structure Eigen-modes. Explicit partitioned strong coupling considered in time domain was implemented in a Turb’Flow flow solver. As there is a risk of time shift at the fluid-structure interface, careful attention should be paid to energy conservation at the interface. This conservation is crucial when displacements are large and when strong non-linear behaviors occur in both fluid and structure domains, namely shock waves, flow separations and non-linear structural damping. In parallel with coupling technique development, the three-order implicit Runge-Kutta scheme (RKI-3) was implemented and validated on a structure dynamic case (transonic turbine blade vibration) and on a case of shock waves propagation. The RKI-3 scheme allows increasing the time step of one order of magnitude with the same accuracy. There is a CPU time gain for structure dynamics simulations, but no for URANS simulations. However, the RKI-3 scheme can be to use for fluid-structure coupling simulations. The coupling technique was validated on a test case involving tube in which the shock wave impinges on a cross flow flexible panel, initially at rest. This case allows modeling an interaction between sonic flow and a panel movement with a tip clearance. Some numerical simulations were carried out with different temporal schemes. The RKI-3 scheme has no influence on results (compared with Gear and/or Newmark scheme) on the energy conservation at the fluid-structure interface. Compared to experimental results, pressure is in fairly good ix Liste des publications agreement. The analysis of numerical results highlighted that a vertical shock tube with up and down waves creates pressure fluctuation. Frequency is under predicted and amplitude is not in fairly good agreement. The panel root modeling might be questionable.

Diese Arbeit beschäftigt sich mit der Untersuchung der starken Kopplung und Laseremission in Strukturen, die ZnO, ZnCdO oder organische Moleküle als aktives Material enthalten. Die ZnCdO basierten Vielfachquantengräben erreichen ihre Laserschwelle durch optische Ruckkopplung an streuenden Luftlöchern. Diese Emitter nennt man random laser. Die Dynamik ihrer Emission unter quasi-stationären Bedingungen ist der hier gezeigte Fokus. Hoch reproduzierbare Anregungen werden verwendet um sowohl die Dynamik eines einzelnen Beschusses aber auch die Unterschiede verschiedener Anregungen zu untersuchen. Die experimentellen Daten werden durch numerische Simulation qualitativ reproduziert und mit Methoden der Netzwerktheorie interpretiert. Die verbreitetere optische Rückkopplung durch einen Resonator wird in der Untersuchung des Moleküls L4P und seiner Spiro-derivate benutzt. Zwei identische Braggspiegel umschließen die aktive Schicht aus L4P-SP2, das in eine Polymermatrix eingebettet ist, eine Dicke von 12 Mikrometer hat und in einer einzelnen Mode lasert (schwache Kopplung). Durch Verringerung der aktiven Schicht auf die Hälfte der Resonanzwellenlänge wird das System in den Bereich der starken Kopplung gebracht. Eine Rabi-Aufspaltung von 90 meV wird zu beiden vibronischen Resonanzen beobachtet. Die energetische Position in Resonanz zu ZnO macht dieses Molekül zu einem guten Kandidaten für die Fertigung einer hybriden Mikrokavität im Bereich der starken Kopplung. Dies wurde in einer teilweise epitaktisch gewachsenen Mikrokavität angewandt, die aus einem ZnMgO basierten Braggspiegel und sechs Quantengräben besteht. Darauf folgt eine aufgeschleuderte Schicht von L4P in der Polymermatrix. Der Resonator wird mit einem dielektrischen Spiegel fertiggestellt. Tieftemperatur Reflektion zeigt eine deutlichen ausweichen und eine gleichverteilte Mischung der drei Resonanz im mittleren Polaritonzweig. / This thesis presents the investigation of strong coupling and lasing in structures using ZnO, ZnCdO or organic molecules as active material. The ZnCdO based multi quantum well structures reach the lasing threshold by using scattering at air holes as the optical feedback. Such emitters are called random lasers. The dynamics of their emission under quasi-stationary condition is the point of interest presented. Highly reproducible excitations are used to investigate the single shot dynamics and their shot to shot differences. The experimental data is qualitatively reproduced by numerical simulation and interpreted by means of network theory. The more common optical feedback by a cavity is applied in the investigation of the molecule L4P and its spiro-derivatives. Using two identical SiO2/ZrO2 based Bragg reflectors surrounding an active layer of L4P-SP2 in a polymer matrix of approximately 12 microns thickness reached single mode lasing (weak coupling). Reducing the active layer thickness to half the resonance wavelength pushes the system into the strong coupling regime. Angular resolved reflectivity shows the anticrossing of the tuned cavity resonance to two vibronic transitions of the molecule. The Rabi-splitting to both vibronic resonances reaches around 90 meV. The energetic position in resonance to ZnO makes this molecule a promising candidate for a hybrid inorganic/organic microcavity in the strong coupling regime. This is used in a partially epitaxially grown microcavity composed of a ZnMgO based Bragg reflector (alternating layers of different Mg content) and six quantum wells. This is followed by a spincoated layer of L4P in a polymer matrix. The cavity is finished by a dielectric mirror. Low temperature reflectivity shows a clear anticrossing reaching an equal mixing of all resonances for the middle branch.

