By exploiting the versatility of ultracold atoms experiments, a variety of many-body phe- nomena can be studied. Ferromagnetism in a trapped ultracold gas of repulsively interacting fermions is considered within a local-density approximation and beyond, where energetic sig- natures indicate its onset. Transport of a Bose-Einstein condensate is explored experimentally in a tunable double-well potential, and a crossover from hydrodynamic to Josephson transport is observed as the barrier between condensates is raised. To add a degree of freedom for the manipulation of ultracold gases, two schemes for species-specific optical lattices are developed theoretically.

Open quantum dots (OQDs) are now commonly used as an experimental tool for the investigation of a particular regime of quantum transport where the electron dynamics is both ballistic and coherent. In particular, the Universal Conductance Fluctuations (UCFs), observed in ballistic quantum dots, arise from the complex quantum interferences occurring between electron trajectories that bounce multiple times against the dot walls before escaping through its leads. Central to quantum interference phenomena is the presence of a magnetic field B that breaks the time-reversal symmetry and changes the phase experienced by electrons in the dot. OQDs are typically patterned on top of two-dimensional electron gases (2DEGs). Interestingly, when confined to wide GaAs quantum wells (QWs), 2DEGs are known to exhibit a rich physics arising from the interplay of a strong in-plane magnetic field, multiple subband occupation, and the finite thickness of the electronic wavefunction. In this thesis, we use 2DEGs, confined to wide (WQW) and narrow (NQW) quantum wells with one and two occupied subbands at B = 0 T, respectively, to study the parallel field-induced transport in open quantum dots as a function of the well width and the tilt angle of B with respect to the electron gas. Both the WQW and NQW dots feature a rich spectrum of UCFs at intermediate tilt angles and, quite unexpectedly, under a strictly parallel B. Combined with the observation, in the case of the WQW dot, of a reduction in UCFs amplitude at large parallel B, our data indicates that the finite thickness of the electron layer and the orbital effect are responsible for the in-plane field-induced UCFs. In the second part of this work, we observe a saturation of the UCFs spectral distribution, expressed in terms of an effective tilt angle, as B approaches a strictly parallel configuration, along with the persistence of a limited number of frequency components in the case of the narrow quantum well dot. It is found that the saturation angle strongly depends on the width of the 2DEG confining well. Using the results of self-consistent Poisson-Schrödinger simulations, the magnetoconductance is rescaled as a function of the Fermi level E_F in the 2DEG. A power spectrum analysis of the parallel B UCFs in energy space and its good agreement with theoretical predictions suggest that such a B to E_F mapping is indeed relevant for the interpretation of parallel B-induced UCFs

This thesis describes experiments on quantum dots made by locally gating one-dimensional quantum wires. The first experiment studies a double quantum dot device formed in a Ge/Si core/shell nanowire. In addition to measuring transport through the double dot, we detect changes in the charge occupancy of the double dot by capacitively coupling it to a third quantum dot on a separate nanowire using a floating gate. We demonstrate tunable tunnel coupling of the double dot and quantify the strength of the tunneling using the charge sensor. The second set of experiments concerns carbon nanotube double quantum dots. In the first nanotube experiment, spin-dependent transport through the double dot is compared in two sets of devices. The first set is made with carbon containing the natural abundance of \(^{12}C\) (99%) and \(^{13}C\) (1%), the second set with the 99% \(^{13}C\) and 1% \(^{12}C\). In the devices with predominantly \(^{13}C\), we find evidence in spin-dependent transport of the interaction between the electron spins and the \(^{13}C\) nuclear spins that was much stronger than expected and not present in the \(^{12}C\) devices. In the second nanotube experiment, pulsed gate experiments are used to measure the timescales of spin relaxation and dephasing in a two-electron double quantum dot. The relaxation time is longest at zero magnetic field and goes through a minimum at higher field, consistent with the spin-orbit-modified electronic spectrum of carbon nanotubes. We measure a short dephasing time consistent with the anomalously strong electron-nuclear interaction inferred from the first nanotube experiment. / Physics

To study transport properties in single InAs nanowires (NW) with etched constrictions, a bunch of back-gated single InAs NW devices were made. The standard device contained a NW section with an etched constriction, placed between two pre-patterned side-gates. For comparison, devices either without etched constriction or without side-gates were also fabricated. Transport measurement results of three devices were presented and discussed. The device without side-gates exhibited Coulomb blockade due to electron tunneling through double quantum dots (QDs). The device without the etched constriction displayed conductance quantization. The standard device showed both Coulomb blockade (due to electron tunneling through either multiple QDs or single QD) and Fabry-Perot conductance oscillation at different gate bias regime. A 3-D electrostatic and 2-D eigenvalue coupled simulation was conducted to explain the observed conductance quantization. This model suggests that the nonuniform potential distribution in a thick NW dramatically modifies the confinement energies in the NW.

