This dissertation discusses the Landau-Zener (LZ) theory and its application in noisy environments and in many-body systems. The first project considers the effect of fast quantum noise on LZ transitions. There are two important time intervals separated by the characteristic LZ time. For each interval we derive and solve the evolution equation, and match the solutions at the boundaries to get a complete solution. Outside the LZ time interval, we derive the master equation, which differs from the classical equation by a quantum commutation term. Inside the LZ time interval, the mixed longitudinal-transverse noise correlation renormalizes the LZ gap and the system evolves according to the renormalized LZ gap. In the extreme quantum regime at zero temperature our theory gives a beautiful result which coincides with that of other authors. Our initial attempts to solve two experimental puzzles - an isotope effect and the quantized hysteresis curve of a single molecular magnet - are also discussed. The second project considers an ultracold dilute Fermi gas in a magnetic field sweeping across the broad Feshbach resonance. The broad resonance condition allows us to use the single mode approximation and to neglect the energy dispersion of the fermions. We then propose the Global Spin Model Hamiltonian, whose ground state we solve exactly, which yields the static limit properties of the BEC-BCS crossover. We also study the dynamics of the Global Spin Model by converting it to a LZ problem. The resulting molecular production from the initial fermions is described by a LZ-like formula with a strongly renormalized LZ gap that is independent of the initial fermion density. We predict that molecular production during a field-sweep strongly depends on the initial value of magnetic field. We predict that in the inverse process of molecular dissociation, immediately after the sweeping stops there appear Cooper pairs with parallel electronic spins and opposite momenta.

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.

This dissertation introduces some new properties of both superfluid phases of fermions with spin-orbit coupling (SOC) and superradiant phases of photons in an optical cavity. The effects of SOC on the phase transition between normal and superfluid phase are revealed; an unconventional crossover driven by SOC from the Bardeen-Cooper-Schrieffer (BCS) state to the Bose-Einstein condensate (BEC) state is verified in three different systems; and two kinds of excitations, a Goldstone mode and a Higgs mode, are demonstrated to occur in a quantum optical system. We investigate the BCS superfluid state of two-component atomic Fermi gases in the presence of three kinds of SOCs. We find that SOC drives a class of BCS to BEC crossover that is different from the conventional one without SOC. Here, we extend the concepts of the coherence length and Cooper-pair size in the absence of SOC to Fermi systems with SOC. We study the dependence of chemical potential, coherence length, and Cooper-pair size on the SOC strength and the scattering length in three dimensions (3D) (or the twobody binding energy in two dimensions (2D)) for three attractively interacting Fermi gases with 3D Rashba, 3D Weyl, and 2D Rashba SOC respectively. By adding a population imbalance to a Fermi gas with Rashba-type SOC, we also map out the finite-temperature phase diagram. Due to a competition between SOC and population imbalance, the finite-temperature phase diagram reveals a large variety of new features, including the expanding of the superfluid state regime and the shrinking of both the phase separation and the normal regimes. We find that the tricritical point moves toward a regime of low temperature, high magnetic field, and high polarization as the SOC strength increases. Besides Fermi fluids, this dissertation also gives a new angle of view on the superradiant phase in the Dicke model. Here, we demonstrate that Goldstone and Higgs modes can be observed in an optical system with only a few atoms inside a cavity. The model we study is the U(1)/Z2 Dicke model with N qubits (two-level atoms) coupled to a single photon mode.

