Time-varying fields are widely used to extend the accessible range of trapping potentials for ultracold atoms. This work explores two very different examples of such fields, in the radiofrequency and optical regimes, whose interactions with trapped atoms can both be described in terms of the dressed atom picture. Forming the basis of this work are radiofrequency dressed adiabatic potentials based on macroscopic trapping coils. Atoms are confined at the south pole of the resultant oblate spheroidal trapping surfaces. This work describes the extension of these potentials by two different methods: the application of multiple dressing radiofrequencies, and addition of a rapidly-scanned optical dipole trap. This is the first experimental demonstration of a multiple-radiofrequency dressed adiabatic potential, explored using ultracold ⁸⁷Rb atoms confined in a highly configurable double well. Due to the independent generation of each constituent dressing frequency, the depth of each trapping well and the height of the barrier are easily manipulated, enabling precise and reliable transfer of atoms between the available trapping geometries. Experimental work includes an exploration of the potential-shaping capabilities of the three-radiofrequency system, and characterisation of the potential landscape using radiofrequency spectroscopy with good agreement to the eigenvalues numerically calculated using Floquet theory. This initial exploration of multiple-radiofrequency techniques lays the groundwork for applications in studying double well physics in a two-dimensional system, and independent state or species selective manipulation of trapped atoms. The potential shaping capabilities of this method can also be extended by applying additional trapping frequencies. In a supplementary line of experimental work, an optical dipole trapping system has been constructed, and the trapping beam aligned to the lower surface of the radiofrequency dressed trapping shell in order to sculpt the radial confinement. Beam shaping is achieved using an acousto-optic deflector, which can be used to produce either a composite array of static deflected beams, a rapidly-scanned painted potential, or some combination of the two approaches. The development and extension of the experimental apparatus required to implement these enhanced dressed state potentials is explored, and the challenges of their experimental implementation considered.

Quantum computing has generated a lot of interested in the past two decades. Research into powerful models of quantum computation has yielded important and elegant results like an efficient algorithm for factoring and a quadratic speed-up for unordered search. At the same time, given the current difficulty in the physical implementation of these general purpose models, considerable effort has also been made in estimating the power of weaker models of quantum computation: models that have a small quantum component. The first part of this thesis is an investigation into the power of interference in quantum computing. While interference in probability amplitudes is a central feature even in powerful models, it is the only extra resource available to quantum finite automata. Of particular interest is interference in automata that have both classical and quantum states (2QCFA) as proposed by Ambainis and Watrous, since it inquires into the power of a classical deterministic finite automaton when augmented with a quantum component of constant size. Our contributions in this part are as follows: • To abstract out the phenomenon of interference in quantum computing, we propose a model called the 2-way Optical Interference Automata (2OIA). The model consists of a 2DFA augmented with a simple optical arrangement. We show different ways of harnessing the power of interference in the form of algorithms on this model to recognize some non-trivial languages. We then go on to show a language recognizable by a Turing machine using O(n2) space but by no 2OIA. • A natural classical model for comparison with 2QCFA is the weighted automaton, since it has the potential to capture interference in sum of path weights. Using the Cortes-Mohri definition of language recognition, we give an efficient simulation of 2QCFAwith algebraic amplitudes by weighted automata over the complex semi ring. • We introduce quantum non-determinism to the Measure-Once 1-way Quantum Finite Automata of Moore and Crutchfield and Kondacs and Watrous and show that even then, the model can recognize only regular languages with bounded error. • We propose a group theoretic generalization of counter automata that allows a notion of counter reversal complexity. To obtain this generalization, we combine concepts from classical counter automata theory with results in 2QCFA. We examine specific instances of this generalization and compare their ii iii powers. We also show an instance recognizing a language that is not recognized by conventional 2-way counter automata. Finally, we show a strict hierarchy among the 1-way versions of the instances Discussed. The second part of the thesis deals with Quantum Adiabatic Optimization algorithms. A common trick for designing faster quantum adiabatic algorithms is to apply the adiabatic condition locally at every instant. However it is often difficult to determine the instantaneous gap between the lowest two eigen values, which is an essential ingredient in the adiabatic condition. We present a simple linear algebraic technique for obtaining a lower bound on the instantaneous gap even in such a situation. As an illustration, we investigate the adiabatic unordered search of van Dam et al. and Roland and Cerf when the non-zero entries of the diagonal final Hamiltonian are perturbed by a polynomial (in logN, where N is the length of the unordered list) amount. We use our technique to derive a bound on the running time of a local adiabatic schedule in terms of the minimum gap between the lowest two eigenvalues.