To study transport properties in single InAs nanowires (NW) with etched constrictions, a bunch of back-gated single InAs NW devices were made. The standard device contained a NW section with an etched constriction, placed between two pre-patterned side-gates. For comparison, devices either without etched constriction or without side-gates were also fabricated. Transport measurement results of three devices were presented and discussed. The device without side-gates exhibited Coulomb blockade due to electron tunneling through double quantum dots (QDs). The device without the etched constriction displayed conductance quantization. The standard device showed both Coulomb blockade (due to electron tunneling through either multiple QDs or single QD) and Fabry-Perot conductance oscillation at different gate bias regime. A 3-D electrostatic and 2-D eigenvalue coupled simulation was conducted to explain the observed conductance quantization. This model suggests that the nonuniform potential distribution in a thick NW dramatically modifies the confinement energies in the NW.

In this thesis we study the quantum transport of matter waves with ultracold atoms. Such ultracold atom systems provide a very good control and a high flexibility of the parameters of the systems like the interactions, its dimensionality and the external potentials. This makes them a great tool for the investigation of several fundamental concepts of condensed matter physics. We focus on the quantum transport in disordered media. It differs to classical transport by the fundamental role played by inference phenomena, which can eventually lead to the suppression of transport; known as Anderson Localization. Observing the expansion of a Bose-Einstein condensate in a strong light disorder, we show evidence for Localization of ultracold atoms in three dimensions. In the last part of this manuscript we discuss the observation of Coherent Backscattering of ultracold atoms, which is a direct signal of the role of quantum coherence in quantum transport in disordered media. We observe the time evolution of the momentum distribution of a cloud of ultra-cold atoms, launched with a narrow velocity distribution in a disordered potential. A peak emerges in the backwards direction, corresponding to the CBS signal.