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La théorie des spins élevés est le domaine de la physique théorique au centre de cette thèse. Le contexte général de la naissance de cette théorie est présentée dans l’introduction. La première partie est axée sur les ingrédients (méthode de Noether, fonctions génératrices et formalisme ambiant) permettant la construction de vertex cubiques entre un champ scalaire de matière et un champ de jauge de spin élevé dans un espace-temps à courbure constante à partir des courants conservés en espace-temps plat. Dans un second temps, nous préparons les éléments pour un futur test de la correspondance holographique à l’ordre cubique voire quartique en la constante de couplage. Plus précisément, nous révisons en détail le calcul de certains propagateurs, ce qui nous mène à calculer les fonctions à trois points impliquant deux scalaires. La dernière partie, bien que concernant toujours l’holographie des spins élevés, traite de la physique non-relativiste. Les symétries et les courants d’un gaz parfait/unitaire de Fermi y sont étudiés. Le lien entre physiques relativiste et non-relativiste est obtenue grâce à la réduction dimensionnelle de Bargmann. / The higher spin theory is the field of theoretical physics at the center of this thesis. The general context of the birth of this theory is presenting in the introduction. The first part focuses on the ingredients (Noether method, generating functions and ambient formalism) for the construction of cubic vertices between a scalar matter field and a higher spin gauge field in a constant curvature space-time from conserved currents in flat space-time. In a second step, we prepare the around for a future test of the holographic correspondence in the cubic or quartic order in the coupling constant. More specifically, we review in detail the computation of some propagators, which leads us to calculate three-point functions involving two scalars. The last part, although always on the higher spin holography, deals with non-relativistic physics. Symmetries and currents of an ideal or unitary Fermi gas are studied. The link between relativistic and non-relativistic physics is obtained by Bargmann dimensional reduction.

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La compréhension des effets des interactions dans un ensemble de particules quantiques représente un enjeu majeur de la physique moderne. Les atomes ultra-froids sont rapidement devenus un outil incomparable pour étudier ces systèmes quantiques fortement corrélés. Dans cette thèse, nous présentons plusieurs travaux portant sur les propriétés d’un mélange de superfluides de Bose et de Fermi créé à l’aide de vapeurs ultra-froides de ⁷Li et de ⁶Li. Nous étudions tout d'abord les propriétés hydrodynamiques du mélange en créant un contre-courant entre les superfluides. L'écoulement est dissipatif uniquement au dessus d'une vitesse critique que nous mesurons dans le crossover BEC-BCS. Une simulation numérique d’un contre-courant de deux condensats permet de mieux comprendre les mécanismes sous-jacents mis en jeu dans la dynamique. En particulier, l'étude numérique fournit des preuves supplémentaires que l'origine de la dissipation dans nos expériences est liée à l'émission d'excitation élémentaires dans chaque superfluide. Finalement, nous nous intéressons aux pertes inélastiques par recombinaison à trois corps qui peuvent limiter la stabilité de nos nuages. Ces pertes sont intimement liées aux corrélations à courte distance présentes dans le système et sont ainsi connectées aux propriétés universelles du gaz quantique. Cela se manifeste notamment par l’apparition de dépendances en densité ou en température inusuelles du taux de perte lorsque le système devient fortement corrélé. Nous démontrons cet effet dans deux exemples où les interactions sont résonantes, le cas du gaz de Bose unitaire et celui de notre mélange de superfluides Bose-Fermi. Plus généralement, nos travaux montrent que ces pertes inélastiques peuvent être utilisées pour sonder les corrélations quantiques dans un système en fortes interactions. / Understanding the effect of interactions in quantum many-body systems presents some of the most compelling challenges in modern physics. Ultracold atoms have emerged as a versatile platform to engineer and investigate these strongly correlated systems. In this thesis, we study the properties of a mixture of Bose and Fermi superfluids with tunable interactions produced using ultracold vapors of ⁷Li and ⁶Li. We first study the hydrodynamic properties of the mixture by creating a counterflow between the superfluids. The relative motion only exhibit dissipation above a critical velocity that we measure in the BEC-BCS crossover. A numerical simulation of counterflowing condensates allows for a better understanding of the underlying mechanisms at play in the dynamics. In particular, this numerical study provides additional evidence that the onset of friction in our experiment is due to the simultaneous generation of elementary excitations in both superfluids. Finally, we consider the inelastic losses that occur via three-body recombination in our cold gases. This few-body process is intimately related to short-distance correlations and is thereby connected to the universal properties of the many-body system. This manifests as the apparition of an unusual dependence on density or temperature in the loss rate when increasing the interactions. We demonstrate this effect in two examples where interactions are resonant: the case of a dilute unitary Bose gas and the one of impurities weakly coupled to a unitary Fermi gas. More generally, our work shows that inelastic losses can be used to probe quantum correlations in a many-body system.