The processing of information based on the generation of common quantum optical states (e.g. coherent states) and the measurement of the quadrature components of the light field (e.g. homodyne detection) is often referred to as continuous-variable quantum information processing. It is a very fertile field of investigation, at a crossroads between quantum optics and information theory, with notable successes such as unconditional continuous-variable quantum teleportation or Gaussian quantum key distribution. In quantum optics, the states of the light field are conveniently characterized using a phase-space representation (e.g. Wigner function), and the common optical components effect simple affine transformations in phase space (e.g. rotations). In quantum information theory, one often needs to determine entropic characteristics of quantum states and operations, since the von Neuman entropy is the quantity at the heart of entanglement measures or channel capacities. Computing entropies of quantum optical states requires instead turning to a state-space representation of the light field, which formally is the Fock space of a bosonic mode.<p>This interplay between phase-space and state-space representations does not represent a particular problem as long as Gaussian states (e.g. coherent, squeezed, or thermal states) and Gaussian operations (e.g. beam splitters or squeezers) are concerned. Indeed, Gaussian states are fully characterized by the first- and second-order moments of mode operators, while Gaussian operations are defined via their actions on these moments. The so-called symplectic formalism can be used to treat all Gaussian transformations on Gaussian states, including mixed states of an arbitrary number of modes, and the entropies of Gaussian states are directly linked to their symplectic eigenvalues.<p>This thesis is concerned with the Gaussian transformations applied onto arbitrary states of light, in which case the symplectic formalism is unapplicable and this phase-to-state space interplay becomes highly non trivial. A first motivation to consider arbitrary (non-Gaussian) states of light results from various Gaussian no-go theorems in continuous-variable quantum information theory. For instance, universal quantum computing, quantum entanglement concentration, or quantum error correction are known to be impossible when restricted to the Gaussian realm. A second motivation comes from the fact that several fundamental quantities, such as the entanglement of formation of a Gaussian state or the communication capacity of a Gaussian channel, rely on an optimization over all states, including non-Gaussian states even though the considered state or channel is Gaussian. This thesis is therefore devoted to developing new tools in order to compute state-space properties (e.g. entropies) of transformations defined in phase-space or conversely to computing phase-space properties (e.g. mean-field amplitudes) of transformations defined in state space. Remarkably, even some basic questions such as the entanglement generation of optical squeezers or beam splitters were unsolved, which gave us a nice work-bench to investigate this interplay. <p>In the first part of this thesis (Chapter 3), we considered a recently discovered Gaussian probabilistic transformation called the noiseless optical amplifier. More specifically, this is a process enabling the amplification of a quantum state without introducing noise. As it has long been known, when amplifing a quantum signal, the arising of noise is inevitable due to the unitary evolution that governs quantum mechanics. It was recently realized, however, that one can drop the unitarity of the amplification procedure and trade it for a noiseless, albeit probabilistic (heralded) transformation. The fact that the transformation is probabilistic is mathematically reflected in the fact that it is non trace-preserving. This quantum device has gained much interest during the last years because it can be used to compensate losses in a quantum channel, for entanglement distillation, probabilistic quantum cloning, or quantum error correction. Several experimental demonstrations of this device have already been carried out. Our contribution to this topic has been to derive the action of this device on squeezed states and to prove that it acts quite surprisingly as a universal (phase-insensitive) optical squeezer, conserving the signal-to-noise ratio just as a phase-sensitive optical amplifier but for all quadratures at the same time. This also brought into surface a paradoxical effect, namely that such a device could seemingly lead to instantaneous signaling by circumventing the quantum no-cloning theorem. This paradox was discussed and resolved in our work.