Ultracold Fermi gas is an exciting field benefiting from atomic physics, optical physics and condensed matter physics. It covers many aspects of quantum mechanics. Here I introduce some of my work during my graduate study. We proposed an optical spectroscopic method based on electromagnetically-induced transparency (EIT) as a generic probing tool that provides valuable insights into the nature of Fermi paring in ultracold Fermi gases of two hyperfine states. This technique has the capability of allowing spectroscopic response to be determined in a nearly non-destructive manner and the whole spectrum may be obtained by scanning the probe laser frequency faster than the lifetime of the sample without re-preparing the atomic sample repeatedly. Both quasiparticle picture and pseudogap picture are constructed to facilitate the physical explanation of the pairing signature in the EIT spectra. Motivated by the prospect of realizing a Fermi gas of 40 K atoms with a synthetic non-Abelian gauge field, we investigated theoretically BEC-HCS crossover physics in the presence of a Rashba spin-orbit coupling in a system of two-component Fermi gas with and without a Zeeman field that breaks the population balance. A new bound state (Rashba pair) emerges because of the spin-orbit interaction. We studied the properties of Rashba pairs using a standard pair fluctuation theory. As the two-fold spin degeneracy is lifted by spin-orbit interaction, bound pairs with mixed singlet and triplet pairings (referred to as rashbons) emerge, leading to an anisotropic superfluid. We discussed in detail the experimental signatures for observing the condensation of Rashba pairs by calculating various physical observables which characterize the properties of the system and can be measured in experiment. The role of impurities as experimental probes in the detection of quantum material properties is well appreciated. Here we studied the effect of a single classical impurity in trapped ultracold Fermi superfluids. Although a non-magnetic impurity does not change macroscopic properties of s-wave Fermi superfluids, depending on its shape and strength, a magnetic impurity can induce single or multiple mid-gap bound states. The multiple mid-gap states could coincide with the development of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase within the superfluid. As an analog of the Scanning Tunneling Microscope, we proposed a modified radio frequency spectroscopic method to measure the focal density of states which can be employed to detect these states and other quantum phases of cold atoms. A key result of our self consistent Bogoliubov-de Gennes calculations is that a magnetic impurity can controllably induce an FFLO state at currently accessible experimental parameters.

In this thesis, the boundary errors are defined for the NFM to explore the convergence rates, and the condition numbers are derived for simple cases to explore numerical stability. The optimal convergence (or exponential) rates are discovered numerically. This thesis is also devoted to seek better choice of locations for the field nodes of the FS expansions. It is found that the location of field nodes Q does not affect much on convergence rates, but do have influence on stability. Let £_ denote the distance of Q to ∂S. The larger £_ is chosen, the worse the instability of the NFM occurs. As a result, £_ = 0 (i.e., Q ∈ ∂S) is the best for stability. However, when £_ > 0, the errors are slightly smaller. Therefore, small £_ is a favorable choice for both high accuracy and good stability. This new discovery enhances the proper application of the NFM. However, even for the Dirichlet problem of Laplace¡¦s equation, when the logarithmic capacity (transfinite diameter) C_£F = 1, the solutions may not exist, or not unique if existing, to cause a singularity of the discrete algebraic equations. The problem with C_£F = 1 in the BEM is called the degenerate scale problems. The original explicit algebraic equations do not satisfy the conservative law, and may fall into the degenerate scale problem discussed in Chen et al. [15, 14, 16], Christiansen [35] and Tomlinson [42]. An analysis is explored in this thesis for the degenerate scale problem of the NFM. In this thesis, the new conservative schemes are derived, where an equation between two unknown variables must satisfy, so that one of them is removed from the unknowns, to yield the conservative schemes. The conservative schemes always bypasses the degenerate scale problem; but it causes a severe instability. To restore the good stability, the overdetermined system and truncated singular value decomposition (TSVD) are proposed. Moreover, the overdetermined system is more advantageous due to simpler algorithms and the slightly better performance in error and stability. More importantly, such numerical techniques can also be used, to deal with the degenerate scale problems of the original NFM in [15, 14, 16]. For the boundary integral equation (BIE) of the first kind, the trigonometric functions are used in Arnold [3], and error analysis is made for infinite smooth solutions, to derive the exponential convergence rates. In Cheng¡¦s Ph. Dissertation [18], for BIE of the first kind the source nodes are located outside of the solution domain, the linear combination of fundamental solutions are used, error analysis is made only for circular domains. So far it seems to exist no error analysis for the new NFM of Chen, which is one of the goal of this thesis. First, the solution of the NFM is equivalent to that of the Galerkin method involving the trapezoidal rule, and the renovated analysis can be found from the finite element theory. In this thesis, the error boundary are derived for the Dirichlet, the Neumann problems and its mixed types. For certain regularity of the solutions, the optimal convergence rates are derived under certain circumstances. Numerical experiments are carried out, to support the error made.