Cold bosonic atoms trapped in optical lattices formed by standing wave interference patterns of multiple laser beams constitute excellent emulators of models of strongly correlated quantum systems of bosons. In this thesis, we develop and deploy strong-coupling expansion (i.e., an expansion in terms of the ratio of the inter-site hopping amplitude of the bosons to the strength of their interactions) techniques for studying the properties of three different instances of such systems. In the first instance, we have used strong coupling expansion techniques to calculate the density pro le for bosonic atoms trapped in an optical lattice with an overall harmonic trap at finite temperatures and large on site interaction in the presence of super fluid regions. Our results match well with quantum Monte Carlo simulations at finite temperature. We present calculations for the entropy per particle as a function of temperature which can be used to calibrate the temperature in experiments. Our calculations for the scaled density in the vacuum-to-super fluid transition agree well with the experimental data for appropriate temperatures. We also discuss issues connected with the demonstration of universal quantum critical scaling in the experiments. Experimental realizations of “atomtronic" Josephson junctions have recently been created in annular traps in relative rotation with respect to potential barriers that generate the weak links. If these devices are additionally subjected to optical lattice potentials, then they can incorporate strong-coupling Mott physics within the design, which can modify the behaviour and can allow for interesting new configurations of system generated barriers and of super fluid ow patterns. we have examined theoretically the behavior of a Bose super fluid in an optical lattice in the presence of an annular trap and a barrier across the annular region which acts as a Josephson junction. As the fluid is rotated relative to the barrier, it generates circulating super-currents until, at larger speeds of rotation, it develops phase slips which are typically accompanied by vortices. We use a finite temperature strong-coupling expansion about the mean- held solution of the Bose Hubbard model to calculate various properties of the device. In addition, we discuss some of the rich behavior that can result when there are Mott regions within the system. Rubidium-Cesium dipolar molecule formation through Feshbach resonance is an area of great current interest, for, the dipolar molecules, once formed, interact via v long range dipolar forces, leading to possibilities of novel phases. Experimentalists currently make such systems mostly using trial and error, and the resulting efficiencies for molecule formation tend to be low. With a goal to assist cold-atom experimentalists to achieve higher e ciencies of molecule formation, we have estimated the trap parameters for Rb and Cs atoms in a 3D optical lattice required to create single occupancy per site Mott phase for both the species in the same regions of the trap. We thus identify the ne tuning of the external magnetic held near Rb-Cs Feshbach resonance required to achieve highest probability for creating single Rb-Cs Feshbach molecules in the system. We have used the Falicov-Kimball model to describe the relevant system and strong-coupling expansions about the mean- held solution to calculate the density pro les for both species and efficiency for molecule formation, determined by overlapping regions of single occupancy for both Rb and Cs, up to second order in the expansion. We also calculate the entropy per particle which serves as an estimation of the temperature in the experimental system

