This thesis presents research on the initialization, control, and readout of electron spin states in gate defined GaAs quantum dots. The first three experiments were performed with Singlet-Triplet spin qubits in double quantum dots, while the remaining two experiments were performed with an Exchange-Only spin qubit in a triple quantum dot. / Physics

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.

Spin properties of donor impurities in silicon have been investigated by electron spin resonance (ESR) techniques for more than sixty years. These studies gave us a contribution towards understanding some of the physics of doped semiconductor materials in general, which is the platform for much of our current technology. Despite the fact that donor electron and nuclear spins have been researched for so long, ESR studies of their properties are still giving us interesting insights. With the introduction of the concept of quantum information in the 1980s, some properties of donor spins in silicon, that were known from the fifties (such as long relaxations), have been reinterpreted for their potential application in this field. Since then, incredible experimental results have been achieved with magnetic resonance control, including manipulation and read-out of individual spins. However, some open questions are still to be answered before the realisation of a spin-based silicon quantum architecture will be achieved. Currently, ESR studies still contribute to help answering some of those questions. In this thesis, we demonstrate electrical and optical methods for donor charge state manipulation measured by ESR. Recent experiments have demonstrated that coherence time of nuclear spins may be enhanced by manipulating the state of donors from neutral to singly charged. We investigate electric field ionisation/neutralisation of arsenic donors in a silicon SOI device measured by ESR. Below ionisation threshold, we also measure the hyperfine Stark shift of arsenic donors spins in silicon. These results have, for instance, implications on how fast individual addressability of donor spins may be achieved in certain quantum computer architectures. Here, we also study optical-driven charge state manipulation of selenium impurities in silicon. Selenium has two additional electrons when it replaces an atom in the silicon crystal (i.e. double donor). The electronic properties of singly-ionised selenium make it potentially advantageous as spin qubit, compared to the more commonly studied group-V donors. For instance, we find here that the electron spin relaxation and coherence times of selenium are up to two orders of magnitude longer than phosphorus at the same temperature. Finally, we demonstrate that it is possible to bring selenium impurity in singly-charged state and subsequently re-neutralise them leaving a potential long-lived ⁷⁷Se nuclear spin.

<p dir="ltr">This work is the first report of optically addressable spin qubits in a semi-1D material, Boron Nitride Nanotubes (BNNTs). We perform the characterization of these spin defects and utilize their properties to do omnidirectional magnetic field sensing. We transfer these BNNTs with spin defects onto an AFM cantilever and perform scanning probe magnetometry of a 2D Nickel pattern on a gold waveguide. </p>

