Squeezing ground in tunnelling is a unique method of failure, typically occurring in ductile rock at depth. To accommodate this mechanism of failure, liners have been designed such that they reduce in circumference as the support takes on initial load. Technological development in this area is all the more important for tunnels mined in heterogeneous rockmasses. Currently, the state of practice is to design support based on a normalised average of the strength parameters of the rock units present in the tunnel face. Under many configurations of heterogeneity, this approach is perfectly valid, however there are styles and magnitudes of heterogeneity that require deeper analysis. The purpose of this study is to introduce an empirical relationship between liner response in heterogeneous rockmasses and liner response in the homogenised equivalent. A suite of parameters that define heterogeneity were numerically modelled, using finite element analysis, such that a comprehensive set of the various permutations was evaluated. The three styles of heterogeneity that were modelled were chaotic structure, folded structure and laminar structure, these represent common and discrete structures found in alpine regions. Laminar structure was considered at three orientations, and all structures were considered under hydrostatic and differential stress regimes. Granularity, or scale, and contrast ratio of units were also varied. These data were analysed with respect to mean axial thrust, range of axial thrust and range of moment on the liner. Liner response analysis was also conducted on the case study of St. Martin-la-Porte, an adit to the Lyon-Turin Ferroviaire base tunnel in southern France. This adit has been excavated in a highly variable, heterogeneous rockmass and provides realistic examples of the nature of heterogeneity present in current tunnelling projects. Ultimately, three equations were developed to provide preliminary predictions of heterogeneous axial thrust and moment variability from the analysis of homogeneous equivalents. / Thesis (Master, Geological Sciences & Geological Engineering) -- Queen's University, 2011-01-14 19:16:42.908

This thesis concerns the relationship between bounded and controlled topology and in particular how these can be used to recognise which homotopy equivalences of reasonable topological spaces are homotopic to homeomorphisms. Let f : X → Y be a simplicial map of finite-dimensional locally finite simplicial complexes. Our first result is that f has contractible point inverses if and only if it is an ε- controlled homotopy equivalences for all ε > 0, if and only if f × id : X × R → Y × R is a homotopy equivalence bounded over the open cone O(Y +) of Pedersen and Weibel. The most difficult part, the passage from contractible point inverses to bounded over O(Y +) is proven using a new construction for a finite dimensional locally finite simplicial complex X, which we call the fundamental ε-subdivision cellulation X'ε. This whole approach can be generalised to algebra using geometric categories. In the second part of the thesis we again work over a finite-dimensional locally finite simplicial complex X, and use the X-controlled categories A*(X), A*(X) of Ranicki and Weiss (1990) together with the bounded categories CM(A) of Pedersen and Weibel (1989). Analogous to the barycentric subdivision of a simplicial complex, we define the algebraic barycentric subdivision of a chain complex over that simplicial complex. The main theorem of the thesis is then that a chain complex C is chain contractible in ( A*(X) A*(X) if and only if “C ¤ Z” 2 (A*(X × R) A*(X × R) is boundedly chain contractible when measured in O(X+) for a functor “ − Z” defined appropriately using algebraic subdivision. In the process we prove a squeezing result: a chain complex with a sufficiently small chain contraction has arbitrarily small chain contractions. The last part of the thesis draws some consequences for recognising homology manifolds in the homotopy types of Poincare Duality spaces. Squeezing tells us that a PL Poincare duality space with sufficiently controlled Poincare duality is necessarily a homology manifold and the main theorem tells us that a PL Poincare duality space X is a homology manifold if and only if X × R has bounded Poincare duality when measured in the open cone O(X+).

Quantum mechanics allows us to use nonclassical states of light to make measurements with a greater precision than comparable classical states. Here an experiment is presented that squeezes the polarization state of three photons. We demonstrate the deep connection that exists between squeezing and entanglement, unifying the squeezed state and multi-photon entangled state approaches to quantum metrology. For the first time we observe the phenomenon of over-squeezing where a system is squeezed to the point that further squeezing leads to a counter-intuitive increase in measurement uncertainty. Quasi-probability distributions on the surface of a Poincaré sphere are the most natural way to represent the topology of our polarization states. Using this representation it is easy to observe the squeezing and over-squeezing behaviour of our photon states. Work is also presented on two different technologies for generating nonclassical states of light. The first is based on the nonlinear process of spontaneous parametric downconversion to produce pairs of photons. With this source up to 200,000 pairs of photons/s have been collected into single-mode fibre, and over 100 double pairs/s have been detected. This downconversion source is suitable for use in a wide variety of multi-qubit quantum information applications. The second source presented is a single-photon source based on semiconductor quantum dots. The single-photon character of the source is verified using a Hanbury Brown-Twiss interferometer.

