Cette thèse est dédiée à l'étude théorique de phases exotiques dans un gaz dilué de bosons avec deux composantes (spins) en présence d'un couplage spin-orbite (SOC) entre ces deux états internes. En ajoutant ce dernier couplage à une description de type champs classiques de notre système, nous montrons que cette méthode permet de prédire le diagramme de phase à température finie de manière quantitative, efficace et fiable. Notre étude porte particulièrement sur un système de bosons bidimensionnels avec SOC dont nous dessinons le diagramme de phase en fonction de l'anisotropie du couplage spin-orbite ainsi que des interactions. Dans le cas d'un SOC anisotrope, une transition de phase de type Berenzinskii-Kosterlitz-Thouless sépare une phase dite normale d'une phase superfluide à plus basse température. L'ordre des spins du quasi-condensat dans la phase superfluide est alors guidé par les interactions de contact dépendantes du spin. Elles favorisent l'apparition soit d'un état onde plane avec moment non-nul (PW) soit d'une superposition linéaire de deux ondes planes appelée état de bande (SP). Pour des interactions indépendantes du spin des particules, nos simulations indiquent une fractionalisation du quasi-condensat. Les états PW et SP restent alors dégénérés. Dans le cas d'un SOC isotrope, nos calculs n'indiquent aucune transition de phase à la limite thermodynamique et à température finie. Un changement de comportement non critique subsiste pour un nombre important mais fini d'atomes. / In this thesis, we theoretically study the occurrence of exotic phases in a dilute two component (spin) Bose gas with artificial spin-orbit coupling (SOC) between the two internal states. Including spin-orbit coupling in classical field Monte Carlo calculations, we show that this method can be used for reliable, quantitative predictions of the finite temperature phase diagram. In particular, we have focused on SOCed bosons in two spatial dimensions and established the phase diagram for isotropic and anisotropic SOC and interparticle interactions. In the case of anisotropic SOC, the system undergoes a Berenzinskii-Kosterlitz-Thouless transition from a normal to a superfluid state at low temperature. The spin order of the quasicondensate in the low temperature superfluid phase is driven by the spin dependence of the interparticle interaction, favoring either the occurence of a single plane wave state at non-vanishing momentum (PW) or a linear sperposition of two plane waves with opposite momenta, called stripe phase (SP). For spin-independent interparticle interaction, our simulations indicate a fractionalized quasicondensate where PW and SP remain degenerate. For isotropic SOC, our calculations indicate that no true phase transition at finite temperature occurs in the thermodynamic limit, but a cross-over behavior remains visible for large, but finite number of atoms.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22824号 / 理博第4634号 / 新制||理||1666(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 高橋 義朗, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Ce manuscrit présente une étude expérimentale d'un gaz de 87Rb ultra-froid confiné à deux dimensions et en présence de désordre. Dans une première partie, nous mettons en place les outils expérimentaux développés pour manipuler les gaz confinés. Après un état de l'art sur l'apport de la communauté des atomes froids aux gaz de Bose 2D, nous détaillons notre expérience, en l'absence de désordre, qui par une comparaison fine avec des simulations Monte-Carlo quantique et grâce à une thermométrie en temps de vol très précise, a permis de quantifier l'apparition de la cohérence autour la transition de phase superfluide Berzinskii-Kosterlitz-Thouless (BKT). La seconde partie est dédiée à l'effet d'un potentiel désordonné généré optiquement et corrélé microscopiquement sur les propriétés de transport et de cohérence du gaz 2D en interaction. Cette partie suit la progression de l'expérience du régime de transport classique, dans lequel nous avons mesuré la dépendance du coefficient de diffusion classique en fonction de l'énergie de la particule, jusqu'au transport quantique, que nous avons atteint grâce à une ultime méthode de ralentissement. Sur la route entre ces deux régimes, nous observons un décalage vers les faibles entropies de l'établissement de la cohérence autour de la transition BKT provoqué par l'ajout adiabatique d'une quantité modérée de désordre ainsi que sa suppression pour un désordre de l'ordre de la température du nuage. Ce travail est une étape vers une étude expérimentale de la transition quantique vers le verre de Bose mettant en jeu à la fois désordre et interactions. / This manuscript shows an experimental study of a disordered ultra-cold 87Rb gas confined in two dimensions.In the first part, we set up the experimental tools used to manipulate the confined gases. After a state of the art in ultracold 2D Bose gases, we describe our disorder-free experiment from which, by a comparison with quantum Monte-Carlo calculations and thanks to an accurate time-of-flight thermometry, we are able to quantify the emergence of coherence around the Berezinskii-Kosterlitz-Thouless superfluid phase transition. The second part is devoted to the effect of a micrometer-range optically generated disordered potential on the transport and coherence properties of the interacting 2D gas. This part follows the experimental road from the regime of classical transport, in which we have measured the energy dependence of the classical diffusion coefficient, to the regime of quantum transport we have just reached thanks to a last cooling step. On the road between those two regimes, we observe a shift towards lower entropy of the emergence of coherence close to the BKT transition as a response of an adiabatic addition of a moderate amount of disorder. It is strongly suppressed for an amount of disorder of the order of the cloud temperature. This work is a first step to an experimental study of the quantum transition to the Bose-Glass phase involving disorder and interaction.