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A física de partículas vem atualmente estudando tópicos como o plasma de quarks e glúons (QGP), o bóson de Higgs e a matéria escura, que requerem experimentos de colisões entre partículas cada vez mais energéticas. Para isso, são necessários aceleradores capazes de gerar partículas projéteis a cada vez mais altas energias, o que pode levar a uma nova física. Quando novos dados surgem nos laboratórios, novos processos são necessários para explicar estes dados e algumas vezes a estrutura interna das partículas envolvidas é desconhecida. Nos modelos teóricos, usados para descrever estes processos de espalhamento, é comum introduzir o fator de forma. O fator de forma é simplesmente uma maneira de simular a sub-estrutura das partículas envolvidas nestes processos com função da energia ou momento. A obtenção dos atores de forma pode ser feita usando o método conhecido como Regras de Soma da QCD (RSQCD). Neste trabalho, será estudado o vértice D*Dp usando as RSQCD, de modo que seja possível obter os seus fatores de forma e sua constante de acoplamento. Para isso, foram estudados os casos em que o méson ρ e o méson D estão fora de suas camadas de massa. O vértice D*Dp é muito importante para entender melhor o ρπ Puzzle, onde o méson Ј/ψ decai ρπ em com um branching ratio maior do que o esperado (este é um processo suprimido pela regra de OZI). Estudando este processo com graus de liberdade mesnicos, é possível escapar da regra de OZI, uma vez que o processo Ј/ψ→ DD → ρπ não é suprimido por OZI. Ao se fazer isso, aparecerá, entre outros, o vértice D*Dp . Este é um vértice que também aparece em outros decaimentos, como por exemplo X(3872) →Ј/ψp e B→Ј/ψD. Ao final do desenvolvimento, os resultados obtidos neste trabalho para o vértice D*Dp foram comparados com outros encontrados na literatura, se mostrando compatíveis com estes outros trabalhos. / The particle physics have been studying topics like the Quark-Gluon Plasma (QGP), Higgs boson and dark matter, which require experiments in heavy-ion collisions. Therefore, accelerators capable of generate high energy particle beams are necessary and may generate new physics. When new data arise in the laboratories, new processes are necessary to explain this data and sometimes, the internal structure of the involved particles is unknow or are virtual. In the theoretical models, used to describe this scattering processes, is common to introduce the form factors. The form factor is a way to simulate the sub-structure of the involved particles as function of energy or momentum. The form factor can be obtained using a method called QCD Sum Rules (QCDSR). In this work, the vertex D*Dp will be studied using the QCDSR, in order to obtain its form factors and coupling constant.The D*Dp vertex is very important to understand the ρπ Puzzle, where the Ј/ψ meson decays in ρπ with a branching ratio bigger than expected (this is a suppressed process by the OZI Rule). Studying this process with hadronic degrees of freedom, its possible to escape of the OZI rule, once the Ј/ψ→ DD → ρπ is not suppressed by the OZI rule. In this process, the D*Dp vertex is necessary. There are other processes where this vertex is necessary: X(3872)→Ј/ψp and B→Ј/ψD for example. In this work, was only possible to obtain results from the ρ off-shell diagram. This results were compared with others obtained in the literature.

Plasmonic cavities confine optical fields at metal-dielectric interfaces via collective charge oscillations of free electrons within metals termed surface plasmon polaritons (SPPs). SPPs are confined in nanometre gaps formed between two metallic surfaces which creates an optical resonance. This optical resonance of the system is controlled by the geometry and the material of the nanogap. The focus of this work is to understand and utilize these confined optical modes to probe and manipulate the dynamics of single-molecules at room temperature. In this thesis, nanogap cavities are constructed by placing nanoparticles on top of a metal-film separated by molecular spacers. Such nanogaps act as cavities with confined optical fields in the gap. Precise position and orientation of single-molecules in the gap is obtained by supramolecular guest-host assembly and DNA origami breadboards. The interaction of light and single-molecules is studied in two different regimes of interaction strength. In the perturbative regime molecular light emission from electronic and vibrational states is strongly enhanced and therefore is used for the detection of single-molecules. In this regime the energy states remain unaltered, however profound effects emerge when the gap size is reduced to < 1 nm. New hybridized energy states which are half-light and half-matter are then formed. Dispersion of these energies is studied by tuning the cavity resonance across the molecular resonance, revealing the anti-crossing signature of a strongly coupled system. This dressing of molecules with light results in the modification of photochemistry and photophysics of single-molecules, opening up the exploration of complex natural processes such as photosynthesis and the possibility to manipulate chemical bonds.