<p>In a second step, the action of the noiseless optical amplifier and it dual operation (i.e. heralded noiseless attenuator) on non-Gaussian states has been examined. We have observed that the mean-field amplitude may decrease in the process of noiseless amplification (or may increase in the process of noiseless attenuation), a very counterintuitive effect that Gaussian states cannot exhibit. This work illustrates the above-mentioned phase-to-state space interplay since these devices are defined as simple filtering operations in state space but inferring their action on phase-space quantities such as the mean-field amplitude is not straightforward. It also illustrates the difficulty of dealing with non-Gaussian states in Gaussian transformations (these noiseless devices are probabilistic but Gaussian). Furthermore, we have exhibited an experimental proposal that could be used to test this counterintuitive feature. The proposed set-up is feasible with current technology and robust against usual inefficiencies that occur in optical experiment. <p>Noiseless amplification and attenuation represent new important tools, which may offer interesting perspectives in quantum optical communications. Therefore, further understanding of these transformations is both of fundamental interest and important for the development and analysis of protocols exploiting these tools. Our work provides a better understanding of these transformations and reveals that the intuition based on ordinary (deterministic phase-insensitive) amplifiers and losses is not always applicable to the noiseless amplifiers and attenuators.<p>In the last part of this thesis, we have considered the entropic characterization of some of the most fundamental Gaussian transformations in quantum optics, namely a beam splitter and two-mode squeezer. A beam splitter effects a simple rotation in phase space, while a two-mode squeezer produces a Bogoliubov transformation. Thus, there is a well-known phase-space characterization in terms of symplectic transformations, but the difficulty originates from that one must return to state space in order to access quantum entropies or entanglement. This is again a hard problem, linked to the above-mentioned interplay in the reverse direction this time. As soon as non-Gaussian states are concerned, there is no way of calculating the entropy produced by such Gaussian transformations. We have investigated two novel tools in order to treat non-Gaussian states under Gaussian transformations, namely majorization theory and the replica method.<p>In Chapter 4, we have started by analyzing the entanglement generated by a beam splitter that is fed with a photon-number state, and have shown that the entanglement monotones can be neatly combined with majorization theory in this context. Majorization theory provides a preorder relation between bipartite pure quantum states, and gives a necessary and sufficient condition for the existence of a deterministic LOCC (local operations and classical communication) transformation from one state to another. We have shown that the state resulting from n photons impinging on a beam splitter majorizes the corresponding state with any larger photon number n’ > n, implying that the entanglement monotonically grows with n, as expected. In contrast, we have proven that such a seemingly simple optical component may have a rather surprising behavior when it comes to majorization theory: it does not necessarily lead to states that obey a majorization relation if one varies the transmittance (moving towards a balanced beam splitter). These results are significant for entanglement manipulation, giving rise in particular to a catalysis effect.<p>Moving forward, in Chapter 5, we took the step of introducing the replica method in quantum optics, with the goal of achieving an entropic characterization of general Gaussian operations on a bosonic quantum field. The replica method, a tool borrowed from statistical physics, can also be used to calculate the von Neumann entropy and is the last line of defense when the usual definition is not practical, which is often the case in quantum optics since the definition involves calculating the eigenvalues of some (infinite-dimensional) density matrix. With this method, the entropy produced by a two-mode squeezer (or parametric optical amplifier) with non-trivial input states has been studied. As an application, we have determined the entropy generated by amplifying a binary superposition of the vacuum and an arbitrary Fock state, which yields a surprisingly simple, yet unknown analytical expression. Finally, we have turned to the replica method in the context of field theory, and have examined the behavior of a bosonic field with finite temperature when the temperature decreases. To this end, information theoretical tools were used, such as the geometric entropy and the mutual information, and interesting connection between phase transitions and informational quantities were found. More specifically, dividing the field in two spatial regions and calculating the mutual information between these two regions, it turns out that the mutual information is non-differentiable exactly at the critical temperature for the formation of the Bose-Einstein condensate.<p>The replica method provides a new angle of attack to access quantum entropies in fundamental Gaussian bosonic transformations, that is quadratic interactions between bosonic mode operators such as Bogoliubov transformations. The difficulty of accessing entropies produced when transforming non-Gaussian states is also linked to several currently unproven entropic conjectures on Gaussian optimality in the context of bosonic channels. Notably, determining the capacity of a multiple-access or broadcast Gaussian bosonic channel is pending on being able to access entropies. We anticipate that the replica method may become an invaluable tool in order to reach a complete entropic characterization of Gaussian bosonic transformations, or perhaps even solve some of these pending conjectures on Gaussian bosonic channels.<p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

