Notre dispositif d'électrodynamique quantique en cavité permet de faire interagir dans le régime de couplage fort deux systèmes simples et parfaitement contrôlés : des atomes à deux niveaux et un seul mode du champ électromagnétique. Des miroirs supraconducteurs permettent de stocker le champ électromagnétique micro-onde dans une cavité pendant plus d'un dixième de seconde. Afin de sonder et de manipuler le champ piégé, nous utilisons des atomes de Rubidium excités dans les états de Rydberg circulaires. Les atomes interagissent un à un avec la cavité dans le régime dispersif. Ils se comportent alors comme de petites horloges dont la fréquence est affectée par les photons piégés grâce au phénomène de déplacement lumineux. Les petites modifications de la phase atomique après la traversée du mode sont mesurées par interférométrie de Ramsey, permettant de compter le nombre de photons piégés. En adaptant légèrement la méthode, on parvient à reconstruire complètement la matrice densité du champ piégé. Cette technique a été appliquée à différents états non-classiques du champ : des états de Fock, dont le nombre de photons est parfaitement déterminé, et des états chat de Schrödinger. Ces derniers sont formés de la superposition quantique de deux champs classiques de phases différentes. En répétant la procédure de reconstruction pour plusieurs délais successifs après la préparation, on obtient un film image par image de l'évolution temporelle de l'état. L'étude de l'évolution de l'état chat de Schrödinger sous l'effet de la décohérence apporte un éclairage intéressant sur le problème de la mesure en mécanique quantique et la frontière entre les mondes classique et quantique.

In this thesis work, time-frequency filtering of nonstationary signals in noise using Wigner-Ville Distribution is investigated. Continuous-time, discrete-time and discrete Wigner Ville Distribution definitions, their relations, and properties are given. Time-Frequency Peak Filtering Method is presented. The effects of different parameters on the performance of the method are investigated, and the results are presented. Time-Varying Wiener Filter is presented. Using simulations it is shown that the performance of the filter is good at SNR levels down to -5 dB. It is proposed and shown that the performance of the filter improves by using Support Vector Machines. The presented time-frequency filtering techniques are applied on test signals and on a real world signal. The results obtained by the two methods and also by classical zero-phase low-pass filtering are compared. It is observed that for low sampling rates Time-Varying Wiener Filter, and for high sampling rates Time-Frequency Peak Filter performs better.

Multiple Signal Classification (MUSIC) Algorithm based and Wigner Distribution-Principal Component Analysis (WD-PCA) based classification techniques are very recently suggested resonance region approaches for electromagnetic target classification. In this thesis, performances of these two techniques will be compared concerning their robustness for noise and their capacity to handle large number of candidate targets. In this context, classifier design simulations will be demonstrated for target libraries containing conducting and dielectric spheres and for dielectric coated conducting spheres. Small scale aircraft targets modeled by thin conducting wires will also be used in classifier design demonstrations.

The Self-Organizing Map (SOM) is a type of neural network that forms a regular grid of neurons where clusters of neurons represent different classes of targets. The aim of this thesis is to design electromagnetic target classifiers by using the Self-Organizing Map (SOM) type artificial neural networks for dielectric and conducting objects with simple or complex geometries. Design simulations will be realized for perfect dielectric spheres and also for small-scaled aircraft targets modeled by thin conducting wires. The SOM classifiers will be designed by target features extracted from the scattered signals of targets at various aspects by using the Wigner distribution. Noise performance of classifiers will be improved by using slightly noisy input data in SOM training.

In this thesis, entanglement under fully relativistic settings are discussed. The thesis starts with a brief review of the relativistic quantum mechanics. In order to describe the effects of Lorentz transformations on the entangled states, quantum mechanics and special relativity are merged by construction of the unitary irreducible representations of Poincar&eacute / group on the infinite dimensional Hilbert space of state vectors. In this framework, the issue of finding the unitary irreducible representations of Poincar&eacute / group is reduced to that of the little group. Wigner rotation for the massive particles plays a crucial role due to its effect on the spin polarization directions. Furthermore, the physical requirements for constructing the correct relativistic spin operator is also studied. Then, the entanglement and Bell type inequalities are reviewed. The special attention has been devoted to two historical papers, by EPR in 1935 and by J.S. Bell in 1964. The main part of the thesis is based on the Lorentz transformation of the Bell states and the Bell inequalities on these transformed states. It is shown that entanglement is a Lorentz invariant quantity. That is, no inertial observer can see the entangled state as a separable one. However, it was shown that the Bell inequality may be satisfied for the Wigner angle dependent transformed entangled states. Since the Wigner rotation changes the spin polarization direction with the increased velocity, initial dichotomous operators can satisfy the Bell inequality for those states. By choosing the dichotomous operators taking into consideration the Wigner angle, it is always possible to show that Bell type inequalities can be violated for the transformed entangled states.