Chirality is a nuclear symmetry which is suggested to occur in nuclei when the total angular momentum of the system has an aplanar orientation [Fra97, Fra01]. It can occur for nuclei with triaxial shape, which have valence protons and neutrons with predominantly particle and hole nature. It is expected that the angular momenta of an odd particle and an odd hole (both occupying high-j orbitals) are aligned predominantly along the short and the long axes of the nucleus respectively, whereas the collective rotation occurs predominantly around the intermediate axis of a triaxially deformed nucleus in order to minimize the total energy of the system. Such symmetry is expected to be exhibited by a pair of degenerate DI = 1 rotational bands, i.e. all properties of the partner bands should be identical. The results suggested that spin independence of the energy staggering parameter S(I ) within two-quasiparticle chiral bands (previously suggested a fingerprint of chirality) is found only if the Coriolis interaction can be completely neglected. However, if the configuration is nonrestricted, the Coriolis interaction is often strong enough to create considerable energy staggering. It was also found that staggering in the intra- and inter-band B(M1) reduced transition probabilities (proposed as another fingerprint of chirality) may be a result of effects other than strongly broken chirality. Therefore, the use of the B(M1) staggering as a fingerprint of strongly broken chiral symmetry seems rather risky, in particular if the phase of the staggering is not checked.

Transparent conductive oxides (TCOs) are key functional materials in existing and future electro-optical devices in the fields of energy efficiency, energy generation and information technology. The main application of TCOs is as thin films transparent electrodes where a combination of maximum electrical conductivity and transmittance in the visible to nearinfrared spectral range is required. However, due to the interdependence of the optical properties and the free electron density and mobility, respectively, these requirements cannot be achieved simultaneously in degenerately doped wide band-gap oxide semiconductors. Therefore, a detailed understanding of the mechanisms governing the generation of free charge carriers by extrinsic doping and the charge transport in these materials is essential for further development of high performance TCOs and corresponding deposition methods. The present work is aimed at a comprehensive investigation of the electrical, optical and structural properties as well as the elemental composition of (Al,Ga) doped ZnO and Nb doped TiO2 thin films prepared by pulsed DC reactive magnetron sputtering. The evolution of the film properties is studied in dependence of various deposition parameters through a combination of characterization techniques including Hall-effect, spectroscopic ellipsometry, spectral photometry, X-ray diffraction, X-ray near edge absorption, Rutherford backscattering spectrometry and particle induced X-ray emission. This approach resulted in the development of an alternative process control method based on the material specific current-voltage pressure characteristics of the reactive magnetron discharge which allows to precisely control the oxygen deficiency of the sputter deposited films. Based on the experimental data, models have been established that describe the room temperature charge transport properties and the dielectric function of the obtained ZnO and TiO2 based transparent conductors. On the one hand, these findings allow the prediction of material specific electron mobility limits by identifying the dominating charge carrier scattering mechanisms. On the other hand, new insight is gained into the origin of the observed transition from highly conductive to electrically insulating ZnO layers upon the incorporation of increasing concentrations of Al at elevated growth temperatures. Moreover, the Al and Ga dopant activation in ZnO have been quantified systematically for a wide range of Al concentrations and deposition conditions. A direct comparison of the Ga and Al doping efficiency demonstrates that Ga is a more efficient electron donor in ZnO. Further, it has been shown that high free electron mobilities in polycrystalline and epitaxial Nb:TiO2 layers can be achieved by reactive magnetron sputtering of TiNb alloy targets. The suppression of rutile phase formation and the control of the Nb dopant activation by fine tuning the oxygen deficiency have been identified as crucial for the growth of high quality TiO2 based TCO layers.