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A física de partículas vem atualmente estudando tópicos como o plasma de quarks e glúons (QGP), o bóson de Higgs e a matéria escura, que requerem experimentos de colisões entre partículas cada vez mais energéticas. Para isso, são necessários aceleradores capazes de gerar partículas projéteis a cada vez mais altas energias, o que pode levar a uma nova física. Quando novos dados surgem nos laboratórios, novos processos são necessários para explicar estes dados e algumas vezes a estrutura interna das partículas envolvidas é desconhecida. Nos modelos teóricos, usados para descrever estes processos de espalhamento, é comum introduzir o fator de forma. O fator de forma é simplesmente uma maneira de simular a sub-estrutura das partículas envolvidas nestes processos com função da energia ou momento. A obtenção dos atores de forma pode ser feita usando o método conhecido como Regras de Soma da QCD (RSQCD). Neste trabalho, será estudado o vértice D*Dp usando as RSQCD, de modo que seja possível obter os seus fatores de forma e sua constante de acoplamento. Para isso, foram estudados os casos em que o méson &#961; e o méson D estão fora de suas camadas de massa. O vértice D*Dp é muito importante para entender melhor o &#961;&#960; Puzzle, onde o méson &#1032;/&#968; decai &#961;&#960; em com um branching ratio maior do que o esperado (este é um processo suprimido pela regra de OZI). Estudando este processo com graus de liberdade mesnicos, é possível escapar da regra de OZI, uma vez que o processo &#1032;/&#968;&#8594; DD &#8594; &#961;&#960; não é suprimido por OZI. Ao se fazer isso, aparecerá, entre outros, o vértice D*Dp . Este é um vértice que também aparece em outros decaimentos, como por exemplo X(3872) &#8594;&#1032;/&#968;p e B&#8594;&#1032;/&#968;D. Ao final do desenvolvimento, os resultados obtidos neste trabalho para o vértice D*Dp foram comparados com outros encontrados na literatura, se mostrando compatíveis com estes outros trabalhos. / The particle physics have been studying topics like the Quark-Gluon Plasma (QGP), Higgs boson and dark matter, which require experiments in heavy-ion collisions. Therefore, accelerators capable of generate high energy particle beams are necessary and may generate new physics. When new data arise in the laboratories, new processes are necessary to explain this data and sometimes, the internal structure of the involved particles is unknow or are virtual. In the theoretical models, used to describe this scattering processes, is common to introduce the form factors. The form factor is a way to simulate the sub-structure of the involved particles as function of energy or momentum. The form factor can be obtained using a method called QCD Sum Rules (QCDSR). In this work, the vertex D*Dp will be studied using the QCDSR, in order to obtain its form factors and coupling constant.The D*Dp vertex is very important to understand the &#961;&#960; Puzzle, where the &#1032;/&#968; meson decays in &#961;&#960; with a branching ratio bigger than expected (this is a suppressed process by the OZI Rule). Studying this process with hadronic degrees of freedom, its possible to escape of the OZI rule, once the &#1032;/&#968;&#8594; DD &#8594; &#961;&#960; is not suppressed by the OZI rule. In this process, the D*Dp vertex is necessary. There are other processes where this vertex is necessary: X(3872)&#8594;&#1032;/&#968;p and B&#8594;&#1032;/&#968;D for example. In this work, was only possible to obtain results from the &#961; off-shell diagram. This results were compared with others obtained in the literature.