Investigamos a existência de uma fase de Kosterlitz-Thouless no estado fundamentai de um sistema de rotores quânticos em uma dimensão. Provamos que o modelo não exibe uma transição de primeira ordem, já que a estimativa de McBryan-Spencer é válida para os rotores. Obtemos a função de partição do modelo nas representações de Lie-Trotter, de sine-Gordon, e na representação das cargas. Nessa última, provamos um limite inferior para a função de correlação entre cargas externas. Ainda na representação das cargas, damos uma nova prova do decaimento polinomial do limite superior para a função de correlação de um gás de dipolos (caroço duro) na presença de cargas externas. / We investigate the existence of a Kosterlitz-Thoules phase in the ground state of a one-dimensional array of quantum rotators. We prove that this model does not exhibit a first-order phase transition since a McBryan-Spencer bound holds for it. We obtain the partition function of the rotators in the Lie-Trotter, sine-Gordon, and charge representations. In this latter representation, we give a new proof of the upper bound polynomial decay on the external charges correlation function of a dipole gas with hardcore.

Investigamos a existência de uma fase de Kosterlitz-Thouless no estado fundamentai de um sistema de rotores quânticos em uma dimensão. Provamos que o modelo não exibe uma transição de primeira ordem, já que a estimativa de McBryan-Spencer é válida para os rotores. Obtemos a função de partição do modelo nas representações de Lie-Trotter, de sine-Gordon, e na representação das cargas. Nessa última, provamos um limite inferior para a função de correlação entre cargas externas. Ainda na representação das cargas, damos uma nova prova do decaimento polinomial do limite superior para a função de correlação de um gás de dipolos (caroço duro) na presença de cargas externas. / We investigate the existence of a Kosterlitz-Thoules phase in the ground state of a one-dimensional array of quantum rotators. We prove that this model does not exhibit a first-order phase transition since a McBryan-Spencer bound holds for it. We obtain the partition function of the rotators in the Lie-Trotter, sine-Gordon, and charge representations. In this latter representation, we give a new proof of the upper bound polynomial decay on the external charges correlation function of a dipole gas with hardcore.