This thesis applies an electromagnetic feature extraction technique to design electromagnetic target classifiers for conductors, dielectrics and dielectric coated conductors using their natural resonance related late-time scattered responses. Classifier databases contain scattered data at only a few aspects for each candidate target. The targets are dielectric spheres of varying sizes and refractive indices, perfectly conducting spheres varying sizes and dielectric coated conducting spheres of varying refractive indices and thickness in coating. The applied classifier design technique is suitable for real-time target classification because of the computational efficiency of feature extraction and decision making approaches. The Wigner-Ville Distribution (WD) is employed in this study in addition to the Principal Components Analysis (PCA) technique to extract target features mainly from late-time target responses. WD is applied to the back-scattered responses at different aspects. To decrease aspect dependency, feature vectors are extracted from selected late-time portions of the WD outputs that include natural resonance related information. Principal components analysis is also used to fuse the feature vectors and/or late-time target responses extracted from reference aspects of a given target into a single characteristic feature vector for each target to further reduce aspect dependency.

Quantum annealing is expected to be a powerful generic algorithm for solving hard combinatorial optimization problems faster than classical computers. Finding the solution to a combinatorial optimization problem is equivalent to finding the ground state of an Ising Hamiltonian. In today's quantum annealers the spins of the Ising Hamiltonian are mapped to superconducting qubits. On the other hand, dissipation processes degrade the success probability of finding the solution. In this thesis we set out to explore a newly proposed architecture for a noise-resilient quantum annealer that instead maps the Ising spins to continuous variable quantum states of light encoded in the field quadratures of a two-photon pumped Kerr- nonlinear resonator based on the proposal by Puri et al. (2017). In this thesis we study the Wigner negativity for this newly proposed architecture and evaluate its performance based on the negativity of the Wigner function. We do this by determining an experimental value to when the presence of losses become too detrimental, such that the Wigner function of the quantum state during the evolution within the anneal becomes positive for all times. Furthermore, we also demonstrate the capabilities of this continuous variable quantum annealer by simulating and finding the best solution of a small instance of the NP-complete subset sum problem and of the number partitioning problem.

This thesis deals with the topic of high resolution spectral analysis. In the first part, selected methods are presented and afterwards compared based on the Matlab implementations. The problematics of reduction of crossterms in quadratic time–frequency distributions is also covered. The second part is focused on the implementation and optimization of the algorithm for real-time computation of smoothed Wigner distribution function.

Quantum systems with finite Hilbert space where position x and momentum p take values in Z(d) (integers modulo d) are considered. Symplectic tranformations S(2¿,Z(p)) in ¿-partite finite quantum systems are studied and constructed explicitly. Examples of applying such simple method is given for the case of bi-partite and tri-partite systems. The quantum correlations between the sub-systems after applying these transformations are discussed and quantified using various methods. An extended phase-space x¿p¿X¿P where X, P ¿ Z(d) are position increment and momentum increment, is introduced. In this phase space the extended Wigner and Weyl functions are defined and their marginal properties are studied. The fourth order interference in the extended phase space is studied and verified using the extended Wigner function. It is seen that for both pure and mixed states the fourth order interference can be obtained. / Ministry of Higher Education, Sultanate of Oman

No / Vortices circulating in a ring made from a Josephson array in the insulating phase are studied. The ring contains a `dual Josephson junction' through which the vortices tunnel. External non-classical microwaves are coupled to the device. The time evolution of this two-mode fully quantum mechanical system is studied, taking into account the dissipation in the system. The effect of the quantum statistics of the photons on the quantum statistics of the vortices is discussed. Entropic calculations quantify the entanglement between the two systems. Quantum phenomena in the system are also studied through Wigner functions. After a certain time (which depends on the dissipation parameters) these quantum phenomena are destroyed due to dissipation.