Prior to the commencement of this project, few plant viruses had been identified from Vietnam despite virus-like symptoms being commonly observed on many crops and weeds. In limited surveys in the late 1990's, preliminary evidence was obtained indicating that potyviruses and geminiviruses were causing significant diseases. As a result, this study was aimed at developing generic PCR-based methods for the rapid detection of viruses belonging to viruses in the families Potyviridae and Geminiviridae in plant samples collected from Vietnam, and to characterise the viruses at the molecular level. Novel degenerate PCR primers were developed for the identification of begomoviruses. Using these primers, 17 begomoviruses species infecting seven crop and nine weed species in Vietnam were identified and characterised. Sequence analyses showed that ten of the viruses (six monopartite and four bipartite) were new species. Of the seven previously characterized begomoviruses, five were identified in Vietnam for the first time. Additionally, eight DNA-ß and three nanovirus-like DNA-1 molecules were also found associated with the monopartite viruses. Five of the DNA-β molecules were putatively novel. Two novel bipartite begomoviruses, named Corchorus yellow vein virus (CoYVV) and Corchorus golden mosaic virus (CoGMV), were isolated from jute plants. Analysis of these viruses showed that they were more similar to New World begomoviruses than to viruses from the Old World. This was based on the absence of an AV2 open reading frame, the presence of an N-terminal PWRLMAGT motif in the coat protein and phylogenetic analysis of the DNA A and DNA B nucleotide and deduced amino acid sequences. This is the first known occurrence of Old World viruses bearing features of New World viruses, and their presence in Vietnam suggests the presence of a &quotNew World" virus in the Old World prior to Gondwana separation. Other interesting features relating to begomoviruses identified in Vietnam were; (i) the detection of several recombination events, particularly between the newly identified Tomato yellow leaf curl Vietnam virus (TYLCVNV), and the previously characterised, Tomato leaf curl Vietnam virus (ToLCVV), (ii) the identification of new natural hosts of Sida leaf curl virus (SiLCV), Papaya leaf curl China virus (PaLCuCNV) and Alternanthera yellow vein virus (AlYVV), (iii) the first report of variation in the geminivirus stem-loop nonanucleotide sequence (CoGMV sequence was TATTATTAC rather than TAATATTAC) and (iv) the first report of different stem sequences in the stem-loop structure of two genomic components from a bipartite begomovirus, Kudzu mosaic virus (KuMV). The sequence and phylogenetic analyses of the begomoviruses and begomovirus-associated DNAs identified in this study suggested that South East Asia, and Vietnam in particular, may be a centre of begomovirus diversity. Two pairs of degenerate primers, designed in the CI gene (CIFor/CIRev) and HC-Pro gene (HPFo/HPRev), were developed for the detection of viruses in the genus Potyvirus. Using these primers, three novel potyviruses from Vietnam were detected, namely Telosma mosaic virus (TelMV) infecting telosma (Telosma cordata), Peace lily mosaic virus (PeLMV) infecting peace lily (Spathiphyllum patinii) and Wild tomato mosaic virus (WTMV) infecting wild tomato (Solanum torvum). The fragments amplified by the two sets of primers enabled additional PCR and complete genomic sequencing of these three viruses and a Banana bract mosaic virus (BBrMV) isolate from the Philippines. All four viruses shared genomic features typical of potyviruses. Sequence comparisons and phylogenetic analyses indicated that WTMV was most closely related to Chilli veinal mottle virus (ChiVMV) and Pepper veinal mottle virus (PVMV) while PeLMV, TelMV were related to different extents with members of the BCMV subgroup. The incidence of potyviruses infecting plants in Vietnam was investigated using the potyvirus-specific primers. Fifty two virus isolates from 13 distinct potyvirus species infecting a broad range of crops were identified in Vietnam by PCR and sequence analysis of the 3' region of the genome. The viruses were Bean common mosaic virus (BCMV), Potato virus Y (PVY), Sugarcane mosaic virus (SCMV), Sorghum mosaic virus (SrMV), Chilli veinal mottle virus (ChiVMV), Zucchini yellow mosaic virus (ZYMV), Leek yellow stripe virus (LYMV), Shallot yellow stripe virus (SYSV), Onion yellow dwarf virus (OYDV), Turnip mosaic virus (TuMV), Dasheen mosaic virus (DsMV), Sweet potato feathery mottle virus (SPFMV) and a novel potyvirus infecting chilli, which was tentatively named Chilli ringspot virus (ChiRSV). With the exception of BCMV and PVY, this is first report of these viruses in Vietnam. Further, rabbit bell (Crotalaria anagyroides) and typhonia (Typhonium trilobatum) were identified as new natural hosts of the Peanut stunt virus (PStV) strain of BCMV and of DsMV, respectively. Sequence and phylogenetic analyses, based on the nucleotide sequence of the entire CP-coding region of all 52 virus isolates, revealed considerable variability in BCMV, SCMV, PVY, ZYMV and DsMV. The phylogenetic analyses also suggested the possible presence of ancestral groups of BCMV, SCMV and ZYMV in Vietnam.

Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-05-03T14:55:18Z No. of bitstreams: 1 Arquivototal.pdf: 864117 bytes, checksum: a54f5341fc1386510bbc10ef32cee483 (MD5) / Made available in DSpace on 2018-05-03T14:55:18Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 864117 bytes, checksum: a54f5341fc1386510bbc10ef32cee483 (MD5) Previous issue date: 2017-07-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work presents Carleman estimates to a class of degenerate parabolic problems over a square (in the two dimensional case) or a bounded interval (in the one dimensional case). We consider a differential operator that degenerate only in a part of the boundary. Using semigroup theory, we prove well posedness results. Then, using suitables weight functions, we prove Carleman estimates and, as application, results on multi-objective controllability. / Neste trabalho apresentamos estimativas de Carleman para uma classe de problemas parabólicos degenerados sobre um quadrado (no caso bidimensional) ou sobre um intervalo limitado (no caso unidimensional). Consideramos um operador diferencial que degenera apenas em uma parte da fronteira. Provamos resultados de existência, unicidade e estimativas de energia via teoria do semigrupo. Em seguida usamos funções peso adequadas para obter estimativas de Carleman e, como aplicações, resultados de controlabilidade multi-objetivo.

Estudamos o efeito de Conjugação de Fase por Mistura Degenenerada de Quatro Ondas em Al2O3:Cr+3 (Rubi) e GdAlO3:Cr+3 com um laser de Ar (λ=5145 Å). Obtivemos eficiência aproximadamente quatro vezes maior no GdAlO3:Cr+3 (onde este trabalho é original) que no Rubi o que nos motivou a investigar as propriedades físicas que são relevantes para o fenômeno nestes sistemas (isto não foi bem compreendido no trabalho anterior em Rubi). Desenvolvemos um método interferométrico muito sensível para medida dos coeficientes não lineares do índice de refração n2 destes materiais (que não eram conhecidos) Com estes valores de n2 calculamos a eficiência de Conjugação de Fase em bom acordo com experiência. / We have studied the effect of Phase Conjugation by Degenerate Four Wave Mixing in Al2O3:Cr+3 (Rubi) and GdAlO3:Cr+3 with an Ar (λ=5145 Å). We obtained efficiency ?approximately? 4 times greater in GdAlO3:Cr+3 (where this work is original) than in Rubi and this have motivated us to investigate the physical properties that are important to explain this phenomenon in these materials (what wasn\'t well understood in the previous paper on Rubi(10)). We developed an interferometric method very sensitive to measure the nonlinear coeficient of refractive index n2 of these materials (what wasn\'t known). With these values of n2 we calculated the efficiency of the Phase Conjugation in good agreement with the experience.