La première partie de cette thèse est consacrée à l'élaboration théorique de processus adiabatiques permettant le transfert de population entre un état initial et un état cible d'un système quantique. La stratégie du passage adiabatique parallèle pour laquelle les paramètres de couplage sont conçus de telle sorte que la différence des valeurs propres du système reste constante à chaque instant, permet de minimiser à zéro les transitions non-adiabatiques données par la formule DDP. Cette technique permet de combiner à la fois l'efficacité énergétique des méthodes impulsion-pi et la robustesse du passage adiabatique. La seconde partie de cette thèse concerne les effets de la dissipation sur le passage adiabatique. La formule de probabilité de transition d'un système à deux niveaux tenant compte des effets de la dissipation est établie. Cette formule permet de reformuler la solution générale d'un système dissipatif à deux niveaux dans la limite adiabatique qui est valable au-delà du régime de faible dissipation. / The first part of this thesis is devoted to the theoretical analysis of adiabatic processes allowing the transfer of population from an initial state to a target state of a quantum system. The strategy of parallel adiabatic passage, in which the coupling parameters are specifically designed to optimize the adiabatic passage corresponding to parallel eigenvalues at all times, allows one to combine the energetically efficiency of pi-pulse and related strategies with the robustness of standard adiabaticpassage. The second part of this thesis concerns the effects of the dissipation in adiabatic passage. The non-adiabatic transition probability formula of a two state system with dissipation is established. This formula allows on in particular to derive the general solution of a dissipative two-level system in the adiabatic limit which is valid beyond weak dissipation regimes.

This thesis consists of two parts. The first part explores a 2-d edge dislocation model to demonstrate characteristics of Field Dislocation Mechanics (FDM) in modeling single and collective behavior of individual dislocations. The second work explores the possibility of modelling adiabatic shear bands propagation within the timespace averaged framework of Mesoscopic Field Dislocation Mechanics (MFDM). It is demonstrated that FDM reduces the study of a significant class of problems of discrete dislocation dynamics to questions of the modern theory of continuum plasticity. The explored questions include the existence of a Peierls stress in translationally-invariant media, dislocation annihilation, dislocation dissociation, finite-speed-of-propagation effects of elastic waves vis-a-vis dynamic dislocation fields, supersonic dislocation motion, and short-slip duration in rupture dynamics. A variety of dislocation pile-up problems are studied, primarily complementary to what can be dealt by existing classical pile-up models. In addition, the model suggests the possibility that the tip of a shear band can be modelled as a localized spatial gradient of elastic distortion with the dislocation density tensor in continuum dislocation mechanics; It is demonstrated that the localization can be moved by its theoretical driving force and forms a diffuse traveling band tip, thereby extending the thin layer of the deformation band. A 3-d, parallel finite element framework of MFDM is developed in a geometrically nonlinear context for the purpose of modelling shear bands. The numerical formulations and algorithm are presented in detail. Constitutive models appropriate for single crystal plasticity response and J2 plasticity with thermal softening are implemented.

There are many problems that lead to analysis of dynamical systems with phase variables of two types, slow and fast ones. Such systems are called slow-fast systems. The dynamics of such systems is usually described by means of different versions of perturbation theory. Many questions about accuracy of this description are still open. The difficulties are related to presence of resonances. The goal of the proposed thesis is to establish some estimates of the accuracy of the perturbation theory for slow-fast systems in the presence of resonances. We consider slow-fast Hamiltonian systems and study an accuracy of one of the methods of perturbation theory: the averaging method. In this thesis, we start with the case of slow-fast Hamiltonian systems with two degrees of freedom. One degree of freedom corresponds to fast variables, and the other degree of freedom corresponds to slow variables. Action variable of fast sub-system is an adiabatic invariant of the problem. Let this adiabatic invariant have limiting values along trajectories as time tends to plus and minus infinity. The difference of these two limits for a trajectory is known to be exponentially small in analytic systems. We obtain an exponent in this estimate. To this end, by means of iso-energetic reduction and canonical transformations in complexified phase space, we reduce the problem to the case of one and a half degrees of freedom, where the exponent is known. We then consider a quasi-linear Hamiltonian system with one and a half degrees of freedom. The Hamiltonian of this system differs by a small, ~ε, perturbing term from the Hamiltonian of a linear oscillatory system. We consider passage through a resonance: the frequency of the latter system slowly changes with time and passes through 0. The speed of this passage is of order of ε. We provide asymptotic formulas that describe effects of passage through a resonance with an improved accuracy O(ε3/2). A numerical verification is also provided. The problem under consideration is a model problem that describes passage through an isolated resonance in multi-frequency quasi-linear Hamiltonian systems. We also discuss a resonant phenomenon of scattering on resonances associated with discretisation arising in a numerical solving of systems with one rotating phase. Numerical integration of ODEs by standard numerical methods reduces continuous time problems to discrete time problems. For arbitrarily small time step of a numerical method, discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical solution of an ODE may demonstrate dynamical phenomena that are absent in the original ODE. We show that numerical integration of systems with one fast rotating phase leads to a situation of such kind: numerical solution demonstrates phenomenon of scattering on resonances, that is absent in the original system.