We report experimentally results on the low temperature properties of two classes of materials with a special emphasizes near the QCP induced by substitution and magnetic 1.field: (1) the HF systems YbRh2(Si0.95Ge0.05)2, Yb1-yLayRh2Si2 (y = 0.05, 0.1),and YbIr2Si2 with tetragonal structures and CeIn3-xSnx (x = 0.55, 0.6, 0.65, 0.7, 0.8) with cubic structure; (2) the quantum spin systems: Cs2CuCl4 and Cs2CoCl4. In all the HF compounds we have observed NFL behavior in zero magnetic field close to the QCP. The La substituted system does not show an antiferromagnetic (AFM) transition down to the lowest accessible temperature (0.03 K) while in YbRh2(Si1-xGex)2 with x = 0 and x = 0.05 AFM transitions occur at TN =0.07 K and 0.02 K, respectively. For Yb0.9La0.1Rh2Si2 we observe below 0.07 K saturation of DeltaC/T indicating clearly a LFL state for this concentration. For YbIr2Si2, DeltaC/T saturates below 0.5 K. In contrast to the Yb based compounds in the vicinity of the QCP, CeIn3-xSnx shows no evidence of a divergence in Delta C/T, with B or with x. Furthermore, we used specic heat measurements in the mK temperature range and at high fields (up to 12 T) to probe the phase diagrams in the low dimensional quantum antiferromagnets Cs2CuCl4 and Cs2CoCl4. In applied magnetic field, we have presented experimental evidence that in Cs2CuCl4 the field dependence of the critical temperature Tc(B) ~ (Bc-B)^1-Phi close to the critical field Bc = 8.51 T is well described with Phi=1.5. This is in very good agreement with the exponent expected in the mean-field approximation and support the notion of a Bose-Einstein condensation of magnons in Cs2CuCl4.

Nous investiguons dans ce travail la création d'échantillons permettant l'étude du comportement des polaritons excitoniques dans les matériaux semi-conducteurs organiques. Le couplage fort entre les états excités d'électrons et des photons impose la création de nouveaux états propres dans le milieu. Ces nouveaux états, les polaritons, ont un comportement bosonique et sont donc capables de se condenser dans un état fortement dégénéré. Une occupation massive de l'état fondamental permet l'étude de comportements explicables uniquement par la mécanique quantique. La démonstration, au niveau macroscopique, d'effets quantiques promet d'éclairer notre compréhension de la matière condensée. De plus, la forte localisation des excitons dans les milieux organiques permet la condensation des polaritons excitoniques organiques à des températures beaucoup plus hautes que dans les semi-conducteurs inorganiques. À terme, les échantillons proposés dans ce travail pourraient donc servir à observer une phase cohérente macroscopique à des températures facilement atteignables en laboratoire. Les cavités proposées sont des résonateurs Fabry-Perot ultraminces dans lesquels est inséré un cristal unique d'anthracène. Des miroirs diélectriques sont fabriqués par une compagnie externe. Une couche d'or de 60 nanomètres est ensuite déposée sur leur surface. Les miroirs sont ensuite mis en contact, or contre or, et compressés par 2,6 tonnes de pression. Cette pression soude la cavité et laisse des espaces vides entre les lignes d'or. Une molécule organique, l'anthracène, est ensuite insérée par capillarité dans la cavité et y est cristallisée par la suite. Dans leur état actuel, les cavités présentent des défauts majeurs quant à la planarité des miroirs et à l'uniformité des cristaux. Un protocole détaillé est présenté et commenté dans ce travail. Nous y proposons aussi quelques pistes pour régler les problèmes courants de l'appareil. / In this work we investigate the creation of samples for the study of the behavior of excitonic polaritons in organic semiconductor materials. The strong coupling between the excited states of electrons and photons implies the creation new eigenstates in the medium. These new states, called polaritons, are composite bosons and are therefore capable of condensing in a strongly degenerated state. A massive occupation of the ground state allows the study of behaviors that are only explainable by quantum mechanics. A macroscopic demonstration of quantum effects offers a rare opportunity for scientific research and discoveries. The strong localization of excitons in organic materials allows condensation of exciton polaritons at temperatures much higher than in inorganic semiconductors. Therefore the samples proposed in this work could ultimately be used to observe a macroscopic coherent phase at temperatures easily attainable in a laboratory. The cavities proposed in this work are Fabry-Perot resonators in which anthracene is inserted and crystalized. The mirrors used in the resonator are dielectric reflectors made by a external company according to our specifications. A gold layer of 60 nm is deposited on their surface. The mirrors are then brought into contact, gold against gold, and compressed by 2.6 tons of pressure. This pressure seals the cavity and leaves voids between the gold lines. An organic molecule, anthracene, is then inserted in by capillary inside the cavity voids and subsequently crystallized by controlled cooling. In their current state cavities have defects regarding the planarity of the mirrors and the uniformity of the crystals. A detailed protocol is presented and discussed in this work.