Orientadores: Alex Eduardo de Bernardini, Marcelo Moraes Guzzo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataglin / Made available in DSpace on 2018-08-17T16:24:26Z (GMT). No. of bitstreams: 1 DuartePerico_EderLeonardo_M.pdf: 2896271 bytes, checksum: 3596fcdea9450fe936e36e96d5ffbad3 (MD5) Previous issue date: 2011 / Resumo: O assunto deste estudo é formação de estruturas em grandes escalas em um universo plano dominado por radiação, matéria escura fria e constante cosmológica como modelo de energia escura no caso particular de presença de um gás degenerado de férmions (GDF) não interagentes como fluído de teste. Nosso modelo admite uma evolução linear das perturbações cosmológicas como também se limita a perturbações escalares, responsáveis pela formação de estruturas. O objetivo principal é analisar a contribuição do GDF no espectro de potências da matéria no presente após uma evolução isentrópica das perturbações primordiais, e compará-la com resultados obtidos para neutrinos cosmológicos. Neste caso, teremos uma mudança contínua de comportamento do GDF de gás ultra-relativístico para não relativístico, o qual aconteceria durante o período de domínio da matéria. Com o objetivo de obter expressões analíticas para a evolução temporal das perturbações do GDF tivemos que fazer o estudo destas em quatro casos diferentes: no período de domínio da radiação, no período de domínio da matéria escura, na escala de super-horizonte durante a transição entre estes dois períodos, e finalmente no período de domínio da constante cosmológica. Fomos bem sucedidos ao chegar a resultados consistentes utilizando dois caminhos diferentes: no primeiro, usando a equação de conservação do tensor momento energia para um gás ideal de férmions totalmente degenerado e não interagente, e no segundo, usando a equação de Boltzmann para um gás de férmions fortemente degenerado e também não interagente. Os dois métodos analíticos levam à mesma solução para as perturbações do GDF quanto escritas até primeira ordem em teoria de perturbações. De forma complementar, os nossos resultados numérico mostram um aumento no espectro de potências da matéria para escalas intermediárias se comparado com a contribuição dos neutrinos massivos. Finalmente estendemos nossa análise numérica ao substituirmos a matéria escura fria CDM e a constante cosmológica por um gás generalizado de Chaplygin GCG como modelo efetivo para o setor escuro do universo, mantendo as condições de contorno que envolvem as densidades médias, e as condições iniciais para as perturbações / Abstract: The subject of this study is the formation of large scale structures (LSS) in a at universe dominated by radiation, cold dark matter and cosmological constant - as a dark energy model - in presence of a degenerate fermionic gas (GDF) as non-interacting test fluid. Our model assumes a linear evolution of cosmological perturbations as well as merely scalar perturbations responsible for structure formation. Our main objective is to analyze the contribution of the GDF in the matter power spectrum today, after an isentropic evolution of primordial perturbations and a continuous change of behavior of ultra-relativistic for non-relativistic GDF, which occurs during the matter domination era in our model. To obtaining analytical expressions for temporal evolution of the GDF perturbations we did study them in four different cases: during the radiation domination era, the dark matter domination, the super-horizon scale limit during the transition between these first two periods and finally during the cosmological constant domination era. We get these results using two different approaches: first, using the conservation equation of the stress-energy tensor for a perfect and non-interacting and fully degenerated fermionic gas, and second, using the Boltzmann equation for a non-interacting and strongly degenerated fermionic gas. Both methods lead to the same analytical solution for GDF perturbations at first order on perturbation theory. On the other hand, our numerical results show an increase in the power spectrum of matter for intermediate scales if compared it with the contribution of massive neutrinos. Finally, we show the change on the results of the standard model of cosmology (CDM) when we exchanging the cold dark matter CDM and the cosmological constant for a generalized Chaplygin gas GCG how effective model of twice old fluids with the same mean density of energy / Mestrado / Cosmologia / Mestre em Física

Dans cette thèse, nous avons étudié expérimentalement les propriétés physiques des fermions ultra-froids grâce à une machine conçue pour refroidir un mélange fermionique de 6Li et 40K. Après une courte description concernant la construction de l'expérience et quelques améliorations que j'ai implémentées pendant ma thèse (telles que la désorption atomique par lumière ultraviolette dans le 2D-MOT), l'exposé se concentre sur deux observations principales de l'origine fermionique des gaz de potassium et de lithium.La première partie présente la quasithermalization du 6Li dans un potentiel quadrupolaire, créé par un piège magnétique. Malgré l'absence de collisions dans un gaz fermionique polarisé en dessous d'une température donnée, nous observons une redistribution d'énergie dans l'ensemble statistique après une excitation dans le piège linéaire. Une étude expérimentale détaillée ainsi