La physique quantique appliquée à la théorie de l’information se révèle être pleine de promesses pour notre société. Conscients de ce potentiel, des groupes de scientifiques du monde entier ont pour objectif commun de créer un ordinateur utilisant les principes de la mécanique quantique. La premières étape de cet ambitieux cheminement menant à l’ordinateur quantique est la réalisation du bloc de base de l’encodage quantique de l’information, le qubit. Dans le large choix de qubits existants, ceux utilisant un spin sont très attrayants puisqu’ilspeuvent être lus et manipulés de façon cohérente uniquement en utilisant des champs électriques. Enfin, plus un système est isolé, plus son comportement demeure quantique, ce qui fait du spin nucléaire un sérieux candidat dans la course aux long temps de cohérence et donc aux grands nombres d’opérations quantiques.Dans ce contexte, j’ai étudié un transistor de spin moléculaire. Ce dispositif, placé dans un réfrigérateur à dilution assurant des mesures à 40mK, est composé d’une molécule magnétique TbPc2 couplée à des électrodes (source, drain et grille) et à une antenne hyperfréquence. Il nous a permis de lire à l’aide d’une mesure de conductance, à la fois l’état de spin électronique et nucléaire de l’ion Terbium. Ma thèse se focalise sur l’étude de la dynamique de ces spins et plus particulièrement celle du spin nucléaire 3/2 sous l’influence d’un champ micro-onde. La première étape consiste à mesurer la différence d’énergie entreces quatre états de spin nucléaire pour ensuite parvenir à manipuler de façon cohérente ses trois transitions en utilisant uniquement un champ électrique. Pour caractériser davantage les processus de décohérence à l’origine de la perte de phase des états quantique, j’ai réalisé des mesures Ramsey et Hahn-echo révélant des temps de cohérence de l’ordre de 0.3ms. Ces résultats préliminaires montrent que nous sommes en présence de 3 qubits ayant une figure de mérite supérieure à deux milles, répondant ainsi aux attentes suscitées par l’utilisation d’un spin nucléaire comme bloc de base de l’information quantique.Plus que démontrer expérimentalement la dynamique de trois qubits, ces mesures nous prouvent qu’un spin nucléaire intégré dans une géométrie de type transistor à aimant moléculaire est un système à quatre états contrôlé de façon cohérente. Des propositions théoriques démontrent qu’un traitement quantique de l’information, telle que l’application de portes quantiques et la réalisation d’algorithmes, peuvent être implémentées sur un tel système. Je me suis concentré sur un algorithme de recherche. Il s’agit de la succession d’une porteHadamard, qui crée une superposition cohérente de tous les états de spin nucléaire, et une évolution unitaire qui amplifie l’amplitude d’un état désiré. Il permet une accélération quadratique de la recherche d’un élément dans une liste non ordonnée comparée à un algorithme classique. Pendant ma thèse, j’ai apporté la preuve expérimentale de la faisabilité de cet algorithme de Grover sur un système à plusieurs niveaux. La première étape a été de créer une superposition cohérente de 2, 3 et 4 états par l’application d’un pulsation radio-fréquence. Enfin, j’ai mesuré une oscillation cohérente entre une superposition de trois états et un état sélectionné qui est la signature de l’implémentation de l’algorithme de recherche.En résumé, cette thèse expose la première implémentation d’un algorithme quantique de recherche sur un qudit de type aimant moléculaire. Ces résultats, combinés à la grande polyvalence des molécules magnétiques, sont autant de promesses pour la suite de ce défi scientifique qu’est la construction d’un ordinateur quantique moléculaire. / The application of quantum physics to the information theory turns out to be full of promises for our information society. Aware of this potential, groups of scientists all around the world have this common goal to create the quantum version of the computer. The first step of this ambitious project is the realization of the basic block that encodes the quantum information, the qubit. Among all existing qubits, spin based devices are very attractive since they reveal electrical read-out and coherent manipulation. Beyond this, the more isolated a system is, the longer its quantum behaviour remains, making of the nuclear spin a serious candidate for exhibiting long coherence time and consequently high numbers of quantum operation.In this context I worked on a molecular spin transistor consisting of a TbPc2 singlemolecule magnet coupled to electrodes (source, drain and gate) and a microwave antenna. This setup enabled us to read-out electrically both the electronic and the nuclear spin states and to coherently manipulate the nuclear spin of the Terbium ion. I focus during my Ph.D. on the study of the spins dynamic and mainly the 3/2 nuclear spin under the influence of a microwave pulse. The first step was to measure the energy difference between these statesleading in a second time to the coherent manipulation of the three nuclear spin transitions using only a microwave electric field. To further characterize the decoherence processes that break the phase of the nuclear spin states, I performed Ramsey and Hahn-echo measurements. These preliminary results show that we were in presence of three qubits with figure of merit higher than two thousands, thus meeting the expectations aroused by the use of a nuclearspin as the basic block of quantum information.More than demonstrating the qubit dynamic, I demonstrated that a nuclear spin embedded in the molecular magnet transistor is a four quantum states system that can be fully controlled, a qudit. Theoretical proposal demonstrated that quantum information processing such as quantum gates and algorithms could be implemented using a 3/2 spin. I focused on a research algorithm which is a succession of an Hadamard gate, that creates a coherent superposition of all the nuclear spin sates, and an unitary evolution, that amplified the amplitude of a desired state. It allows a quadratic speed-up to find an element in an unordered list compared to classical algorithm. During my Ph.D., I demonstrated the experimental proof of feasibility of this Grover like algorithm applied to a multi-levels system. The first step was to experimentally create coherent superposition of 2, 3 and 4 states. Then I measured coherent oscillations inbetween a 3 state superposition and a selected state which is the signature of the research algorithm implementation.In summary, this Ph.D. exposed the first quantum search algorithm on a single-molecule magnet based qudit. These results combined to the great versatility of molecular magnet holds a lot of promises for the next challenge: building up a scalable molecular based quantum computer.