Durant les 15 dernières années, le couplage fort lumière-matière avec des matériaux organiques a attiré un intérêt croissant, notamment à cause des valeurs extrêmes que peut atteindre l'écart énergétique entre les modes couplés dans ces systèmes. Ces modes couplés sont des hybrides lumière-matière, aussi appelés états polaritons et notés habituellement P+ et P-. La valeur de I' écart énergétique entre les modes couplés, également appelé énergie de Rabi-splitting, est provoqué par une transition efficace de dipôle moments entre des molécules et aussi par des cavités ou des plasmons en surface de petits volumes en mode de micro-Fabry-Pérot métalliques (FP) qui sont utilisés dans ces études. Rabi-splittings - 1eV représente souvent une fraction importante de l'énergie de transition électronique, dans ce cas, le système est appelé dans le régime de couplage ultra-forte. Dans ce régime, la physico-chimie des molécules ou des propriétés des matériaux du système couplé peuvent être modifié. En effet, d'effet a déjà été montré sur les voies de relaxation dans le système couplé, les taux de réactions photochimiques, le travail d'extraction et de la conductivité des semi-conducteurs organiques dans l'obscurité, entre autres choses. Une étude récente a pu montrer que l'énergie de l'état non-excité dans une étude thermodynamique peut également être décalée dans le régime de couplage ultra-fort. De plus, le couplage fort ne se limite pas à des transitions électroniques, mais peut aussi être utilisé pour perturber les vibrations de l'état non-excité de molécules dans la région infrarouge. Tous ces résultats montrent que le couplage fort en lumière-molécule a beaucoup de potentiel pour le matériel et la science moléculaire et mérite donc une étude plus approfondie. / Over the past 15 years, light-matter strong coupling involving organic materials has been of increasing interest due to the very large energy splitting such systems exhibit between the two hybrid light-matter states, also known as the polaritonic states typically denoted P+ and P-. The large energy splitting, so-called Rabi splitting, is the result of the high transition dipole moments of the molecules and the small mode volumes of micro-metallic Fabry-Pérot (FP) cavities or surface plasmons used in these studies. Rabi-splittings -1 eV have been observed, often representing a significant fraction of the electronic transition energy in which case the system is said to be in the ultra-strong coupling regime. ln this regime the physical chemistry of molecules or the properties of materials of the coupied system should be modified. lndeed, it has already been shown to affect the relaxation pathways in the coupled system, the rates of photochemical reactions, thework-function and conductivity of organic-semiconductors in the dark, among other things. A recent thermodynamic study demonstrated that the ground state energy can also be shifted in theultra-strong coupling regime. Moreover, the strong coupling is not limited to electronic transitions, but also can be used to perturb the ground-state vibrations of molecules in the infrared region. Ali these results suggest that light-molecule strong coupling has much potential for material and molecular science and therefore merits further study.

The goal of the original research presented in this thesis is to study the strong coupling regime of Quantum Field Theories (QFTs) with different methods, making concrete predictions about the phase structure and the dynamics of these theories, and on their observables. The focus is on (gauge) field theories in three spacetime dimensions, which are an interesting laboratory to understand the properties of strong coupling in setups that are usually simpler than in the more familiar case of gauge theories in four dimensions. Importantly, topological effects play a relevant role in three dimensions, thanks to the presence of the so-called Chern-Simons term.The thesis contains a short introduction to QFTs in 3d, principles and applications of infrared dualities, large N techniques, and holography. Indeed, the web of infrared dualities, the large N expansion, and the holographic correspondence between QFT and gravity are the main tools which we use to investigate the strongly coupled regimes of 3d QFTs.Then, the original material is presented. In a first line of research, we focus on the study of the phase diagram of a 3d gauge theory making use of conjectured infrared dualities, extending such dualities to the case where more than one mass parameter can be dialed. In a second line of research, we study a class of 3d gauge theories by engineering their gravity dual in a string theory setup. We prove the existence of multiple phase transitions between phases characterized by both massless particles and topological sectors. In a third line of research, we use holography as a tool to explore the interplay between the physics of 4d QCD and 3d gauge theories. In particular, we analyze the properties of 3d domain walls, which appear as soliton-like solutions of 4d QCD in specific parametric regimes. Finally, we propose a boundary construction of 3d large N vector models, which appear as critical points of theories obtained by coupling degrees of freedom localized on a 3d boundary to a 4d bulk theory. This construction allows to prove new dualities and uncovers a new computational tool for 3d vector models. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