qu'une analyse théorique du phénomène sont présentées. De plus, une transformation canonique de l'hamiltonien du système permet la description de particules sans masses dans un piège harmonique. Les résultats expérimentaux du système réel (gaz 6Li dans un potentiel quadrupolaire) sont donc réinterprétés pour décrire ces particules non massiques, difficiles à observer. Un développement supplémentaire de notre système expérimental permet également la réalisation d'un couplage spin-orbite non-abélien dans le gaz fermionique sans interactions.Dans la deuxième partie, on décrit la réalisation d'un gaz dégénéré de 40K à l'aide du refroidissement évaporatif. Une succession d'étapes d'évaporation, utilisant différentes technologies de piégeage, nous permet d'obtenir 1.5e5 atomes dans l'état fondamental à une température de 62nK, température équivalente à 17% de la température de Fermi. / In this thesis we investigate experimentally the physics of a cold fermionic mixture consisting of 6Li and 40K. After a short description of the experimental apparatus and of a few technical particularities implemented during my PhD, for example the light-induced atomic desorption in the 2D-MOT by UV-light, we focus on two main observations of the fermionic nature of the gas.The first part describes the quasithermalization of 6Li in a magnetic quadrupole potential. Even though collisions are absent in a spin-polarized fermionic gas below a given temperature, the statistical ensemble undergoes energy redistribution after an excitation within the linear potential. We present an extensive experimental study as well as a comprehensive theoretical analysis. Moreover, the studied Hamiltonian can be canonically mapped onto a system of massless, harmonically trapped particles and the previously developed results are re-interpreted in order to describe this experimentally inaccessible system. A further development of the realized experiment allows even for the implementation of spin-orbit coupling in a gas of non-interacting fermions.In the second part, we describe the evaporative cooling of 40K to quantum degeneracy. Through different evaporative cooling stages we reach with a final number of 1.5e5 atoms in the ground-state a temperature of 62nK, which corresponds to 17% of the Fermi temperature.

Au cours de ma thèse, j'ai travaillé à la construction de l'expérience Fermix, consacrée à l'étude d'un mélange de fermions (6Li-40K) à très basses températures où les effets quantiques sont prédominants. Nous présentons ici deux résultats principaux. Premièrement, nous avons développé une nouvelle méthode de refroidissement sub-Doppler qui tire parti de l'existence d'états noirs dans la raie optique D1. Cette mélasse grise permet d'atteindre une densité de l'espace des phases de 10^-4, la valeur la plus élevée rapportée dans la littérature pour le refroidissement laser simultané des deux espèces. Grâce à cette étape, nous avons pu réaliser un gaz fortement dégénéré de 3x10^5 atomes de 40K, répartis dans deux états de spins, à une température de 62 nK, soit 17% de la température de Fermi. D'autre part, nous introduisons une transformation canonique pour montrer l'équivalence formelle entre le comportement de particules ultra-relativistes sans interactions (particules de Weyl) dans un potentiel harmonique et celui de fermions froids confinés dans un piège quadrupolaire. Nous étudions expérimentalement, numériquement et théoriquement la relaxation de tels systèmes vers un état stationnaire, non-Botlzmanien, caractérisé par des températures effectives fortement anisotropes. Cette analogie permet également d'interpréter des propriétés caractéristiques des particules relativistes. Ainsi, nous montrons que le paradoxe de Klein est analogue aux pertes Majorana. Pour finir, nous proposons une étude théorique des interactions médiées à longue distance par un système en dimensions mixtes. / During my PhD, I contributed to the design and construction of the Fermix experiment, dedicated to the study of a 6Li-40K fermionic mixture at ultra low temperatures. Our main results are twofold. First, we developed a new sub-Doppler laser cooling scheme, taking advantage of the existence of dark states in the D1 line of alkali atoms. This so-called \emph{grey molasses} allows for a phase space density up to $10^{-4}$, the highest value reported for the simultaneous laser cooling of those two species. The improvement due to this cooling step enabled the production of a quantum degenerate 40K gas in a dipole trap, with 3x10^5 atoms in two spin states at 62 nK, corresponding to 17% of the Fermi temperature. Second, introducing a canonical mapping, we showed that non-interacting ultra-relativistic particles (Weyl fermions) in a harmonic trap can be simulated by cold fermions confined in a quadrupole potential. We study experimentally, numerically and theoretically the relaxation of these systems towards a steady state which can not be described by a Boltzman distribution, but rather presents strongly anisotropic effective temperatures. This analogy also allows us to translate fundamental properties of relativistic particles in the language of cold atoms. In particular, we demonstrate that the Klein paradox is equivalent to Majorana losses.Finally, we present a theoretical study of the long range interactions between particles confined in two 2D layers immersed in a 3D atomic cloud.