The vortex fluctuations have proved to be responsible for the onset of dissipation in thin type-II superconducting Aims. There is also growing evidence that dissipation in high- temperature superconductors exhibits the same kind of two-dimensional (2D) behavior. However, a proper analysis of these materials requires a thorough understanding of the two-dimensional fluctuations. This thesis may be considered to consist of two parts. The first is concerned with two models that have often been used as models for 2D superconductors, the 2D Coulomb gas and the 2D XY model. The second part contains analyses related to high-temperature sup er conductivity. Through analysis of some renormalization equations for the Kosterlitz-Thouless (KT) transition, it is shown that the region governed by the KT critical behavior is very small and only applies at very low values for the flux-flow resistance. It is concluded that this critical behavior not is observable in superconductors, and, furthermore, that the only available method to test for 2D fluctuations at the onset of resistance, is through comparison with the 2D resistance scaling function. The critical temperature for the 2D XY model is determined by means of a finite- size scaling relation for the helicity modulus. The linearly screened potential in the XY model is written in terms of a correlation function. The analogy to the 2D Coulomb gas is found to be exact with a temperature-dependent bare interaction and a new expression for vorticity. It is also demonstrated that the Coulomb gas scaling concept may be applied to XY-type models. An analysis of resistance data for YBCO/PBCO superlattices in terms of the 2D resistance scaling function gives evidence for 2D behavior in the cases with large separation of the superconducting layers. In the superlattices with stronger interlayer coupling, the crossover to three-dimensional behavior is seen as a deviation from the scaling function as Tc is approached from above. The anisotropic three-dimensional (3D) XY model is examined as a model for high- temperature superconductors. It is shown that the density of vortices above Tc are closely equal in the anisotropic 3D model and the 2D model. This is taken as evidence that the 3D to 2D crossover found in the superlattices also is present in the anisotropic 3D XY model. / digitalisering@umu.se

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23450号 / 理博第4744号 / 新制||理||1680(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 早川 尚男, 教授 佐々 真一, 教授 川上 則雄 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The magnetic susceptibility of 3-4ML ultrathin Fe/W(001) films was measured in situ under ultrahigh vacuum using the surface magneto-optic Kerr effect (SMOKE). Susceptibility measurements indicate that Fe/W(001) is a 2DXY system, and therefore undergoes a finite-size Kosterlitz-Thouless (KT) transition at the critical temperature T_KT. The films were grown using molecular beam epitaxy (MBE) and were characterized using Auger electron spectroscopy (AES) and low-energy electron diffraction (LEED). Three distinct categories of susceptibility signals were observed, and are referred to as Type I, II, and III. The primary difference between these signals is the size of the imaginary susceptibility, which likely corresponds to dissipative effects such as domain wall motion. The critical behaviour of the susceptibility in the paramagnetic region is described in the theory by χ(T) ~exp⁡〖〖(B/(T/T_KT-1) 〗^a)〗. A least-squares fit to this paramagnetic region from many independently grown films gives values of a=0.50±0.03 and B=3.48±0.16, which are in quantitative agreement with the KT theory. In comparison to 2nd order phase transitions, a power law fit to the paramagnetic region of the susceptibility yields an effective critical exponent of γ_eff≈3.7±0.7, which does not correspond to any known universality class. / Thesis / Master of Science (MSc) / The magnetic properties of atomically thin iron films, referred to as Fe/W(001), were investigated using the highly sensitive phenomenon known as the surface magneto-optic Kerr effect (SMOKE). Fe/W(001) films were grown using the well-developed technique known as molecular beam epitaxy (MBE), which involved a slow and controlled thermal evaporation of an iron source onto a tungsten substrate. Film thickness and uniformity were verified using Auger electron spectroscopy, and film structure was determined using low energy electron diffraction. Film growth and all subsequent measurements were performed in situ under ultrahigh vacuum (10-10 mbar) to limit surface contamination. Using SMOKE, the magnetic susceptibility of the Fe/W(001) films was measured as a function of temperature to look for evidence of a unique phase transition known as the Kosterlitz-Thouless (KT) transition. Fitting experimental susceptibility data to the theoretical model for the KT transition presented persuasive evidence that Fe/W(001) films undergo a KT transition.

