Quantum optimal control theory is applied to find optimal pulses for controlling the motion of an ion and a molecule for two different applications. Those optimal pulses enable the control of the dynamics of the system by driving the atom or the molecule from an initial state to desired states.The evolution equations obtained by means of the quantum optimal control theory are resolved iteratively using a monotonic convergent algorithm. A number of simulation parameters are varied in order to get the optimal pulses including the duration of the pulses, the time step of the time grid, a penalty factor that limits the maximal intensity of the fields, and a guess pulse which is used to start the optimal control.The optimal pulses obtained for each application are analyzed by Fourier transform, and also by looking at the time evolution of the populations that they generate in the system.The first application is the preparation of specific vibrational states of acetylene that are usually not reachable from the ground state, and that would remain unpopulated by usual spectroscopy. Relevant state energies and transition dipole moments are extracted from the experimental literature and especially from the global acetylene Hamiltonian conferring an uncommon precision to the control simulation. The control starts from the ground state. The target states belongs to the polyad Ns=1, Nr=5 of acetylene which includes two vibrational dark states and one vibrational bright state. First, the simulation is performed with the Schrödinger equation and in a second step, with the Liouville--von Neumann equation, as mixed states are prepared. Indeed, the control starts from a Boltzmann distribution of population in the rotational levels of the vibrational ground state chosen in order to simulate an experimental condition. But the distribution is truncated to limit the computational effort. One of the dark states appears to be a potential target for a realistic experimental investigation because the average population of the Rabi oscillation remains high and decoherence is expected to be weak. The optimal pulses obtained have a high fidelity, have a spectrum with well-resolved peak frequencies, and their experimental feasibility seems achievable within the current abilities of experimental laboratories.The second application is to propose an experimental realization of a microscopic physical device able to simulate quantum dynamics. The idea is to use the motional states of a Cd^+ ion trapped in an anharmonic potential to realize a quantum dynamics simulator of a single-particle Schrödinger equation. In this way, the motional states store the information and the optimal pulse manipulates this information to realize operations. In the present case, the simulated dynamics was the propagation of a wave packet in a harmonic potential. Starting from an initial quantum state, the pulse acts on the system to modify the motional states of the ion in such a way that the final superposition of motional states corresponds to the results of the dynamics. This simulation is performed with the Liouville--von Neumann equation and also with the Lindblad equation as dissipation is included to test the robustness of the pulse against perturbations of the potential. The optimal pulses that are obtained have a high fidelity which shows that the ion trap system has correctly realized the quantum dynamics simulation. The optimal pulses are valid for any initial condition if the potential of the simulation or the mass of the propagated wave packet is unchanged. / La théorie du contrôle optimal quantique est utilisée pour trouver des impulsions optimales permettant de contrôler la dynamique d'un atome et d'une molécule les menant d'un état initial à un état final. Les équations d'évolution obtenues grâce au contrôle optimal limitent l'intensité maximale de l'impulsion et sont résolues itérativement grâce à l'algorithme de Zhu--Rabitz. Le contrôle optimal est utilisé pour réaliser deux objectifs. Le premier est la préparation d'états vibrationnels de l'acétylène qui sont généralement inaccessibles par transition au départ de l'état vibrationnel fondamental. Ces états, appelés états sombres, sont les états cibles de la simulation. Ils appartiennent à la polyade Ns=1, Nr=5 de l'acétylène qui en contient deux ainsi qu'un état, dit brillant, qui lui est accessible depuis l'état fondamental. Les énergies des états du système et les moments de transitions dipolaires sont déterminés à partir d'un Hamiltonien très précis qui confère une précision inhabituelle à la simulation. Un des états sombres apparaît être un candidat potentiel pour une réalisation expérimentale car la population moyenne de cet état reste élevée après l'application de l'impulsion.Les niveaux rotationnels des états vibrationnels sont également pris en compte.Les impulsions optimales obtenues ont une fidélité élevée et leur spectre en fréquence présente des pics résolus.Le deuxième objectif est de proposer la réalisation expérimentale d'un dispositif microscopique capable de simuler une dynamique quantique. Ce travail montre qu'on peut utiliser les états de mouvement d'un ion de Cd^+ piégé dans un potentiel anharmonique pour réaliser la propagation d'un paquet d'onde dans un potentiel harmonique. Ce dispositif stocke l'information de la dynamique simulée grâce aux états de mouvements et l'impulsion optimale manipule l'information pour réaliser les propagations. En effet, démarrant d'un état quantique initial, l'impulsion agit sur le système en modifiant les états de mouvements de l'ion de telle sorte que la superposition finale des états de mouvements corresponde aux résultats de la dynamique. De la dissipation est incluse pour tester la robustesse de l'impulsion face à des perturbations du potentiel anharmonique. Les impulsions optimales obtenues ont une fidélité élevée ce qui montre que le système a correctement réalisé la simulation de dynamique quantique. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