Quantum mechanics allows us to use nonclassical states of light to make measurements with a greater precision than comparable classical states. Here an experiment is presented that squeezes the polarization state of three photons. We demonstrate the deep connection that exists between squeezing and entanglement, unifying the squeezed state and multi-photon entangled state approaches to quantum metrology. For the first time we observe the phenomenon of over-squeezing where a system is squeezed to the point that further squeezing leads to a counter-intuitive increase in measurement uncertainty. Quasi-probability distributions on the surface of a Poincaré sphere are the most natural way to represent the topology of our polarization states. Using this representation it is easy to observe the squeezing and over-squeezing behaviour of our photon states. Work is also presented on two different technologies for generating nonclassical states of light. The first is based on the nonlinear process of spontaneous parametric downconversion to produce pairs of photons. With this source up to 200,000 pairs of photons/s have been collected into single-mode fibre, and over 100 double pairs/s have been detected. This downconversion source is suitable for use in a wide variety of multi-qubit quantum information applications. The second source presented is a single-photon source based on semiconductor quantum dots. The single-photon character of the source is verified using a Hanbury Brown-Twiss interferometer.

Quantum control of many body atomic spins is often pursued in the context of an atom-light quantum interface, where a quantized light field acts as a "quantum bus" that can be used to entangle distant atoms. One key challenge is to improve the coherence of the atom-light interface and the amount of atom-light entanglement it can generate, given the constraints of working with multilevel atoms and optical fields in a 3D geometry. We have explored new ways to achieve this, through rigorous optimization of the spatial geometry, and through control of the internal atomic state. Our basic setup consists of a quantized probe beam passing through an atom cloud held in a dipole trap, first generating spin-probe entanglement through the Faraday interaction, and then using backaction from a measurement of the probe polarization to squeeze the collective atomic spin. The relevant figure of merit is the metrologically useful spin squeezing determined by the enhancement in the resolution of rotations of the collective spin, relative to the commonly used spin coherent state. With an optimized free-space geometry, and by using a 2-color probe scheme to suppress tensor light shifts, we achieve 3(2) dB of metrologically useful spin squeezing. We can further increase atom-light coupling by implementing internal state control to prepare spin states with larger initial projection noise relative to the spin coherent state. Under the right conditions this increase in projection noise can lead to stronger measurement backaction and increased atom-atom entanglement. With further internal state control the increased atom-atom entanglement can then be mapped to a basis where it corresponds to improved squeezing of, e.g., the physical spin-angular momentum or the collective atomic clock pseudospin. In practice, controlling the collective spin of N ~ 10⁶ atoms in this fashion is an extraordinarily difficult challenge because errors in the control of individual atoms tend to be highly correlated. By employing precise internal state control, we have prepared and detected projection noise limited "cat" states (which have initial projection noise that is larger by a factor of 2f = 8 for Cs relative to the spin coherent state) and estimate that we can generate up to 6.0(5) dB of metrologically useful spin squeezing, demonstrating the advantage of using the internal atomic structure as a resource for ensemble control.