La mécanique quantique affiche déjà toute son étrangeté en considérant l’équation de Schrödingerdans un puits de potentiel à une dimension. L’effet tunnel qui en résulte, en est un exemple frappant.La possibilité de récréer cette situation dans un système matériel est un enjeu excitant et un grandpas vers le contrôle des effets quantiques.Le confinement spatial des spins électroniques a été suggéré comme une approche possible pour laréalisation d’un ordinateur quantique. Chaque spin formant un système à deux niveaux pouvant coderune bit élémentaire pour l’information quantique (spin qubit). Cette proposition par Loss etDiVincenzo a contribué à l’ouverture d’un domaine de recherche important dénommé spintroniquequantique. L’intérêt des qubits de spin s’appuie sur le fait que les états de spin ont des temps decohérence beaucoup plus long que les qubits de charge (états orbitaux).Un potentiel de confinement de spin peut être créé de différentes façons, comme par exemple enutilisant l’alignement des bandes d’énergies de semi-conducteurs de différentes natures. Cependant,les dimensions spatiales du système obtenu doivent toujours être inférieures à la longueur decohérence de phase des quasi-particules considérées afin de préserver leur comportement quantique.Jusqu’à présent, la plupart des progrès ont été réalisés en utilisant des hétérostructures semiconductricesà base d’arséniure de Gallium(GaAs). Dans de tels systèmes, lemouvement des porteursde charges est limité à un plan bidimensionnel et le confinement latéral peut être obtenu par destechniques de lithographie. De cette façon, des systèmes quasi-zéro-dimensionnels dont les étatsélectroniques sont parfaitement quantifiés (boîtes quantiques), sont réalisés.Diverses techniques utilisant des signaux hautes fréquences ont permis de manipuler et lire l’état despin de tels boîtes quantiques de GaAs et, il y a quelques années, les premiers qubits de spin ont étédémontrés. Cependant, ces systèmes ont montré des temps de cohérence relativement courts enraison de l’interaction hyperfine avec les spins nucléaires. En dépit de progrès significatifs sur lecontrôle de la polarisation, ce problème n’est toujours pas résolu.Au cours de ces dernières années, un effort croissant s’est donc concentré sur des systèmes à base dematériaux alternatifs pour lesquels l’interaction hyperfine est naturellement absente ou rendue trèsfaible par des techniques de purification. Même si le Silicium, qui est le matériau de base enmicroélectronique, remplit cette condition, il souffre d’une faible mobilité par rapport aux semiconducteursIII-V, ce qui pose problème pour la spintronique quantique. Les structures à base Silicium-Germanium (SiGe) offrent un moyen de contourner ce problème tout en gardant un matériaucompatible avec les procédés de fabrication standards.Durant mon travail de thèse, je me suis concentrée principalement sur l’étude des propriétésélectroniques d’îlots auto-assemblés (nanocristaux) de SiGe. Le manuscrit de thèse qui relate lesprincipaux aspects de cette étude est organisé en six chapitres. Dans le premier chapitre, je décris lesprincipaux concepts de la croissance cristalline d’îlots auto-assemblés de SiGe ainsi que les propriétésdu potentiel de confinement qu’ils définissent. Le chapitre 2 est consacré aux principes du transportélectronique dans de telles structures. Le chapitre 3 traite de la modulation électrique du facteur deLandé (g) des trous confinés dans les îlots en vu de la manipulation rapide des états de spin. Dans lechapitre 4, je présente les résultats théoriques et expérimentaux relatifs à la sélectivité en spin dansles nanocristaux de SiGe. Le chapitre 5 décrit les résultats sur la réalisation d’une pompe électroniqueobtenue à partir de nanofils d’InAs/InP. Enfin, le chapitre 6montre les progrès technologiques que j’aiobtenus vers la réalisation et l´étude de dispositifs couplés à base de nanocristaux de SiGe. / Quantum mechanics displays all its exciting strangeness already by considering the Schrödingerequation in a one-dimensional square well potential; tunnelling events put this statement in evidence.To recreate this situation in a given material system is an inspiring playground and a big step towardstaking control of quantum mechanisms. For instance, it is now possible to confine electrons in solidstatedevices enabling amore efficient solar-cell technology. Confining individual electron spins has infact been suggested as a possible approach to the realization of a quantum computer. Each electronspin forms a natural two-level systems encoding an elementary bit of quantum information (a socalledspin qubit). This proposal, by Loss and DiVincenzo, has contributed to the opening of an activeresearch field referred to as quantum spintronics. Spin qubits rely on the fact that spin states canpreserve their coherence on much longer time scales than charge (i.e. orbital) states.A confinement potential can be created artificially in many different ways; producing constantmagnetic fields and spatially inhomogeneous electric fields, applying oscillating electric fields, usingconductive oxide layers, etc. To take advantage of the band-alignment of different semiconductors isamong these. The relevant dimensions of the considered system should still be smaller than the phasecoherence length of the confined particles in order that their quantum behaviour is preserved.So far, most of the progress has been achieved using GaAs-based semiconductor heterostructures. Insuch layered systems themotion of carriers is confined to a plane and further confinement is achievedbymeans of lithographic techniques, which allow lateral confinement to be achieved on a sub-100 nmlength scale. In this way, quasi-zero-dimensional systems whose electronic states are completelyquantized, i.e. quantum dots (QDs), can be devised.Various time-resolved techniques involving high-frequency electrical signals have been developed tomanipulate and read-out the spin state of confined electrons in GaAs QDs, and several years ago thefirst spin qubits were reported. In GaAs-based QDs, however, the quantum coherence of electronspins is lost on relatively short time scales due to the hyperfine interactionwith the nuclear spins (bothGa and As have non-zero nuclear spin moments). In spite of significant advances on controlling thenuclear polarization [3, 4], this problem remains unsolved.In the past few years an increasing effort is concentrating on alternative material systems in whichhyperfine interaction is naturally absent or at least very weak and, in principle, controllable by isotopepurification. While Si fulfils this requirement and it is the dominant material in modernmicroelectronics, it suffers from low mobility compared to III-V semiconductors, which obstructs itsapplication for quantum spintronics. SiGe structures offer a way to circumvent this problem that isstill compatible with standard silicon processes.I have focused mainly on the study of the electronic properties of SiGe self-assembled islands, alsocalled SiGe nanocrystals. This work, which condensates the main points of this study, is organized insix chapters. In the first chapter, I describe the basics of the growth of SiGe self-assembled islands andthe properties of the quasi-zero-dimensional confinement potential that they define. Chapter 2 isdevoted to the basics of electronic transport in these structures. Chapter 3 deals with the electricmodulation of the hole g-factor in SiGe islands, which would enable a fast manipulation of the spinstates. In Chapter 4 I present theoretical and experimental findings related to spin selectivity in SiGeQDs and Chapter 5 is dedicated to the realization of an electron pump in InAs nanowires based on thiseffect. Finally, Chapter 6 exhibits our progress towards the study of coupled SiGe QD devices.