Doctor of Philosophy / Department of Physics / B.D. DePaola / In recent years, coherent excitation techniques have focused on the ability to efficiently prepare atomic or molecular systems into a selected state. Such population control plays a key role in cutting-edge research taking place today, such as in the areas of quantum information and laser-controlled chemical reactions. Stimulated Raman adiabatic passage (STIRAP) is a widely-used coherent excitation technique that provides a relatively robust control mechanism for efficiently exciting a target population into a desired state. While the technique is well proven, current experimental techniques yield little information on the population dynamics taking place throughout the excitation process, and experimentalists rely solely on final excited-state measurements to determine the efficiency of population transfer. This dissertation presents a unique diagnostic tool to measure multilevel coherent population transfer on a short (nanosecond) timescale. The technique described here uses magneto-optical trap recoil ion momentum spectroscopy (MOTRIMS) as a noninvasive probe of a coherently-controlled system. It provides extremely detailed information about the excitation process, and highlights some important characteristics seen in excited populations that would otherwise be misleading or completely overlooked if one were to use more traditional diagnostic techniques. This dissertation discusses both the theoretical and experimental results applied to three-level coherently excited target populations of Rb-87.

In recent years, improved control of the motional and internal quantum states of ultracold neutral atoms and ions has opened intriguing possibilities for quantum simulation and quantum computation. Many-body effects have been explored with hundreds of thousands of quantum-degenerate neutral atoms and coherent light-matter interfaces have been built. Systems of single or a few trapped ions have been used to demonstrate universal quantum computing algorithms and to detect variations of fundamental constants in precision atomic clocks. Now in our experiment we investigate how the two systems can be advantageously combined. We immerse a single trapped Yb+ ion in a Bose-Einstein condensate of Rb atoms. Our hybrid setup consists of a linear RF-Paul trap which is overlapped with a magnetic trap and an optical dipole trap for the neutral atoms. A first synergetic effect is the sympathetic cooling of the trapped ions to very low temperatures through collisions with the ultracold neutral gas and thus without applying laser light to the ions. We observe the dynamics of this effect by measuring the mean ion energy after having an initially hot ion immersed into the condensate for various interaction times, while at the same time monitoring the effects of the collisions on the condensate. The observed ion cooling effect calls for further research into the possibility of using such hybrid systems for the continuous cooling of quantum computers. To this end a good understanding of the fundamental interaction processes between the ion and the neutrals is essential. We investigate the energy dependent elastic scattering properties by measuring neutral atom losses and temperature increase from an ultracold thermal cloud of Rb. By comparison with a Monte-Carlo simulation we gain a deeper understanding of how the different parameters affect the collisional effects. Additionally, we observe charge exchange reactions at the single particle level and measure the energy-independent reaction rate constants. The reaction products are identified by in-trap mass spectrometry, revealing the branching ratio between radiative and non-radiative charge exchange processes.

No description available.