La constante miniaturisation des dispositifs électroniques rend essentiel le contrôle et la compréhension des fluctuations dans le courant les traversant, c'est-à-dire du bruit électronique. Étudié depuis près de 90 ans, ce phénomène omniprésent se trouve limité par les lois de la mécanique quantique à une valeur minimale, la limite de bruit quantique. Quantifier ces fluctuations pose plusieurs problèmes expérimentaux. Principalement, toute mesure électronique est basée sur le passage d'un grand nombre d'électrons dont le comportement est presque aléatoire. Faire ressortir les mécanismes sous-jacents à l'émission du bruit requiert donc une étude statistique poussée de la distribution de probabilité du passage d'électrons, passant entre autres par la mesure du quatrième cumulant de cette distribution. Cet indicateur de l'écart entre les valeurs observées et les valeurs attendues pour un phénomène aléatoire n'était accessible jusqu'à maintenant qu'en comptant un à un les passages d'électrons, ce qui n'est réalisable que pour des dispositifs spécifiques. D'un autre point de vue, diminuer le niveau de bruit sous la limite quantique est un but fort souhaitable pour le développement de technologies électroniques de pointe. Un phénomène du nom de compression d'états démontre la possibilité de connaître une partie des informations disponibles avec une précision supérieure à la limite quantique au dépit de l'autre partie, qui sera noyée dans un bruit plus grand pour respecter cette limite. L'observation de la compression d'états nécessite donc d'atteindre le niveau de bruit minimal et d'enregistrer avec précision les niveaux de bruit de chaque paramètre observé. De surcroît, le domaine de la cryptographie serait fort d'utiliser un outil constitué de deux objets liés entre eux d'une façon non-classique. Ainsi, lire la valeur d'un paramètre A sur un objet limite les valeurs accessibles par le paramètre B du deuxième et vice-versa, ce qui permet de savoir si l'objet a été observé par un troisième observateur. La situation décrite en est une d'enchevêtrement, où la mécanique classique ne peut pas expliquer le lien entre les deux objets étudiés. Une telle manifestation n'est observable que sur des paires d'objets créés simultanément. La préparation identique de plusieurs paires permet une étude statistique des informations de chaque objet et toute corrélation entre eux ne pouvant s'expliquer par la mécanique classique, telle que la compression d'états à deux modes, est indicatrice d'enchevêtrement. Ce texte propose de sonder ces quantités en étudiant un dispositif dont le bruit de grenaille est simple à modéliser, la jonction tunnel. Lorsqu'elle est éloignée de son état d'équilibre par des tensions cc et ca, le courant qu'émet une jonction tunnel présente des fluctuations sur un spectre continu de fréquences. Cette thèse vise à démontrer que l'étude des corrélations entre les fluctuations présentes à deux fréquences distinctes permet la mesure du quatrième cumulant de la distribution statistique du bruit de grenaille. Cet ouvrage a aussi pour but d'utiliser divers outils développés dans le domaine de l'optique quantique afin de démontrer l'existence de compression d'états à deux modes dans ces fluctuations, démontrant ainsi la présence d'états enchevêtrés dans le bruit généré.

Comportement différé, anisotrope à la descenderie de Saint-Martin-la-Porte / Time-dependent, anisotropic behavior of Saint-Martin-la-Porte gallery

Les polaritons sont des quasi-particules bosoniques venant du couplage fort entre des photons de cavité et des excitons confinés dans une hétérostructure semiconductrice. De par leur temps de vie très court et leur très fortes interactions, les polaritons sont un système idéal pour étudier des problèmes fondamentaux d’hydrodynamique quantique hors équilibre ainsi que des aspects plus appliqués d’optique quantique, comme l’implémentation de transistors opto-electroniques ultra-rapides ou la génération d’états non-classiques de la lumière.Ces deux thèmes sont traités dans cette thèse. Dans la première partie j’y dépeins plusieurs méthodes par lesquelles on injecte optiquement un moment angulaire donné dans un superfluide de polaritons, afin d’observer sa nucléation en plusieurs vortex élémentaires. L’impact de la géometrie, du désordre et de l’interaction nonlinéaire de type "polaritonpolariton" sont étudiés. Nous démontrons la conservation du moment angulaire dans le régime stationnaire malgré la nature hors équilibre et ouverte du système. Dans le régime linéaire, un reseau d’interférences contenant des singularités de phase (vortex optiques) est visible. Dans le régime nonlinéaire (superfluide), les interférences disparaissent et des vortex du même signe se forment en conséquence de la conservation du moment angulaire injecté. Enfin, en ajoutant une contrainte sur la géométrie du système nous avons créé de manière controlée un anneau stable de vortex élémentaire du même signe, ce qui pourrait ouvrir la voie à l’étude des interactions inter-vortex dans les fluides quantiques de lumière.Un autre aspect des polaritons sont les propriétés quantiques de la lumière qu’ils émettent. Dans la seconde partie de cette thèse, je décris une source améliorée de lumière comprimée en régime de variables continues dans des micropiliers semiconducteurs en régime de couplage fort. En effet, la génération de lumière comprimée et intriquée est un ingrédient crucial pour l’implémentation de protocoles en information quantique. Dans ce contexte, les matériaux semiconducteurs ont un grand potentiel pour la realization d’éléments sur puce opérant au niveau quantique. Ici, un mélange à quatre ondes dégénérées est obtenu en excitant le micro-pilier à incidence normale. Nous observons un comportement bistable et démontrons la génération de lumière comprimée près du point tournant de la courbe de bistabilité. La nature confinée de la géométrie du piller permet d’atteindre un taux de compression bien supérieur que dans les microcavités planaires, grâce aux niveaux d’énergies discrets protégés des excès de bruits. En analysant le bruit dans la lumière émise par les micro-piliers, nous obtenons une réduction du bruit d’intensité mesurée à 20,3%, et estimée à 35,8% après correction des pertes de détection. / Polaritons are bosonic quasiparticles coming from the strong coupling between photons and excitons in a solid-state semiconductor microcavity. Due to their short lifetime and their strong nonlinear interactions, polaritons are an ideal system to study fundamental problems of out-of-equilibrium quantum hydrodynamics as well as more applied problematic in quantum optics, such as the implementation of ultrafast opto-electronic switches or the generation of non-classical states of light.In this thesis the two themes are treated. In the first part of my thesis I will depict several schemes by which we optically inject a controlled angular momentum in a polartion superfluid, in order to observe its nucleation into elementary vortices. The impact of the geometry, disorder, and polariton-polariton nonlinear interactions is studied. We show the conservation of angular momentum in the steady state regime despite the open, out-of-equilibrium nature of the system. In the linear regime, an interference pattern containing phase defects is visible. In the nonlinear(superfluid) regime, the interference disappear and the vortices nucleate as a consequence of the angular momentum conservation. Finally, constraining the geometry we were able to create in a controlled way a stable ring of elementary vortices of the same sign, opening the way to the study of vortex-vortex interactions in quantum fluids of light.A second aspect of polaritons is the quantum properties of their emitted light. In the second part of the manuscript I describe a novel source of continuous-variable squeezed light in pillar-shaped semiconductor microcavities in the strong coupling regime. Indeed, the generation of squeezedand entangled light fields is a crucial ingredient for the implementation of quantum information protocols. In this context, semiconductor materials offer a strong potential for the implementation of on-chip devices operating at the quantum level. Here, degenerate polariton four-wave mixing is obtained by exciting the pillar at normal incidence. We observe a bistable behavior and we demonstrate the generation of squeezing near the turning point of the bistability curve. The confined pillar geometry allows for a larger amount of squeezing than planar microcavities due to the discrete energy levels protected from excess noise. By analyzing the noise of the emitted light we obtain a measured intensity squeezing of 20,3%, inferred to be 35,8% after corrections for losses in the detection setup.

