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.

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 `a classe de universalidade de Kosterlitz-Thouless (KT). Generalizações do modelo XY, incluindo competição entre um termo ferromagnético e um nemático, foram introduzidas e largamente estudadas por diversos autores. Essas interações nemáticas criam novas transições de fases e novos defeitos topológicos, como vórtices semi-inteiros. Neste trabalho, para um caso particular desses modelos generalizados, exploramos as classes de universalidades e o diagrama de fases através de simulações de Monte Carlo, escalonamento de tamanhos finitos e análise da helicidade. Em particular, encontramos que a competição entre os termos ferromagnético e nemático d´a origem a uma nova linha de transição, neste caso na classe de universalidade do modelo Potts com 3 estados. / 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, and which belongs to the Kosterlitz-Thouless (KT) universality class. Generalizations of the XY model, including competition between a ferromagnetic and a nematiclike term, have been introduced and widely studied by many autors. These nematic-like interactions create new phase transitions and new topologial defects, like half-integer-vortices. In this work, for a particular case of these generalized models, we explore the universality classes of the transitions and the phase diagram through Monte Carlo simulations, finite size scaling and helicity analysis. In particular, we find that the competition between the ferromagnetic and nematic terms gives origin to a new transition line belonging, in this case, to the 3 states Potts universality class.

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 `a classe de universalidade de Kosterlitz-Thouless (KT). Generalizações do modelo XY, incluindo competição entre um termo ferromagnético e um nemático, foram introduzidas e largamente estudadas por diversos autores. Essas interações nemáticas criam novas transições de fases e novos defeitos topológicos, como vórtices semi-inteiros. Neste trabalho, para um caso particular desses modelos generalizados, exploramos as classes de universalidades e o diagrama de fases através de simulações de Monte Carlo, escalonamento de tamanhos finitos e análise da helicidade. Em particular, encontramos que a competição entre os termos ferromagnético e nemático d´a origem a uma nova linha de transição, neste caso na classe de universalidade do modelo Potts com 3 estados. / 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, and which belongs to the Kosterlitz-Thouless (KT) universality class. Generalizations of the XY model, including competition between a ferromagnetic and a nematiclike term, have been introduced and widely studied by many autors. These nematic-like interactions create new phase transitions and new topologial defects, like half-integer-vortices. In this work, for a particular case of these generalized models, we explore the universality classes of the transitions and the phase diagram through Monte Carlo simulations, finite size scaling and helicity analysis. In particular, we find that the competition between the ferromagnetic and nematic terms gives origin to a new transition line belonging, in this case, to the 3 states Potts universality class.

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 `a classe de universalidade de Kosterlitz-Thouless (KT). Generalizações do modelo XY, incluindo competição entre um termo ferromagnético e um nemático, foram introduzidas e largamente estudadas por diversos autores. Essas interações nemáticas criam novas transições de fases e novos defeitos topológicos, como vórtices semi-inteiros. Neste trabalho, para um caso particular desses modelos generalizados, exploramos as classes de universalidades e o diagrama de fases através de simulações de Monte Carlo, escalonamento de tamanhos finitos e análise da helicidade. Em particular, encontramos que a competição entre os termos ferromagnético e nemático d´a origem a uma nova linha de transição, neste caso na classe de universalidade do modelo Potts com 3 estados. / 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, and which belongs to the Kosterlitz-Thouless (KT) universality class. Generalizations of the XY model, including competition between a ferromagnetic and a nematiclike term, have been introduced and widely studied by many autors. These nematic-like interactions create new phase transitions and new topologial defects, like half-integer-vortices. In this work, for a particular case of these generalized models, we explore the universality classes of the transitions and the phase diagram through Monte Carlo simulations, finite size scaling and helicity analysis. In particular, we find that the competition between the ferromagnetic and nematic terms gives origin to a new transition line belonging, in this case, to the 3 states Potts universality class.