L'aimant organique NIT-2Py a été caractérisé expérimentalement et ses propriétés ont été simulées numériquement à partir de la théorie de la fonctionnelle de la densité. Le magnétisme dans ce matériau provient de la présence d'un électron non apparié sur chaque molécule qui a ainsi un moment magnétique non nul. Ceci a été confirmé par des simulations sur une molécule isolée. Les molécules de NIT-2Py cristallisent dans le groupe d'espace P21/c avec huit molécules par maille élémentaire pour former la structure cristalline Alpha étudiée dans ce document. Le moment effectif de la susceptibilité et l'entropie magnétique totale montre que ce matériau est un système de spins 1/2 avec un spin par molécule. Les mesures de chaleur spécifique ont mis en évidence la présence de deux phases magnétiques ordonnées à basse température qui sont séparées par un plateau en aimantation. Une première phase est observée à des champs magnétiques inférieurs à 2.2 T et a une température de transition de 1.32 K en champ nul. Les mesures de susceptibilité magnétique et d'aimantation ont permis d'établir que cette phase ordonnée est antiferromagnétique. Ceci est confirmé par les simulations numériques. La deuxième phase est induite par le champ magnétique avec une température de transition de 0.53 K à 6 T. L'information disponible sur cette phase est limitée et l'étude du système à l'extérieur des phases ordonnées en donne une meilleure compréhension. Un modèle de spins S=1/2 isolés et de dimères S=0 isolés reproduit bien les mesures d'aimantation et de chaleur spécifique au-dessus de 3 K. L'application d'un champ magnétique réduit l'écart d'énergie entre le singulet et le triplet du dimère jusqu'au croisement qui se produit à 6 T. La phase induite émerge précisément à ce croisement et on spécule l'existence d'un condensat de Bose-Einstein des états triplets. / The organic magnet built from NIT-2Py molecules has been characterized experimentally and its properties have been simulated using density functional theory. In this material, an unpaired electron carrying a magnetic moment on each molecule is responsible for the magnetism. This has been confirmed by numeric simulations on an isolated molecule. NIT-2Py molecules crystallize in space group P21/c with eight molecules per unit cell to form crystalline phase Alpha studied in this document. The effective moment obtained from magnetic susceptibility and the total magnetic entropy show that this material is a spin 1/2 system with one spin per molecule. Specific heat measurements have highlighted the presence of two magnetically ordered phases at low temperature, which are separated by a plateau in magnetization. A first phase is observed at magnetic field lower than 2.2 T and has a transition temperature of 1.32 K in zero field. Magnetic susceptibility and magnetization measurements have established that this ordered phase is antiferromagnetic. This is confirmed by numeric simulations. The second phase is induced by a magnetic field and has a transition temperature of 0.53 K at 6 T. Information concerning the field induced phase is limited and a study of the system above the transition temperatures helps to gain a better understanding. A model of isolated spins S=1/2 and isolated dimers S=0 reproduces nicely the specific heat and magnetization data above 3 K. The application of a magnetic field reduces the energy gap between the singlet and the triplet of the dimer and the crossover between these levels is observed at 6 T. The field induced phase emerges precisely at this crossover suggesting the occurrence of a Bose-Einstein condensation of triplets states.