Cette thèse se consacre à l'étude du modèle de dénaturation de l'ADN introduit par Poland et Scheraga dans les années soixante. Les modèles de dépiégeage en milieu aléatoire, avec lesquels la correspondance a été établie, sont également traités. Dans le cas où les interactions entre le système et l’environnement sont homogènes, le problème a été résolu : selon la valeur d'un paramètre géométrique, une transition de phase d'ordre un ou deux se produit. En revanche, lorsque les interactions sont prises aléatoires (on parle d'un système en présence de désordre), nous ne connaissons ni le point critique, ni l'ordre de la transition en régime defort désordre. Pour simplifier le problème, de nombreux auteurs font usage d'une représentation hiérarchique grâce à laquelle une renormalisation exacte de la fonction de partition peut être écrite. Mais à nouveau, la question du point critique et de l'ordre de la transition n'a pas été résolue. Nous avons introduit un nouveau système (Toymodel) plus simple que la version hiérarchique en changeant la forme de la renormalisation. Le problème, ainsi posé, permet de mettre en évidence une famille de distributions qui ne varient presque pas lors d'une renormalisation, avec lesquelles nous avons pu dériver des équations du type Berezinskii-Kosterlitz- Thouless. Aussi, en présence de désordre, la transition de phase n'admet pas de point fixe critique. Ces deux éléments, en accord avec nos résultats numériques, nous poussent à croire que nous sommes en présence d'une transition de phase d'ordre infini. La seconde partie de la thèse rapporte un travail sur le processus simple d'exclusion symétrique, qui est l'un des modèles les plus simples de physique statistique hors d'équilibre pour lequel un état stationnaire est connu. La fonction de grandes déviations a été calculée dans le passé par les approches microscopiques et macroscopiques et ici, nous en avons calculé la première correction de taille finie. Le résultat a ensuite été comparé aux corrections similaires pour des systèmes à l'équilibre. / This thesis is a study of a DNA denaturation model, introduced by Poland and Scheraga during the 1960s. The depinning models with random environment, with which the similarity has been made, are also concerned. If the interactions between the system and the environment are homogeneous, the problem has been solved: depending on the value of a geometrical parameter, a first or a second order phase transition happens. On the other hand, when the interactions are random, we know neither the critical point nor the phase transition order in the case of strong disorder. In order to simplify the problem, some authors have used a hierarchical representation through which an exact renormalization can be written. Despite this simplification, the critical point and the transition order have not been found. By changing the renormalization relation, we introduced a Toy-model which is simpler than the hierarchical version. The new problem leaded us to a family of distributions, which stay almost the same under renormalization, and allow us to derive the Berezinskii-Kosterlitz- Thouless equations. Also, with strong disorder, the phase transition does not have a critical fixed point. These two elements, according to our numerical results, predict that the order transition is infinite. The second part of this thesis reports on a work about the simple symmetric exclusion process, which is one of the simplest out of equilibrium models for which a stationary state is known. The large deviation function has been calculated in the past through microscopic and macroscopic approaches. Here, we calculated the leading finite-size correction. Then the result has been compared to similar corrections for equilibrium systems.

Embora em um sistema bidimensional com simetria contínua não haja ordem de longo alcance para temperaturas finitas, o modelo XY 2D exibe uma transição de fase de ordem infinita não usual, associada com a dissociação de defeitos topológicos chamados de vórtices-inteiros, e que pertence à classe de universalidade de Kosterlitz-Thouless (KT). O modelo XY tridimensional exibe ordem de longo-alcance para baixas temperaturas e, à medida que a temperatura aumenta, passa para o estado desordenado através de uma transição ferromagnética usual. Generalizações do modelo XY, incluindo competição entre um termo ferromagnético e um nemático, foram introduzidas e estudadas por diversos autores. Essas interações nemáticas criam novas transições de fases e novos defeitos topológicos, como vórtices semi-inteiros. Neste trabalho, para casos particulares desses modelos generalizados, exploramos as classes de universalidade e os diagramas de fases em duas e três dimensões através de simulações de Monte Carlo usando algoritmos de cluster em GPUs, escalonamento de tamanhos finitos e análise da helicidade. Em particular, encontramos que a competição entre os termos ferromagnético e nemático dá origem a novas linhas de transição que podem pertencer a uma ampla gama de classes, desde a Kosterlitz-Thouless, 3dXY, Ising, Potts com 3 estados e até mesmo uma transição descontínua. / Although in a two-dimensional system with continuous symmetry there is no long-range order at finite temperature, the 2D XY model exhibits an unusual infinite order phase transition, associated with the unbinding of topological defects called integer-vortices, which belongs to the Kosterlitz-Thouless (KT) universality class. The three dimensional XY model exhibits a ferromagnetic long-range order at low temperatures and goes to the disordered state through a usual ferromagnetic transition. Generalizations of the XY model, including competition between a ferromagnetic and a nematic-like term, have been introduced and studied by many autors. These nematic-like interactions create new phase transitions and new topologial defects, like half-integer-vortices. In this work, for particular cases of these generalized models, we explore the universality classes of the transitions and the phase diagrams in two and three dimensions through Monte Carlo simulations using clusters algorithms on GPUs, finite size scaling and helicity analysis. In particular, we find that the competition between the ferromagnetic and nematic terms gives origin to new transition lines that can belong to a wide spectrum of classes, ranging from Kosterlitz-Thouless, 3dXY, Ising, 3 states Potts and even a discontinuous transition.