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We studied the structural instabilities of one-dimensional (1D) and quasi-one-dimensional (Q1D) electron-phonon systems at low temperature through two models, SuSchrieffer-Heeger (SSH) and molecular crystal (CM) with and without spin. The phase diagrams are obtained using a Kadanoff-Wilson renormalization group approach (GR). For the 1D half-filled system the study of the frequency dependence of the electronic gap allowed us to connect continuously the two limits, adiabatic and non-adiabatic. The Peierls and Cooper channels interference and the quantum fluctuations reduce the gap. A regime change occurs when the frequency becomes of the order of mean field gap, marking a quantum-classical crossover that is the Kosterlitz-Thouless type. At this level, the effective coupling behaves in power law function on frequency. For the case with spin, a gapped Peierls state is maintained in the non-adiabatic limit, while for the case without spin, the system transits to ungapped disordered state, namely the Luttinger liquid stat (LL). For the SSH model without spin, the GR confirms the existence of a threshold phonon coupling beyond which the gap is restored. The study of the rigidities of the two models without spin allowed us to trace the main features of the LL state predicted by the bosonization method. The study of the Holstein-Hubbard model has allowed us not only to reproduce the phase diagrams already obtained by the Monte Carlo method, but to highlight two additional phases, namely, free fermions phase and the bond charge-density-wave phase. We have extended this study to the quarter-filled Q1D Peierls systems at finite temperature. Within the SSH model, an unconventional superconducting phase with spin singlet symmetry SS-s emerges at low temperature when the deviation to the perfect nesting of the Fermi surface is strong enough. Peierls-SS transition is characterized by the presence of a quantum critical point at low frequency and by a power law behavior of the transition temperature as a function of frequency with an exponent identical to one of 1D system. This exponent which universality has been verified contrasts with the BCS result. Coulomb interactions have been introduced through the study of the extended SSH-Hubbard model. The extension of this work to half-filled SSH and CM cases was also performed.

<p>Dynamic properties of type-II superconductors have been experimentally studied in zero and low magnetic fields using SQUID magnetometry and <i>I–V</i> measurements.</p><p>In zero magnetic field close to the critical temperature, the physical properties of type-II superconductors are dominated by spontaneously created vortices. In three dimensions (3D) such vortices take the form of vortex loops and in two dimensions (2D) as vortex-antivortex pairs.</p><p>The 2D vortex dynamics has been probed using mutual inductance and flux noise measurements on YBa₂Cu₃O₇ (YBCO) and MgB₂ thin films in zero and low magnetic fields. In such measurements, information about vortex correlations is obtained through a temperature dependent characteristic frequency, below (above) which the vortex movements are uncorrelated (correlated). The results obtained in zero magnetic field indicate that sample heterogeneities influence the vortex physics and hinder the divergence of the vortex-antivortex correlation length.</p><p>In low magnetic fields the vortex dynamics is strongly dependent on the applied magnetic field and a power law dependence of the characteristic frequency with respect to the magnetic field is observed. The results indicate that there is a co-existence of thermally and field generated vortices.</p><p>The <i>I–V</i> characteristics of untwinned YBCO single crystals show that only a small broadening of the transition region influences the length scale over which the vortex movements are correlated. The dynamic and static critical exponents therefore exhibit values being larger in magnitude as compared to values predicted by relevant theoretical models. The results also suggest that the copper oxide planes in YBCO decouple slightly below the mean field critical temperature and hence, the system has a crossover from 3D to 2D behaviour as the temperature is increased. </p><p>From temperature dependent DC-magnetisation measurements performed on untwinned YBCO single crystals in weak applied fields, detailed information about the critical current density and the irreversibility line is obtained.</p>

Dynamic properties of type-II superconductors have been experimentally studied in zero and low magnetic fields using SQUID magnetometry and I–V measurements. In zero magnetic field close to the critical temperature, the physical properties of type-II superconductors are dominated by spontaneously created vortices. In three dimensions (3D) such vortices take the form of vortex loops and in two dimensions (2D) as vortex-antivortex pairs. The 2D vortex dynamics has been probed using mutual inductance and flux noise measurements on YBa2Cu3O7 (YBCO) and MgB2 thin films in zero and low magnetic fields. In such measurements, information about vortex correlations is obtained through a temperature dependent characteristic frequency, below (above) which the vortex movements are uncorrelated (correlated). The results obtained in zero magnetic field indicate that sample heterogeneities influence the vortex physics and hinder the divergence of the vortex-antivortex correlation length. In low magnetic fields the vortex dynamics is strongly dependent on the applied magnetic field and a power law dependence of the characteristic frequency with respect to the magnetic field is observed. The results indicate that there is a co-existence of thermally and field generated vortices. The I–V characteristics of untwinned YBCO single crystals show that only a small broadening of the transition region influences the length scale over which the vortex movements are correlated. The dynamic and static critical exponents therefore exhibit values being larger in magnitude as compared to values predicted by relevant theoretical models. The results also suggest that the copper oxide planes in YBCO decouple slightly below the mean field critical temperature and hence, the system has a crossover from 3D to 2D behaviour as the temperature is increased. From temperature dependent DC-magnetisation measurements performed on untwinned YBCO single crystals in weak applied fields, detailed information about the critical current density and the irreversibility line is obtained.