Diferentes tipos de sólitons têm sido observados em meios ópticos não-lineares, e seus comportamentos individuais descritos pela equação não-linear de Schrödinger e pela equação não-linear de Schrödinger generalizada, em diferentes dimensões e geometrias. Entretando, há situações onde muitos sólitons são gerados formando uma densa rede de sólitons. Nestes casos, é impossível desprezar as interações entre os sólitons e temos que considerar a evolução da estrutura como um todo. A teoria das ondas de choque dispersivas em meios fotorrefrativos e a teoria da difração não-linear de intensos feixes de luz propagando-se em meios fotorrefrativos com um fio refletor incorporado a esse meio foi desenvolvida, e verificamos que está em excelente acordo com nossas simulações numéricas. No caso da formação de sólitons em condensados, fizemos cálculos numéricos realísticos dentro da aproximação de campo médio usando a equação de Gross-Pitaevskii, incluindo também um potencial de confinamento, um potencial móvel e um potencial dipolar. A maioria dos resultados puderam ser comparados com experimentos recentes. / Different kinds of solitons have already been observed in various nonlinear optical media, and their behavior has been explained in the frameworks of such mathematical models as the nonlinear Schrödinger and generalized nonlinear Shrödinger equations for different dimensions and geometries. However, there are situations when many solitons are generated so that they can comprise a dense soliton train. In such situations, it is impossible to neglect interactions between solitons and one has to consider the evolution of the structure as a whole rather than to trace the evolution of each soliton separately. The theory of optical shock waves in photorefractive media and the theory of nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire was developed and agrees very well with our numerical simulations. In the condensate soliton formation case, we did numerical calculations in the mean field approach using the Gross-Pitaevskii equation, adding a trap potential and a moving potential and a potential of the dipole-dipole interaction. The main results were also checked by recent experiments.

Uma análise dos processos colisionais homonucleares e heteronucleares, responsáveis por perdas em uma armadilha magneto-óptica, foi realizada neste trabalho. Resultados experimentais inéditos para as taxas de perdas, no sistema Rb-Cs, foram obtidos. Os dados experimentais em conjunto com os resultados do modelo sugerem que o processo de escape radiativo é dominante. O modelo utilizado é muito sensível à profundidade da armadilha, a qual depende de outros parâmetros (intensidade, dessintonia, gradiente de campo magnético, etc.). A colaboração com pesquisadores italianos possibilitou uma análise mais detalhada das taxas de perdas heteronucleares em outras regiões de intensidade. Estudamos a dependência das taxas heteronucleares com a razão das massas do par atômico, e uma razoável concordância foi observada. O estudo de processos colisionais em armadilhas magneto-ópticas é importante na obtenção do condensado de BoseEinstein com duas espécies atômicas distintas, e também em experiências de espectroscopia fotoassociativa. / In this work, we had investigated the heteronuclear trap loss rate in a two-species Rb-Cs magneto-optical trap. The experimental results suggest that radiative escape is the main collisional process responsible for heteronuclear losses. An addapted Gallagher - Pritchard model is compared with the data. The model is very sensitive to the trap depth, which depends on the trap parameters (intensity, detuning, magnetic - field gradient, etc.) This observation is also supported by experimental results from a Pisa\' group. We have compared experimental of heteronuclear rates as a function of the masses ratio of the atomic pair with the model, and a reasonable agreement is observed. These studies are relevant for high resolution atomic / molecular spectroscopy, and for the production of mixed - species Bose-Einstein condensates.