No description available.

Quantum computing has been a new and challenging area of research since the concept was put forward in 1980s. A quantum computer is a computer that processes information encoded in systems that exhibit quantum properties and is proved in theory to be more powerful than classical computers. Various approaches to the implementation of the quantum computers have been studied over the decades, each of them having their own advantages and disadvantages in terms of the lifetime of the quantum information, processing time, and scalability of the implementation. Proposals for hybrid quantum processors are interesting because they benefit from the advantages of each comprising system, and thus providing a promising approach to a practical quantum computer. In this thesis, I demonstrate experimentally the principle of utilizing electron spin ensembles as a quantum memory for hybrid quantum processors. I demonstrate the storage and on-demand retrieval of multiple bits of quantum information into and from a single electron spin ensemble by applying magnetic field gradient pulses. I then study the coupling between an electron spin ensemble and a three-dimensional microwave cavity, in the aim of discussing the condition for the coherent information transfer between the excitations in solid-state matter and photons. As an alternative to the high power pulses in electron paramagnetic resonance (EPR), I study the possibility of controlling the electron spin states via adiabatic processes. I demonstrate the implementation of adiabatic geometric phase gates in electron spins and compare their performances to other phase gates achieved with microwave pulses in both simulation and experiment, verifying the robustness of the adiabatic gates against certain type of noises. Finally I present the simulation method developed for simulating the pulsed EPR experiments in this thesis, using a model more general than some currently-existing simulation packages.

Renewable Energy is by nature intermittent and matching the supply of energy to specific time dependent demand poses huge challenges. Energy storage is a useful tool in handling this temporal disparity, although except for regions very suitable for pumped hydroelectric storage schemes, it suffers from being technically difficult to implement and costly as a result. This study investigates the potential benefits offered by various scales of energy storage to different types of renewable energy generation. It also explores the economic drivers behind energy storage operating as part of an electricity spot market. A stochastic optimisation algorithm for determining the maximum possible arbitrage revenue available to energy storage devices is presented and schedule of operation of storage acting in this manner is analysed. The schedule of operation for maximising the revenue is compared to the schedule of operation for minimising the fuel cost to the network and it is demonstrated that because prices are more volatile than the demand which drives them, storage devices do not always act to decrease the fuel cost to the network. It is shown that storage behaving in the right manner can offer significant benefits to electricity systems, and increases the usage of base-load generation, reducing peak electricity demands and the need for expensive peaking plants. The value of storage also increases as the penetration of renewable energy generation increases, although the current electricity market framework is perhaps not the best way to encourage this behaviour. Advanced Adiabatic Compressed Air Energy Storage (AA-CAES) is also identified as a theoretical storage option which deserves further scrutiny. Using thermodynamic modelling the efficiency of this type of system is estimated in the range of 63-67%, and we suggest that this may be increased closer to 73% by using direct contact heat exchangers rather than indirect contact heat exchangers (and a separate thermal fluid), as described in the currently available literature. However, dealing with large pressure ranges (leading to large variations in pressure ratios) encountered in the expansion process is a problematic area which will have to be resolved before this type of system can be constructed with “off-the-shelf” components. Some small scale experiments are used to gain valuable insights into a AA-CAES system. While these suffer from a very low overall efficiency, they highlight the effect of variable pressure ratio on expander efficiency. We conclude that AA-CAES is thermodynamically sound and will be achieved one of two ways: either through the construction of expanders that can work with high efficiency over large pressure ratios, or by resolving the engineering issues with maintaining a constant storage pressure.

This research, is initiated to systematically study the microstructure of AISI 4340 steel prior to impact, after impact and after post-impact annealing to determine the effect of the pre-deformation microstructure on the nucleation and initiation of ASBs, and the mechanism of evolution of ASBs during impact. This study used state-of-the-art microstructural characterization techniques such as the FIB and STEM/HRTEM to reveal that initial microstructural inhomogeneity produces nucleation sites for the initiation of ASBs during impact. It was observed that double misfit interfaces and boundary layers, formed around precipitated carbides (interface between reinforcements and matrix), increased the volume fraction of dislocation sources within the pre-impact specimens. It is demonstrated that the intersection of an activated dislocation source with the direction of maximum shear (regions of stress concentrations) within the specimens during impact, is a necessary condition for the points of intersection to act as possible sites for the nucleation and initiation of ASB depending on the rate of dislocation generation, local strain and strain rate. In addition, the structure that evolves after strain localization starts out with elongation of the grains in the shear direction with the initiation of random and transverse dislocation boundaries along the elongated grains. The elongated grains break along the initiated dislocation boundaries as strain/strain rate increases resulting in the creation of smaller elongated-broken grains and nanograins. Boundary refinement of the broken grains occurring through grain rotation and adiabatic heating results in the evolution of refined grains, subgrains and nanograins. The presence of elongated grains, broken grains, refined grains, subgrains and nanograins within the evolved shear band structures demonstrate that the local deformation is dependent on the imposed local strain and strain rate and that these mechanisms occur concurrently during impact. The results obtained, which are specific to the behavior of BCC ferritic Pearlitic hardenable steels, lead to the conclusion that the evolution of ASBs is a simultaneous layering of microstructures initially driven by dislocations which produce the final structures observed in the shear bands at the end of passage of the stress wave. / February 2015