This thesis presents results of investigations on fields and multipole expansion coefficients in axially symmetric (referred to as 3D)and two dimensional (2D)ion trapmass analysers. 3D mass analysers have a three-electrode geometry with two (electrically shorted) endcap electrodes and one central ring electrode. rf-only or rf/dc potential applied across the electrodes creates a linear trapping field in the central cavity of the mass analyser.2Dmass analysers have four longitudinal electrodes in which the opposite pairs of electrodes are electrically shorted. Here, rf-only or rf/dc potential applied across the pair of electrodes creates a linear trapping field and fragment ions of the analyte gas are trapped along the central axis of the mass analyser. Both these mass analysers have apertures machined on the electrodes (holes in case of 3D traps and slits in case of 2D traps) to permit entry of electrons for ionizing the analyte gas and for collection of destabilized fragment ions. This thesis is concerned with how these apertures influence the fields and multipole expansion coefficients within the traps. This thesis is divided into five chapters. Chapter 1 provides the background information which is required for the thesis. It begins with a description of the geometry of the 3D and the 2D mass analysers used in the present work.These include the quadrupole ion trap (QIT) and cylindrical ion trap (CIT) for 3D structures and the linear ion trap (LIT) and the rectilinear ion trap (RIT) for 2D structures. This is followed by a brief description of the numerical method, the boundary element method (BEM), used in the thesis. Also presented here are the Green’s function for 3D and 2D geometries. In the final section, the scope of the thesis is presented. Chapter 2 presents two approximate analytical expressions for nonlinear electric fields in the principal direction in axially symmetric (3D) and two dimensional (2D) ion trap mass analysers with apertures on the electrodes. Considered together (3D and 2D), we present composite approximations for the principal unidirectional nonlinear electric fields in these ion traps. The composite electric field E has the form E= EnoAperture + EdueToAperture where EnoAperture is the field within an imagined trap which is identical to the practical trap except that the apertures are missing; and where EdueToAperture is the field contribution due to apertures on the two trap electrodes. The field along the principal axis of the trap can in this way be well approximated for any aperture that is not too large. To derive EdueToAperture, classical results of electrostatics have been extended to electrodes with finite thickness and different aperture shapes. EnoAperture is a modified truncated multipole expansion for the imagined trap with no aperture. The first several terms in the multipole expansion are in principle exact (though numerically determined using the BEM), while the last term is chosen to match the field at the electrode. This expansion, once computed, works with any aperture in the practical trap. The composite field approximation for axially symmetric (3D) traps is checked for three geometries: the quadrupole ion trap (QIT), the cylindrical ion trap (CIT) and an arbitrary other trap. The approximation for 2D traps is verified using two geometries: the linear ion trap (LIT)and the rectilinear ion trap (RIT). In each case, for two aperture sizes (10% and 50% of the trap dimension), highly satisfactory fits are obtained. These composite approximations may be used in more detailed nonlinear ion dynamics studies than have been hitherto attempted. In Chapter 3we complement and complete the work presented in Chapter 2 by considering off-axis fields in the axially symmetric (3D) and the two dimensional (2D) ion traps whose electrodes have apertures. Our approximation has two parts. The first, EnoAperture, is the field obtained numerically for the trap under study with no apertures. We have used the boundary element method (BEM) for obtaining this field. The second part, EdueToAperture, is an analytical expression for the field contribution of the aperture. In EdueToAperture, aperture size is a free parameter. A key element in our approximation is the electrostatic field near an infinite thin plate with an aperture, and with different constant valued far field intensities on either side. Compact expressions for this field can be found using separation of variables, wherein the choice of coordinate system is crucial. This field is, in turn, used four times within our trap specific approximation. The off-axis field expressions for the 3D geometries were tested on the quadrupole ion trap (QIT) and the cylindrical ion trap (CIT), and the corresponding expressions for the 2D geometries were tested on the linear ion trap (LIT) and rectilinear ion trap (RIT). For each geometry, we have considered apertures which are 10%, 30% and 50% of the trap dimension. We have found that our analytical correction term EdueToAperture, though based on a classical small-aperture approximation, gives good results even for relatively large apertures. Chapter 4 presents approximate analytical expressions for estimating the variation in multipole expansion coefficients with the size of apertures in axially symmetric (3D) and two dimensional (2D) ion trap mass analysers. Following the approach adopted in Chapter 2 and Chapter 3 which focused on the role of apertures to fields within traps, here too, the analytical expression is a sum of two terms, An,noAperture, the multipole expansion coefficient for a trap with no apertures and An,dueToAperture, the multipole expansion coefficient contributed by the aperture. An,noAperture has been obtained numerically and An,dueToAperture is obtained from the nth derivative of the potential within the trap. The expressions derived have been tested on two 3D geometries and two 2D geometries. These include the quadrupole ion trap (QIT) and the cylindrical ion trap (CIT) for 3D geometries and the linear ion trap (LIT) and the rectilinear ion trap (RIT) for the 2D geometries. Multipole expansion coefficients A2 to A24, estimated by our analytical expressions were compared with the values obtained numerically (using the boundary element method) for aperture sizes varying up to 50% of the trap size. In all the plots presented, it is observed that our analytical expression for the variation of multipole expansion coefficients versus aperture size closely follows the trend of the numerical evaluations for the range of aperture sizes considered. The maximum relative percentage errors, which provide an estimate of the deviation of our values from those obtained numerically for each multipole expansion coefficient, are seen to be in the range of 10% to 15%. The leading multipole expansion coefficient, A2, however, is seen to be estimated very well by our expressions, with most values being within 1% of the numerically determined values, with larger deviations seen for the QIT and LIT only at larger aperture sizes. Chapter 5 presents a few concluding remarks.

Household debt grows up from the second half of the nineties of the century thanks to growing a living standard. More people provide own living and consumer credit increases. Because of financial crisis many people feel deterioration of working conditions and just the loss of regular earnings leads to problem with paying of a debts. The diploma thesis will be concerned with the problem of people's debts in accordance with personal and family finance and deal with responsible approach to loans, impacts of unpaid debts and solutions how to avoid the debt trap.