Este trabalho consiste em um estudo teórico da coexistência de condensados de Bose-Einstein atômicos acoplados. Esta mistura de condensados pode consistir em átomos de um mesmo elemento em vários estados hiperfinos (estado interno). Outra situação em que esta mistura ocorre é quando um átomo em um único estado interno pode ocupar mais de um estados externo. As semelhanças e diferenças entre condensados de Bose-Einstein com vários estados internos e externos serão analisadas cuidadosamente. Somente na aproximação de Bose-Hubbard os estados externos serão tratados como internos. Condensados envolvendo duas ou mais espécies serão estudados com a aproximação de Thomas-Fermi com estados coerentes. Esta aproximação implica em desprezar o termo de energia cinética. Muitos resultados analíticos serão exibidos para a condição em que todos os comprimentos de espalhamento são iguais entre si. Esta condição é bastante próxima da observada em um condensado de vários estados internos. Além disso serão apresentados alguns resultados anaíticos onde o comprimento de espalhamento para espécies diferentes é zero. Esta condição é verificada para a aproximação de Bose-Hubbard para misturas de condensados com estados externos. O objetivo principal destes cálculos é estudar o papel da fase relativa entre as funções de onda nas soluções estacionárias e na evolução temporal destes sistemas. / This work consists of a theoretical study of the coexistance of coupled atomic Bose-Einstein condensates. These mixed condensates can consist of atoms of the same element in different hyperfine internal states. A different situation is that in which an atom in one internal state can ocupate different single particle external states. The similarities and differences between mixed Bose-Einstein condensates involving internal and external states will be analysed carefully. Only in the Bose-Hubbard approximation the external states can be treated like internal states. Condensates involving two or more species will be studied with in a Thomas- Fermi\'s approximation with coherent states. This approximation involves in discarding of the Hamiltonian the kinetic energy term. A number of analytical results are given for the case in which the different channel scatering lenghts are equal to each other. This condition is which well approximated in condensates involving many internal states. Beside some results will also be given for situations where the scatering lenghts for different species vanishes. This condiction is verified for the Bose-Hubbard approximation to externally mixed condensates. The principal goal of this calculations is to study the role of relative phase between the wave functions in the stationary solutions and in the time evolution of the systems.

Nesta tese estudamos dois problemas diferentes na área de átomos ultra frios: Ondas de choque em condensados de Bose-Einstein e Espalhamento inelástico de átomos em um potencial de dois poços. No primeiro problema, estudamos o fluxo supersônico de um condensado de Bose-Einstein (BEC) através de um obstáculo macroscópico impenetrável delgado no sistema da equação de Schrödinger não-linear (NLS) bidimensional. Assumindo-se que a velocidade do fluxo é suficientemente alta, reduzimos assintoticamente o problema bidimensional original de valor de contorno para o fluxo estacionário através de um obstáculo alongado ao problema do pistão dispersivo unidimensional descrito pela NLS 1D dependente do tempo, no qual a coordenada original x reescalonada faz o papel de tempo e o movimento do pistão está vinculado à geometria do obstáculo. Duas ondas de choque dispersivas (DSWs) são geradas no fluxo, cada uma sendo formada em uma extremidade (frontal e traseira) do obstáculo. A DSW frontal é descrita analiticamente construindo-se soluções de modulação exatas para as equações de Whitham e a para a DSW traseira, empregamos a regra de quantização de Bohr-Sommerfeld generalizada para descrever a distribuição dos sólitons escuros. Propomos uma extensão da solução de modulação tradicional, a fim de incluir o padrão de ship-wave linear formado fora da região da DSW frontal. Realizamos simulações numéricas 2D completas e verificamos a validade das previsões analíticas. Os resultados deste problema podem ser relevantes para experimentos recentes sobre o fluxo de BECs através de obstáculos. No segundo problema, estudamos uma mistura atômica de dois átomos fermiônicos leves de spin 1/2 e dois átomos pesados em um potencial de dois poços. Processos de espalhamento inelástico entre ambas as espécies atômicas excitam os átomos pesados e renormalizam a taxa de tunelamento e a interação entre os átomos leves (efeito polarônico). A interação efetiva dos átomos leves muda de sinal e se torna atrativa quando o espalhamento inelástico é