Cette thèse se concentre sur la dynamique d'un système atomique froid qui se composede deux états internes d'atomes piégés dans un potentiel magnétique . La motivation decette thèse est une série d'expériences sur ce système réalisées en 2010, où un grandtemps de cohérence surprenante entre les deux états internes ont été observés. Cephénomène a été expliqué par la théorie cinétique qui a utilisé une approche de champmoyen. Dans cette thèse, nous essayons d'utiliser une approche différente et étudier leseffets de corrélations quantiques dans la dynamique du système. De plus, nous sommeségalement intéressés au phénomène de compression de spin qui est la redistribution desfluctuations quantiques dans le système de spin. Afin d'étudier les effets des corrélationsquantiques, nous proposons un modèle simplifié qui divise les atomes froids en deuxgroupes en fonction de leurs énergies de mouvement orbital dans le potentiel de piégeageet traitons chaque groupe comme un macro-spin. Les principaux ingrédients de ce modèlesont l'inhomogénéité du champ externe qui déphase les deux macro-spins et l'interactiond'échange entre les deux macro-spins, qui imite l'effet de rotation des spins identiques(ISRE), avec la condition initiale que les deux spins sont parallèle dans le plan transversaldu champ externe. Ensuite, nous étudions la dynamique du système classique où ladynamique ne dépendent pas de la taille des spins et une transition de synchronisation esttrouvée lorsque l'interaction d'échange est plus grande que le seuil , la moitié de l'inhomogénéité du champ externe. Une analyse de l'espace de phase révèle que cettetransition de synchronisation est liée à une transition de bifurcation et de la conditioninitiale. Ensuite, la dynamique quantique est étudiée où la taille de spin joue un rôleimportant dans la dynamique. Il n'y a pas de transition de synchronisation dans lessystèmes quantiques et du comportement dynamique très riche est trouvée. Dans ladynamique quantique , plusieurs échelles de temps caractéristiques apparaissent commela taille de spin augmente, ce qui est d'origine quantique. Ces échelles de temps dépendde la taille de spin et tous deviennent infinies lorsque la taille de spin est infinie. De cettefaçon, la limite classique est récupéré. Basé sur l’intensité de l'interaction d'échange ,deux modèles effectifs sont proposés pour calculer les échelles du temps quantiques lesplus petites, ce qui coïncide bien avec les résultats numériques. La compression de spinest également étudié avec ces modèles effectifs. / This thesis focuses on the dynamics of a cold atomic system which consists of two internalstates of atoms trapped in a magnetic trapping potential. The motivation of this thesis is aseries of experiments on such system carried out in 2010, where a surprising longcoherence time between the two internal states were observed. This phenomenon wasexplained by the kinetic theory which has used a mean-field approach. In this thesis, wetry to use a different approach and study the effects of quantum correlations in thedynamics of the system. In addition to that, we are also interested in the phenomenon ofspin squeezing which is the redistribution of quantum fluctuations in the spin system. Inorder to study the effects of the quantum correlations, we propose a simplified which splitsthe cold atoms into two groups based on their orbital movement energies in the trappingpotential and treat each group as a macro-spin. The main ingredients in this model are theinhomogeneity of the external field which dephases the two macro-spins and theexchange interaction between the two macro-spins, which mimics the identical spinrotation effect (ISRE), with the initial condition that the two spins lie parallel in thetransverse plane of the external field. Then we study the classical dynamics of the systemwhere the dynamics do not depend on the size of the spins and a synchronizationtransition is found when the exchange interaction is larger than the threshold, the half ofthe inhomogeneity of the external field. A phase space analysis reveals that thissynchronization transition is related to a bifurcation transition and the initial condition. Thenthe quantum dynamics is studied where the spin size plays an important role in thedynamics. There is no synchronization transition in the quantum systems and very richdynamical behavior is found. In the quantum dynamics, many characteristic time scalesemerge as the size of spin is increased, which are of quantum origin. These time scales isdependent of the spin size and all become infinite when the size of spin is infinite. In theway, the classical limit is recovered. Based on the strength of the exchange interaction,two effective models are proposed to calculate the smallest quantum characteristic timescales, which give very good agreement with the numerical results. Spin squeezing is alsostudied with these effective models.