The purpose of this master thesis is to investigate theoretically the influence of a nanomagnet on the Josephson effect displayed by phase biased point contacts consisting of topological superconductors. The device is modeled using the nonequilibrium Keldysh Green’s function technique. First, the Gor’kov Green’s functions are calculated. From these Green’s functions, the quasi-classical ones, relevant for energies around the Fermi energy, are obtained. Transport properties such as charge currents are calculated and analyzed in terms of the junction’s density of states displaying Andreev and Majorana states. The combination of the nanomagnet coupling and the spin-momentum locking of the topological superconductors generates a magneto-electric effect causing the supercurrent to depend strongly on the nanomagnet’s direction.

Les évolutions rapides du marché des composants électroniques font apparaître de nombreux challenges pour la conception et la fabrication de ces derniers. Lorsque ces éléments deviennent plus petits, leur comportement se complexifie à mesure que de nouveaux phénomènes, liés aux effets d'interférence, entrent en jeu. Comprendre ces derniers nécessite le développement d'outils théoriques avancés. Dans ce contexte cette thèse est consacrée au transport électronique quantique dans des systèmes multi-terminaux. Dans la première partie on développe un formalisme général, utilisant les fonctions de Green de Keldysh, pour le transport électronique quantique dans des systèmes multi-terminaux en présence de perturbations oscillantes. Nous sommes capable d'exprimer toute obervable AC en termes de fonctions de Green à l'équilibre et des self-énergies des contacts. Ceci fait de notre formalisme un outil pratique pour toute une variété de perturbations à fréquence finie. Dans la seconde partie on présente l'idée d'induction d'un fort couplage spin-orbite dans le graphène en déposant à sa surface un certain type d'atomes lourds. Le graphène devient alors un isolant topologique. Nous avons ensuite étudié l'évolution de la phase topologique avec un champ magnétique externe. Une transition entre la phase de Hall quantique et la phase de Hall quantique de spin a été identifiée dans le même système en variant seulement la position du niveau de Fermi. Nous avons montré qu'une hétérojonction entre ces deux phases donnait lieu à un nouveau type d'état chiral à l'interface. / Rapidly changing market of electronic devices sets up a lot of challenges for the manufacturing and design technologies. When electronic circuit elements get smaller, the device behavior becomes increasingly complicated as new physical phenomena due to quantum interference effects come into play. Understanding of the latter necessitates development of advanced theoretical tools. In this thesis we investigate quantum electron transport in multiterminal devices. In the first part making use of the Keldysh Green's functions we develop a general framework for electron quantum transport in multi-terminal systems in the presence of oscillating fields. We are able to express any AC observable in terms of stationary Green's functions and leads self-energies, which makes our formalism a practical numerical tool for a variety of possible finite-frequency perturbations. In the second part we investigate theoretically a proposal to induce strong spin-orbital coupling in graphene by functionalizing its surface with certain type of heavy adatoms. In this case graphene becomes a topological insulator. Then we investigate the evolution of this topological phase in external magnetic field. We were able to see a unique transition between quantum Hall and quantum spin Hall phases in the same system by only varying the position of the Fermi level. A heterojunction between these two phases was shown to give rise to a new type of a chiral state at the interface between the latter.