forte. Observamos também o cruzamento de níveis de energia, de um estado onde cada poço contém apenas um férmion (espalhamento inelástico fraco) para um estado onde um poço contém um par de férmions e ou outra está vazio (espalhamento inelástico forte). Identificamos o efeito polarônico e o cruzamento dos níveis de energia estudando-se a dinâmica quântica do sistema. / In this thesis we study two different problems in the field of ultracold atoms: Shock waves in Bose-Einstein condensates and Inelastic scattering of atoms in a double well. In the first problem, we study the supersonic flow of a Bose-Einstein condensate (BEC) past a slender impenetrable macroscopic obstacle in the framework of the twodimensional (2D) defocusing nonlinear Schr¨odinger equation (NLS). Assuming the oncoming flow speed sufficiently high, we asymptotically reduce the original boundary-value problem for a steady flow past a slender body to the one-dimensional dispersive piston problem described by the nonstationary NLS equation, in which the role of time is played by the stretched x-coordinate and the piston motion curve is defined by the spatial body profile. Two steady oblique spatial dispersive shock waves (DSWs) spreading from the pointed ends of the body are generated in both half-planes. These are described analytically by constructing appropriate exact solutions of the Whitham modulation equations for the front DSW and by using a generalized Bohr-Sommerfeld quantization rule for the oblique dark soliton fan in the rear DSW. We propose an extension of the traditional modulation description of DSWs to include the linear ship-wave pattern forming outside the nonlinear modulation region of the front DSW. Our analytic results are supported by direct 2D unsteady numerical simulations and are relevant to recent experiments on Bose-Einstein condensates freely expanding past obstacles. In the second problem, we study a mixture of two light spin-1/2 fermionic atoms and two heavy atoms in a double well potential. Inelastic scattering processes between both atomic species excite the heavy atoms and renormalize the tunneling rate and the interaction of the light atoms (polaron effect). The effective interaction of the light atoms changes its sign and becomes attractive for strong inelastic scattering. This is accompanied by a crossing of the energy levels from singly occupied sites at weak inelastic scattering to a doubly occupied and an empty site for stronger inelastic scattering. We are able to identify the polaron effect and the level crossing in the quantum dynamics.

In this work we constructed an experimental system to realize a BEC of sodium atoms. In the first part of the work, we study two atomic sources in order to choose the most suitable for our system. The comparison between a Zeeman slower and a bidimensional magnetooptical trap (2D-MOT) was performed to evaluate the capacity of producing an appropiate flux of atoms in order to load a tridimensional magneto-optical trap (3D-MOT). The experimental results show that the 2D-MOT is as efficient as the Zeeman slower with the advantage of being more compact and easier to operate, and for these reasons we choose it as our source of cold atoms. After this, the experimental apparatus to produce a Bose-Einstein condensate was constructed and characterized. With this experimental system we realized all the required stages to achieve the Bose-Einstein condensation (BEC). Initially, we characterized and compared the performance between the Bright-MOT and Dark-SPOT MOT of sodium atoms, observing the great advantages this last configuration offers. Afterward, we implemented the experimental sequence for the achivement of the BEC of sodium atoms. After the optical molasses process, the atoms are tranferred to an optically plugged quadrupole trap (OPT) where the process of evaporative cooling is performed. With this setup, we achive a sodium BEC with &#8764; 5&times;105 atoms and a critical temperature of &#8764; 1.1 &mu;K. Finally, with the constructed and characterized machine, we started to perform experiments of cooperative absorption of two photons by two trapped atoms. With the new system, we wanted to take advantage of the higher densities in the magnetic trap and BEC to explore some features of this phenomenon in the classical and quantum regimes. We were interested in exploring some features of this nonlinear light-matter interaction effect. The idea of having two or more photons interacting with two or more atoms is the beginning of a new possible class of phenomena that we could call many photons-many body intercation. In this new possibity, photons and atoms will be fully correlated, introducing new aspects of interactions. / Neste trabalho, realizamos a construção de um sistema experimental para a