Nesta dissertação, descreveremos as primeiras medidas de ruído quântico em um oscilador paramétrico ótico (OPO) bombeado em 780 nm, construído no nosso laboratório. Esse OPO servirá de fonte de estados não clássicos da luz para interação com átomos de rubídio. Faremos uma revisão da teoria clássica do OPO: o bombeamento de um cristal não linear inserido dentro de uma cavidade ótica, produzindo dois feixes intensos de luz (sinal e complementar) com cores distintas. Calcularemos as expressões para o limiar de oscilação, potências de saída dos feixes convertidos e compararemos as principais diferenças entre OPOs com cristais do tipo I e tipo II. Analisaremos a descrição quântica do OPO, calcularemos os espectros de ruído para as quadraturas do bombeio refletido e para as quadraturas dos feixes gêmeos. Veremos que o OPO gera feixes com correlações quânticas, como o emaranhamento tripartido, entres os três feixes envolvidos no processo não linear. O cristal não linear utilizado no nosso experimento é um PPKTP tipo I. Ajustando a temperatura do cristal, podemos gerar feixes próximos da degenerescência até uma diferença de comprimentos de onda de aproximadamente 350 nm. A compressão de ruído quântico observado na diferença das amplitudes dos feixes sinal e complementar é 44%(-2.5 dB). O próximo passo é a implementação da técnica da rotação da elipse de ruído por cavidades óticas, para medir os ruídos de fase dos três campos . Fazendo a verificação do emaranhamento tripartido e determinando a sua dependência com o ruído de fônons inserido pelo cristal, a caracterização do OPO estará completa. A caracterização deste OPO é um passo importante nos objetivos do LMCAL, que é realizar a troca de informação entre luz e átomos em uma rede quântica. / In this dissertation, we will describe the first measurements of quantum noise in an optical parametric oscillator (OPO) pumped at 780 nm, built at our laboratory. This OPO will be the source of nonclassical states of light to interact with rubidium atoms. We will review the classical OPO theory: the pumping of a nonlinear crystal inside a cavity producing two bright light beams (signal and idler) with different colors. We will calculate the power threshold, output power of the converted beams and compare the main differences between type-I and type-II OPO.We will analyze the quantum description of the OPO, and calculate the noise spectrum of the reflected pump quadratures and for the twin beams quadratures. We will observe that the OPO generates beams with quantum correlations, for example, the tripartite entanglement among the three fields involved in the nonlinear phenomena. The nonlinear crystal used in our experiment is a PPKTP type-I. By adjusting the temperature of the crystal, we can generate beams from close to degenerate regime to a difference between them of 350 nm. The squeezing of quantum noise measured in the amplitude quadratures subtraction for signal and idler is 44%(-2.5 dB). The next step is to implement the method of ellipse noise rotation by an optical cavity, to be able to measure phase quadratures of the three different fields. By verifying the tripartite entanglement and determining the phonon noise due to the crystal, our source characterization will be complete. The characterization of this OPO is an important step in LMCAL goals, which is to realize exchange of information between light and atoms in a quantum network.