Dans cette thèse, nous étudions l'influence du désordre sur les propriétés d'équilibre et de transport de gaz de Bose bidimensionnels dans le régime de dégénérescence quantique. Les échantillons étudiés sont des nuages de Rubidium 87 ultra-froids, refroidis et piégés par des méthodes optiques, confinés à deux dimensions entre deux nappes de lumières. Le potentiel désordonné est un potentiel optique de speckle. La première expérience que nous décrivons est une étude des propriétés de cohérence du gaz en interaction au voisinage de la transition superfluide, appelée transition Berezinskii-Kosterlitz-Thouless. Nous étudions quantitativement le comportement de la distribution d'impulsion du gaz par mesure de temps de vol. Nos résultats sont en accord avec une simulation Monte-Carlo Quantique. En présence de désordre, nous observons que l'augmentation de la cohérence est décalée vers les plus basses entropies. Ce résultat constitue une première étape dans l'étude détaillée des effets combinés des interactions et du désordre pour des gaz de Bose 2D. Notre deuxième expérience est une étude des propriétés de transport d'un gaz 2D en expansion dans le désordre. Nous étudions d'abord le régime de diffusion classique. Nous observons la décroissance caractéristique de la densité centrale en fonction du temps et nous mesurons les coefficients de diffusion dépendant de l'énergie. Les résultats expérimentaux sont en accord avec une simulation numérique classique. Nous décrivons les améliorations expérimentales mises en place pour atteindre le régime de diffusion quantique et la localisation d'Anderson, ainsi qu'une simulation numérique avec laquelle nous explorons des signatures expérimentales de la localisation faible et forte.

It is well known from Mermin-Wagner theorem that a two dimensional(2D) system with continuous symmetry can have no long-range order at finite temperature. However such systems can undergo a transition from a low temperature phase with quasi-long range order to a disordered phase at high temperatures. This is known as Berezinskii Kosterlitz Thouless (BKT) transition. The BKT transition is characterized by the presence of bound vortex pairs at low temperature which dissociate into free vortices above the critical temperature and has been observed in thin superconducting films, 2D superfluids, 2D liquid crystals etc. In this thesis work, we have used resistance/current fluctuations (low frequency/shotnoise) as a probe to investigate the BKT transition in different 2D systems. This work can be divided into three parts: In the first part, we probe the ground state of interacting electrons in 2D in the presence of disorder. We show that at low enough temperatures (~ 270mK),the conductivity tends to zero at a nonzero carrier density with a BKT-like transition. Our experiments with many two dimensional electron systems in GaAs/AlGaAs heterostructures suggest that the charge transport at low carrier densities is due to the melting of an underlying ordered ground state through proliferation of topological defects. Independent measurement of low-frequency conductivity noise supports this scenario. In the second part, we probe the presence of long-range correlations in phase fluctuations by analyzing the higher-order spectrum of resistance fluctuations in ultrathin NbN superconducting films. The non-Gaussian component of resistance fluctuations is found to be sensitive to film thickness close to the transition, which allows us to distinguish between mean field and BKT type superconducting transitions. The extent of non-Gaussianity was found to be bounded by the BKT and mean field transition temperatures and depends strongly on the roughness and structural inhomogeneity of the superconducting films. In the final part of the thesis, we explore the transport mechanism in disordered 2D superconductors using shot noise. The resistivity shows an activated transport in the patterned ultrathin films of NbN at low temperatures signifying the presence of large scale inhomogeneities in the sample. The measurement of current fluctuations yield a giant excess noise at low temperatures which eventually decreases below the measurement background at a temperature corresponding to the normal state of the original sample(before patterning). We attribute the enhancement in the shot noise to a possible occurrence of multiple Andreev reflections occurring in a network of SNS(superconductor-normal-superconductor) junctions formed due to the interplay of disorder and superconducting fluctuations.