realização de um condensado de Bose-Einstein de átomos de sódio. Na primeira parte do trabalho, realizamos o estudo de duas fontes átomicas com o intuito de escolher a mais adequada para nosso sistema experimental. A comparação foi realizada entre um Zeeman slower e uma armadilha magneto-óptica bidimensional (MOT-2D), que são técnicas usadas para fornecer um grande fluxo de átomos com distribuição de velocidades adequadas para serem capturados numa armadilha magneto-óptica tridimensional (MOT-3D). Os resultados experimentais da caracterização de ambos os sistemas mostra que o MOT-2D oferece um grande fluxo atômico da mesma ordem do Zeeman slower, mas com a vantagem de ser um sistema mais compacto em questão de tamanho, razão pela qual foi escolhido como fonte atômica no nosso sistema. A partir daqui, realizamos a construção do sistema experimental para a realização do condensado de sódio. Inicialmente realizamos o aprisionamento numa MOT-3D, realizando subsequentemente os passos de resfriamento sub-Doppler mediante o processo de molasses ópticas. Depois disto, os átomos são transferidos para uma armadilha magnética, que consiste de um par de bobinas em configuração anti-Helmholtz, as mesmas usadas para a MOT-3D mas com um gradiente de campo magnético ao redor de uma ordem de grandeza maior. Esta armadilha é combinada com um laser com dessintonia para o azul focado a 30 &mu;m no centro da armadilha, onde o campo magnético é zero com o objetivo de evitar as perdas por majorana que acontecem nessa região. Com esta configuração, um condensado de &#8764; 5 &times; 105 átomos é obtido a uma temperatura crítica de &#8764; 1.1 &mu;K. Por último, com a máquina construída e caracterizada, começamos re-explorar o experimento de absorção cooperativa de dois fótons por dois átomos aprisionados. Com nosso novo sistema, é possível explorar este efeito no regime clássico e quântico. Estamos interessados em explorar algumas características da interação não linear entre luz e matéria. A ideia de ter dois ou mais fótons interagindo com um ou mais átomos, é possivelmente o começo de uma nova classe de fenômenos que poderíamos chamar de interação de muitos fótons com muitos átomos.

Neste trabalho descrevemos a produção e estudo de excitações topológicas em um condensado de Bose-Einstein em átomos de Rubídio-87. O condensado é produzido através de resfriamento evaporativo forçado por rádio-freqüência em uma armadilha puramente magnética do tipo QUIC. A armadilha magnética é carregada por um sistema de duplo-MOT. A temperatura de transição é de cerca de 150nK. Condensados puros com 1 - 2 × 10^5 átomos de Rb-87 são observados. Realizamos uma caracterização da amostra em relação às suas características fundamentais. Fração condensada, expansão anisotrópica, distribuição espacial e efeitos de temperatura finita são descritos. Com o objetivo de observar excitações coerentes do condensado entre os estados da armadilha, adicionamos um campo magnético do tipo quadrupolo esférico oscilante no tempo. Observamos, no entanto, a transferência de momento angular para a amostra com a formação de vórtices e arranjos de vórtices. Definimos regiões de amplitude que geram números de vórtices crescentes. Observamos a formação de estruturas de três vórtices não convencionais donde supusemos a possibilidade de excitação conjunta de vórtices e anti-vórtices. Observamos evidência de turbulência quântica, um estado onde os arranjos dos vórtices não são regulares nem as linhas de vórtices têm um eixo de rotação comum. / In this work we describe the production and investigation of topological excitations in a Bose-Einstein condensate in Rubidium-87 atoms. The condensate is produced through forced evaporative cooling by radio-frequency in a QUIC-type purely magnetic trap. The magnetic trap is loaded from a double-MOT system. Transition temperature is about 150nK. Pure condensates containing 1-2×105 87Rb atoms are observed. We performed the characterization of the sample in relation to its fundamental aspects. Condensed fraction, anisotropic expansion, spacial distribution and finite temperature effects are described. Aiming to observe coherent topological excitations of the condensate between two states of the trap, we added a spherical quadrupole magnetic fields oscillating in time. We observe, instead, angular momentum tranference to the sample and the formation of vortices and arrays of vortices. We define amplitude regions where an increasing number of vortices are observed. We observe the formation of non-usual three-vortex structures from which we infer the existence of vortices and anti-vortices together in the sample. We observe evidence of quantum turbulence, a state where non-regular vortex arrays appear as well as vortex lines have no preferred direction to form.