When calculating the dynamics of a quantum system, including the effect of its environment is highly relevant since virtually any real quantum system is exposed to environmental influences. It has turned out that the widely used perturbative approaches to treat such so-called open quantum systems have severe limitations. Furthermore, due to current experiments which have implemented strong system-environment interactions the non-perturbative regime is far from being academical. Therefore determining the exact dynamics of an open quantum system is of fundamental relevance. The hierarchy of pure states (HOPS) formalism poses such an exact approach. Its novel and detailed derivation, as well as several numerical aspects constitute the main methodical part of this work. Motivated by fundamental issues but also due to practical relevance for real world devices exploiting quantum effects, the entanglement dynamics of two qubits in contact with a common environment is investigated extensively. The HOPS formalism is based on the exact stochastic description of open quantum system dynamics in terms of the non-Markovian quantum state diffusion (NMQSD) theory. The distinguishing and numerically beneficial features of the HOPS approach are the stochastic nature, the implicit treatment of the environmental dynamics and, related to this, the enhanced statistical convergence (importance sampling), as well as the fact that only pure states have to be propagated. In order to claim that the HOPS approach is exact, we develop schemes to ensure that the numerical errors can be made arbitrarily small. This includes the sampling of Gaussian stochastic processes, the multi-exponential representation of the bath correlation function and the truncation of the hierarchy. Moreover, we incorporated thermal effects on the reduced dynamics by a stochastic Hermitian contribution to the system Hamiltonian. In particular, for strong system-environment couplings this is very beneficial for the HOPS. To confirm the accuracy assertion we utilize the seemingly simple, however, non-trivial spin-boson model to show agreement between the HOPS and other methods. The comparison shows the HOPS method’s versatile applicability over a broad range of model parameters including weak and strong coupling to the environment, as well as zero and high temperatures. With the gained knowledge that the HOPS method is versatile and accurately applicable, we investigate the specific case of two qubits while focusing on their entanglement dynamics. It is well known that entanglement, the relevant property when exploiting quantum effects in fields like quantum computation, communication and metrology, is fragile when exposed to environmental noise. On the other hand, a common environment can also mediate an effective interaction between the two parties featuring entanglement generation. In this work we elucidate the interplay between these competing effects, focusing on several different aspects. For the perturbative (weak coupling) regime we enlighten the difficulties inherent to the frequently used rotating wave approximation (RWA), an approximation often applied to ensure positivity of the reduced state for all times. We show that these difficulties are best overcome when simply omitting the RWA. The seemingly unphysical dynamics can still be used to approximate the exact entanglement dynamics very well. Furthermore, the influence of the renormalizing counter term is investigated. It is expected that under certain conditions (adiabatic regime) the generation of entanglement is suppressed by the presence of the counter term. It is shown, however, that for a deep sub-Ohmic environment this expectation fails. Leaving the weak coupling regime, we show that the generation of entanglement due to the influence of the common environment is a general property of the open two-spin system. Even for non-zero temperatures it is demonstrated that entanglement can still be generated and may last for arbitrary long times. Finally, we determine the maximum of the steady state entanglement as a function of the coupling strength and show how the known delocalization-to-localization phase transition is reflected in the long time entanglement dynamics. All these results require an exact treatment of the open quantum system dynamics and, thus, contribute to the fundamental understanding of the entanglement dynamics of open quantum systems. / Bei der Bestimmung der Dynamik eines Quantensystems ist die Berücksichtigung seiner Umgebung von großem Interessen, da faktisch jedes reale Quantensystem von seiner Umgebung beeinflusst wird. Es zeigt sich, dass