[Mathematical symbols can be only approximated here. For the correct display see the Abstract in the PDF files linked below] This work has demonstrated that hyperfine decoherence times sufficiently long for QIP and quantum optics applications are achievable in rare earth ion centres. Prior to this work there were several QIP proposals using rare earth hyperfine states for long term coherent storage of optical interactions [1, 2, 3]. The very long T_1 (~weeks [4]) observed for rare-earth hyperfine transitions appears promising but hyperfine T_2s were only a few ms, comparable to rare earth optical transitions and therefore the usefulness of such proposals was doubtful. ¶ This work demonstrated an increase in hyperfine T_2 by a factor of 7 × 10^4 compared to the previously reported hyperfine T_2 for Pr^[3+]:Y_2SiO_5 through the application of static and dynamic magnetic field techniques. This increase in T_2 makes previous QIP proposals useful and provides the first solid state optically active Lamda system with very long hyperfine T_2 for quantum optics applications. ¶ The first technique employed the conventional wisdom of applying a small static magnetic field to minimise the superhyperfine interaction [5, 6, 7], as studied in chapter 4. This resulted in hyperfine transition T_2 an order of magnitude larger than the T_2 of optical transitions, ranging fro 5 to 10 ms. The increase in T_2 was not sufficient and consequently other approaches were required. ¶ Development of the critical point technique during this work was crucial to achieving further gains in T_2. The critical point technique is the application of a static magnetic field such that the Zeeman shift of the hyperfine transition of interest has no first order component, thereby nulling decohering magnetic interactions to first order. This technique also represents a global minimum for back action of the Y spin bath due to a change in the Pr spin state, allowing the assumption that the Pr ion is surrounded by a thermal bath. The critical point technique resulted in a dramatic increase of the hyperfine transition T_2 from ~10 ms to 860 ms. ¶ Satisfied that the optimal static magnetic field configuration for increasing T_2 had been achieved, dynamic magnetic field techniques, driving either the system of interest or spin bath were investigated. These techniques are broadly classed as Dynamic Decoherence Control (DDC) in the QIP community. The first DDC technique investigated was driving the Pr ion using a CPMG or Bang Bang decoupling pulse sequence. This significantly extended T_2 from 0.86 s to 70 s. This decoupling strategy has been extensively discussed for correcting phase errors in quantum computers [8, 9, 10, 11, 12, 13, 14, 15], with this work being the first application to solid state systems. ¶ Magic Angle Line Narrowing was used to investigate driving the spin bath to increase T_2. This experiment resulted in T_2 increasing from 0.84 s to 1.12 s. Both dynamic techniques introduce a periodic condition on when QIP operation can be performed without the qubits participating in the operation accumulating phase errors relative to the qubits not involved in the operation. ¶ Without using the critical point technique Dynamic Decoherence Control techniques such as the Bang Bang decoupling sequence and MALN are not useful due to the sensitivity of the Pr ion to magnetic field fluctuations. Critical point and DDC techniques are mutually beneficial since the critical point is most effective at removing high frequency perturbations while DDC techniques remove the low frequency perturbations. A further benefit of using the critical point technique is it allows changing the coupling to the spin bath without changing the spin bath dynamics. This was useful for discerning whether the limits are inherent to the DDC technique or are due to experimental limitations. ¶ Solid state systems exhibiting long T_2 are typically very specialised systems, such as 29Si dopants in an isotopically pure 28Si and therefore spin free host lattice [16]. These systems rely on on the purity of their environment to achieve long T_2. Despite possessing a long T_2, the spin system remain inherently sensitive to magnetic field fluctuations. In contrast, this work has demonstrated that decoherence times, sufficiently long to rival any solid state system [16], are achievable when the spin of interest is surrounded by a concentrated spin bath. Using the critical point technique results in a hyperfine state that is inherently insensitive to small magnetic field perturbations and therefore more robust for QIP applications.

A simplified model of a double quantum dot is presented and analyzed, with applications to spin-qubit quantum computation. The ability to trap single electrons in semiconductor nanostructures has led to the proposal of quantum computers with spin-based qubits coupled by the exchange interaction. Current theory predicts an exchange interaction with a -1 power-law dependence on the detuning ϵ, the energy offset between the two dots. However, experiment has shown a -3/2 power-law dependence on ϵ. Using WKB analysis, this thesis explores one possible source of the modified dependence, namely an ϵ-dependent tunnel coupling between the two wells. WKB quantization is used to find expressions for the tunnel coupling of a one-dimensional double-well, and these results are compared to the exact, numerical solutions, as determined by the finite difference method and the transfer matrix method. Small ϵ-dependent corrections to the tunnel coupling are observed. In typical cases, WKB correctly predicts a constant tunnel coupling at leading-order. WKB also predicts small ϵ-dependent corrections for typical cases and strongly ϵ-dependent tunnel couplings for certain exceptional cases. However, numerical simulations suggest that WKB is not accurate enough to analyze the small corrections, and is not valid in the exceptional cases. Deviations from the conventional form of the low-energy Hamiltonian for a double-well are also observed and discussed.

A simplified model of a double quantum dot is presented and analyzed, with applications to spin-qubit quantum computation. The ability to trap single electrons in semiconductor nanostructures has led to the proposal of quantum computers with spin-based qubits coupled by the exchange interaction. Current theory predicts an exchange interaction with a -1 power-law dependence on the detuning ϵ, the energy offset between the two dots. However, experiment has shown a -3/2 power-law dependence on ϵ. Using WKB analysis, this thesis explores one possible source of the modified dependence, namely an ϵ-dependent tunnel coupling between the two wells. WKB quantization is used to find expressions for the tunnel coupling of a one-dimensional double-well, and these results are compared to the exact, numerical solutions, as determined by the finite difference method and the transfer matrix method. Small ϵ-dependent corrections to the tunnel coupling are observed. In typical cases, WKB correctly predicts a constant tunnel coupling at leading-order. WKB also predicts small ϵ-dependent corrections for typical cases and strongly ϵ-dependent tunnel couplings for certain exceptional cases. However, numerical simulations suggest that WKB is not accurate enough to analyze the small corrections, and is not valid in the exceptional cases. Deviations from the conventional form of the low-energy Hamiltonian for a double-well are also observed and discussed.