La vitesse de flamme adiabatique est un paramètre clé dans l'étude de la combustion d'hydrocarbures. Elle joue en effet un rôle essentiel dans le domaine de la combustion, dans la mesure où elle est utilisée pour valider des modèles numériques, pour construire des brûleurs, ou encore pour prédire d'éventuels retours de flamme ou souffles de la flamme. Le but de cette thèse a été d'étudier les vitesses de flammes laminaires d'un grand nombre d'hydrocarbures présents dans les gaz naturels, les essences et les gazoles. Ce travail comprend une partie expérimentale et une partie de modélisation. La partie expérimentale a permis d'enrichir les bases de données de la littérature pour différentes compositions de mélanges air/hydrocarbures. Les travaux ont été effectués sur un nouveau montage mis au point au LRGP (Laboratoire Réactions et Génie des Procédés) pour la mesure de vitesses de flammes laminaires par la méthode du flux de chaleur à l'aide d'un brûleur adiabatique à flamme plate. Cette méthode est basée sur l'équilibre des pertes thermiques nécessaires pour stabiliser la flamme par le flux de chaleur convectif allant de la surface du brûleur vers le front de flamme. Le brûleur est constitué d'une plaque perforée montée sur une chambre de mélange des gaz et la mesure de la distribution radiale de la température est réalisée grâce à une série de thermocouples. Ce montage a d'abord été utilisé à pression atmosphérique et plusieurs températures pour la mesure de vitesses de flammes de composés gazeux (alcanes, alcènes, méthane enrichi en hydrogène ou oxygène, gaz naturels, mélanges méthane-éthane et méthane-propane) et de composés liquides (alcanes, éthanol, essences commerciale et modèle additionnées ou non d'éthanol, alkylcyclohexanes, alkylbenzènes). Le montage a ensuite été placé dans une enceinte pour pouvoir travailler avec des pressions pouvant théoriquement aller jusqu'à 10 atm. Les vitesses de flammes de deux composés ont été étudiées à température ambiante et à haute pression : un composé gazeux, le méthane, jusqu'à une pression de 6 atm et un composé liquide, le n-pentane, jusqu'à une pression de 4 atm. Une étude de modélisation a complété ce travail par l'utilisation de modèles cinétiques détaillés pour la combustion des composés étudiés. Ces modèles ont été testés par la simulation des résultats expérimentaux précédemment obtenus, dans des conditions de richesse, température et pression variées / The laminar burning velocity is a key parameter in the combustion of hydrocarbons study. It plays an essential role in the combustion science area since it is used for the validation of numerical models, the design of burners or to predict potential flashback or blow off of the flame. The goal of the thesis was the study of laminar burning velocities of many hydrocarbons found in natural gases, gasolines or diesel fuels. This work includes an experimental part and a modeling part. The experimental part allowed the implementation of the literature database for different air/hydrocarbons mixtures. The experiments were performed with a new apparatus developed at LRGP (Laboratoire Réactions et Génie des Procédés) for the measurement of laminar burning velocities by the heat flux method thanks to a flat flame adiabatic burner. This method is based on balancing of the heat loss required for the flame stabilization by the convective heat flux from the burner surface to the flame front. The burner head is a thick perforated plate included in a plenum mixing chamber and the measurement of the radial distribution of the temperature is performed with a thermocouples series. This apparatus was first used at atmospheric pressure and several temperatures to measure laminar burning velocities of gaseous compounds (alkanes, alkenes, hydrogen-enriched or oxygen-enriched methane, natural gases, methane-ethane and methane-propane mixtures) and liquid compounds (alkanes, ethanol, commercial gasoline and model fuel with addition of ethanol or not, alkylcyclohexanes, alkylbenzènes). The apparatus was then placed in a chamber in order to work under pressures theoretically up to 10 atm. Laminar burning velocities of two compounds were studied at room temperature and high pressure : a gaseous compound, methane, for pressures up to 6 atm and a liquid compound, n-pentane, for pressures up to 4 atm. A modelling study completed this work by using detailed kinetic models for the combustion of studied compounds. These models were tested by the simulation of experimental results previously obtained, in various equivalence ratio, temperature and pressure conditions