die viel verwendeten störungstheoretischen Ansätze starken Einschränkungen unterliegen. Außerdem, da es in aktuellen Experimenten gelungen ist starke Wechselwirkung zwischen dem System und seiner Umgebung zu realisieren, gewinnt das nicht-störungstheoretischen Regime stets an Relevanz. Dementsprechend ist die Berechnung der exakten Dynamik offener Quantensysteme von grundlegender Bedeutung. Einen solchen exakten nummerischen Zugang stellt der hierarchy of pure states (HOPS) Formalismus dar. Dessen neuartige und detaillierte Herleitung, sowie diverse nummerische Aspekte werden im methodischen Teil dieser Arbeit dargelegt. In vielerlei Hinsicht relevant folgt als Anwendung eine umfangreiche Untersuchung der Verschränkungsdynamik zweier Qubits unter dem Einfluss einer gemeinsamen Umgebung. Vor allem im Hinblick auf die experimentell realisierbare starke Kopplung mit der Umgebung ist dieses Analyse von Interesse. Der HOPS Formalismus basiert auf der stochastischen Beschreibung der Dynamik offener Quantensysteme im Rahmen der non-Markovian quantum state diffusion (NMQSD) Theorie. Der stochastische Charakter der Methode, die implizite Berücksichtigung der Umgebungsdynamik, sowie das damit verbundene Importance Sampling, als auch die Tatsache dass lediglich reine Zustände propagiert werden müssen unterscheidet diese Methode maßgeblich von anderen Ansätzen und birgt numerische Vorteile. Um zu behaupten, dass die HOPS Methode exakte Ergebnisse liefert, müssen auftretenden nummerischen Fehler beliebig klein gemacht werden können. Ein grundlegender Teil der hier vorgestellten methodischen Arbeit liegt in der Entwicklung diverser Schemata, die genau das erreichen. Dazu zählen die numerische Realisierung von Gauss’schen stochastischen Prozessen, die Darstellung der Badkorrelationsfunktion als Summe von Exponentialfunktionen sowie das Abschneiden der Hierarchie. Außerdem wird gezeigt, dass sich der temperaturabhängige Einfluss der Umgebung durch einen stochastischen Hermiteschen Beitrag zum System-Hamiltonoperator berücksichtigen lässt. Vor allem bei starker Kopplung ist diese Variante besonders geeignet für den HOPS Zugang. Um die Genauigkeitsbehauptung der HOPS Methode zu überprüfen wird die Übereinstimmung mit anderen Methode gezeigt, wobei das vermeintlich einfachste, jedoch nicht triviale spin-boson-Modell als Testsystem verwendet wird. Diese Untersuchung belegt, dass die HOPS Methode für eine Vielzahl an Szenarien geeignet ist. Das beinhaltet schwache und starke Kopplung an die Umgebung, sowie Temperatur null als auch hohe Temperaturen. Mit dem gewonnenen Wissen, dass die HOPS Methode vielseitig einsetzbar ist und genaue Ergebnisse liefert wird anschließend der spezielle Fall zweier Qubits untersucht. Im Hinblick auf die Ausnutzung von Quanteneffekten in Bereichen wie Rechentechnik, Kommunikation oder Messtechnik liegt der primäre Fokus auf der Dynamik der Verschränkung zwischen den Qubits. Es ist bekannt, dass durch von außen induziertes Rauschen die Verschränkung im Laufe der Zeit abnimmt. Andererseits weiß man auch, dass eine gemeinsame Umgebung zu einer effektiven Wechselwirkung zwischen den Qubits führt, welche Verschränkung aufbauen kann. In dieser Arbeit wird das Wechselspiel zwischen diesen beiden gegensätzlichen Effekten untersucht, wobei die folgenden Aspekte beleuchtet werden. Für den Fall schwacher Kopplung, wo eine störungstheoretische Behandlung in Frage kommt, werden die Probleme der rotating wave approximation (RWA) analysiert. Diese Näherung wird häufig verwendet um die Positivität des reduzierten Zustands zu allen Zeiten zu gewährleisten. Es wird gezeigt, dass sich diese Probleme am besten vermeiden lassen, wenn die RWA einfach weggelassen wird. Die auf den ersten Blick nicht-physikalische Dynamik ist sehr gut geeignet um die exakte Verschränkungsdynamik näherungsweise wiederzugeben. Des Weiteren wird der Einfluss der Renormalisierung des sogenannten counter terms untersucht. Unter bestimmten Voraussetzungen (adiabatisches Regime) ist zu erwarten, dass der Verschränkungsaufbau durch den counter term verhindert wird. Es zeigt sich, dass für eine sehr sub-Ohm’sche Umgebung (deep sub-Ohmic regime) diese Erwartung nicht zutrifft. Weiterhin wird der Fall starker Kopplung zwischen dem zwei-Qubit-System und der Umgebung betrachtet. Die Berechnungen zeigen das generelle Bild, dass sich zwei nicht wechselwirkende Qubits durch den Einfluss einer gemeinsamen Umgebung verschränken. Selbst bei Temperaturen größer als null kann Verschränkung aufgebaut werden und auch für beliebig lange Zeiten erhalten bleiben. In einem letzten Punkt wird das Maximum der stationären Verschränkung (Langzeit-Limes) in Abhängigkeit von der Kopplungsstärke bestimmt. Dabei wird gezeigt, dass sich der bekannte Phasenübergang von Delokalisierzung zu Lokalisierung auch in der Langzeitdynamik der Verschränkung widerspiegelt. All diese Erkenntnisse erfordern eine exakte Behandlung der offenen Systemdynamik und erweitern somit das fundamentalen Verständnis der Verschränkungsdynamik offener Quantensysteme.