We demonstrate a remarkable property of metallic Fermi liquids: the transverse conductivity assumes a universal value in the quasi-static (ω → 0) limit for wavevectors q in the regime l −1 mfp q pF, where lmfp is the mean free path and pF is the Fermi momentum. This value is (e2/h)RFS/q in two dimensions (2D), where RFS measures the local radius of curvature of the Fermi surface (FS) in momentum space. Even more surprisingly, we find that U(1) spin liquids with a spinon FS have the same universal transverse conductivity. This means such spin liquids behave effectively as metals in this regime, even though they appear insulating in standard transport experiments. Moreover, we show that transverse current fluctuations result in a universal low-frequency magnetic noise that can be directly probed by a spin qubit, such as a nitrogen-vacancy (NV) center in diamond, placed at a distance z above of the 2D metal or spin liquid. Specifically the magnetic noise is given by CωPFS/z, where PFS is the perimeter of the FS in momentum space and C is a combination of fundamental constants of nature. Therefore these observables are controlled purely by the geometry of the FS and are independent of kinematic details of the quasi-particles, such as their effective mass and interactions. This behavior can be used as a new technique to measure the size of the FS of metals and as a smoking gun probe to pinpoint the presence of the elusive spinon FS in two-dimensional systems. We estimate that this universal regime is within reach of current NV center spectroscopic techniques for several spinon FS candidate materials.

Dans cette thèse, nous étudions des circuits de boîtes quantiques à base de nanotubes de carbone intégrés dans une cavité micro-onde. Cette architecture générale permet de sonder le circuit en utilisant simultanément des mesures de transport et des techniques propre au domaine de l’Electrodynamique quantique sur circuit. Les deux expériences réalisées durant cette thèse exploitent la capacité des métaux de contact à induire des corrélations de spins dans les boites quantiques. La première expérience est l’étude d’une lame s´séparatrice à paires de Cooper, initialement imaginée comme une source d’électrons intriqués. Le couplage du circuit aux photons dans la cavité permet de sonder la dynamique interne du circuit, et a permis d’observer des transitions de charge habillées par le processus de séparation des paires de Cooper. Le couplage fort entre une transition de charge dans un circuit de boîtes quantiques et des photons en cavité, a été observée pour la première fois dans ce circuit. Une nouvelle technique de fabrication a aussi été développé pour intégrer un nanotube de carbone cristallin au sein du circuit de boîtes quantiques. La pureté et l’accordabilité de cette nouvelle génération de circuit a rendu possible la seconde expérience. Cette dernière utilise deux vannes de spins non colinéaire afin de produire une interface cohérente entre le spin d’un électron dans une double boite quantique, et un photon dans une cavité. Des transitions de spins très cohérentes ont été observée, et nous donnons un modèle sur l’origine de la décohérence du spin comprenant le bruit en charge et les fluctuations des spins nucléaires. / In this thesis, we study carbon nanotubes based quantum dot circuits embedded in a microwave cavity. This general architecture allows one to simultaneously probe the circuit via quantum transport measurements and using circuit quantum electrodynamics techniques. The two experiments realized in this thesis use metallic contacts of the circuit as a resource to engineer a spin sensitive spectrum in the quantum dots. The first one is a Cooper pair splitter which was originally proposed as a source of non local entangled electrons. By using cavity photons as a probe of the circuit internal dynamics, we observed a charge transition dressed by coherent Cooper pair splitting. Strong charge-photon coupling in a quantum dot circuit was demonstrated for the first time in such a circuit. A new fabrication technique has also been developed to integrate pristine carbon nanotubes inside quantum dot circuits. The purity and tunability of this new generation of devices has made possible the realization of the second experiment. In the latter, we uses two non-collinear spin-valves to create a coherent interface between an electronic spin in a double quantum dot and a photon in a cavity. Highly coherent spin transitions have been observed. We provide a model for the decoherence based on charge noise and nuclear spin fluctuations.