La communication quantique vise la génération, la distribution et le stockage de qubits afin d'établir de véritables réseaux quantiques. Le stockage cohérent, efficace et réversible d'états photoniques dans des mémoires atomiques est donc nécessaire et représente actuellement un enjeu majeur de la science de l'information quantique. Ainsi, de nombreux supports de stockage, tels que les ensembles d'atomes froids ou à l'état solide, sont envisagés afin de satisfaire au mieux les propriétés attendues d'une mémoire quantique. Les travaux présentés dans ce manuscrit s'inscrivent dans ce contexte et décrivent la réalisation expérimentale d'une mémoire basée sur le protocole DLCZ dans un ensemble d'atomes froids de 87Rb. Un dispositif de double piège magnéto-optique permet de refroidir et de confiner cet ensemble au sein d'un piège dont le temps de vie est ~15 s, et de le manipuler en vue du stockage quantique. Nous disposons ainsi d'un nuage présentant une épaisseur optique à résonance de l'ordre de 5, et dont les atomes sont refroidis à une dizaine de µK. La mise en place du protocole DLCZ dans cet ensemble atomique consiste à créer des états cohérents de la matière puis à les relire, à partir de diffusions Raman qui s'accompagnent de la génération de photons uniques corrélés en impulsion. Les premiers résultats obtenus montrent des corrélations non-classiques, affichant une violation forte de l'inégalité de Cauchy-Schwarz, pour une efficacité de lecture de l'ordre de 4% et un temps de cohérence de l'état stocké de ~800 ns. Cette mémoire, utilisée comme une source de photons uniques annoncés, fait partie d'un projet pour lequel une interface basée sur de l'optique non-linéaire / Quantum communication aims at generating, distributing and storing qubits between distant locations, in view of implementing actual quantum networks. Coherent, efficient and reversible storage of photonic states in atomic memories is thus necessary and represents a major challenge in quantum information science. Several storage medium, such as cold atomic or solid-state ensembles, are considered so as to satisfy at best the different benchmarks of a quantum memory. In this context, the work presented in this manuscript describes the experimental realization of a memory based on the DLCZ protocol in cold atomic ensemble of 87Rb. A double magneto-optical trap system allows cooling and confining this ensemble within a trap showing a lifetime of 15 s, and to manipulate it for quantum storage. This cloud shows a resonant optical thickness of about 5, and atoms are cooled down to 10 µK. The implementation of the DLCZ protocol in this atomic ensemble consists in creating coherent states of matter and then to read them, using Raman scattering events which come along with the generation of pairs of single photons correlated in momentum. First results show non-classical correlations, which exhibit a strong violation of the Cauchy-Schwarz inequality, with a read-out efficiency of about $4\%$ and a coherence time of the stored state on the order of 800 ns. This memory, used as a heralded single photon source, is part of a project in which an interface based on non-linear guided wave optics has been built and caracterized so as to convert the 795 nm single photons generated by the memory to the telecom wavelength of 1560 nm. Both elements, combined with a entangled photon source withi

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This diploma thesis describes the Quantitative easing as an unconvetional tool of the monetary policy. In the first chapter of this thesis there is theoretical analysis of the zero lower bound and also of specific phenomenon that might occur in this situation (the liquidity trap). The second chapter deals with the quantitative easing as a monetary policy with focus on the United States. It summarizes its development during three so called rounds, during which the quantitative easing has been used. This chapter also contains analysis of the entrance and exit strategy of the quantitative easing. In the third chapter, there is an econometric model estimated by ordinary least squares method with robust errors. This model is being used to verify the hypothesis whether the quantitative easing lowered long-term interest rates. The hypothesis has been rejected as the quantitative easing does not have statistically significant effect on any selected long-term bonds.

The thesis analyses problems of eurozone after the beginning of financial crisis in 2008, which continuously changed into economic and debt crisis. The thesis considers eurozone in aggregate and closer focuses on so called GIIPS (Greece, Ireland, Italy, Portugal, Spain) countries. Recent eurozone economic situation is compared to Japanese "lost decade" during 1990s, I seek for parallels and differences. Theoretical part shows approaches by economic schools to causes of cycle and to role of policymakers. Main challenges of fiscal and monetary policy are considered, specifically fiscal policy in time of high public indebtedness, monetary policy in liquidity trap etc. Applicative part considers causes of the economic situation at the beginning, more specifically devoted to balance sheets recession. Key part of the practical part it is analysis of applied fiscal and monetary policy, including helping efforts to financial system. Concluding remarks summarizes key understanding from the thesis, proposals are included and it is considered whether eurozone is going to follow Japanese path since 90's or not. It seems highly probable that eurozone is going to follow Japanese in terms of sluggish economic growth, parallels can be seen in weak impact of monetary policy in liquidity trap, but recommendations to fiscal policy from Japanese experience should be taken into account in very cautious way because of both specifics of eurozone and Japanese economy.