Models of quantum walks which admit continuous time and continuous spacetime limits have recently led to quantum simulation schemes for simulating fermions in relativistic and non relativistic regimes (Di Molfetta and Arrighi, 2020). This work continues the study of relationships between discrete time quantum walks (DTQW) and their ostensive continuum counterparts by developing a more general framework than was done in (Di Molfetta and Arrighi, 2020) to evaluate the continuous time limit of these discrete quantum systems. Under this framework, we prove two constructive theorems concerning which internal discrete transitions ("coins") admit nontrivial continuum limits in 1D+1. We additionally prove that the continuous space limit of the continuous time limit of the DTQW can only yield massless states which obey the Dirac equation. We also demonstrate that for general coins the continuous time limit of the DTQW can be identified with the canonical continuous time quantum walk (CTQW) when the coin is allowed to transition through the continuum limit process. Finally, we introduce the Plastic Quantum Walk, or a quantum walk which admits both continuous time and continuous spacetime limits and, as a novel result, we use our 1D+1 results to obtain necessary and sufficient conditions concerning which DTQWs admit plasticity in 2D+1, showing the resulting Hamiltonians. We consider coin operators as general 4 parameter unitary matrices, with parameters which are functions of the lattice step size 𝜖. This dependence on 𝜖 encapsulates all functions of 𝜖 for which a Taylor series expansion in 𝜖 is well defined, making our results very general.

La simulation quantique consiste à réaliser expérimentalement des systèmes artificiels équivalent à des modèles proposés par les théoriciens. Pour réaliser ces systèmes, il est possible d'utiliser des atomes dont les états individuels et les interactions sont contrôlés par la lumière. En particulier, une fois excités dans un état de haute énergie (appelé état de Rydberg), les atomes peuvent être contrôlés individuellement et leurs interactions façonnées arbitrairement par des faisceaux laser. Cette thèse s'intéresse à deux types de simulateurs quantiques à base d'atomes de Rydberg, et en particulier à leurs potentielles limitations.Dans l'expérience du Joint Quantum Institute (USA), nous observons la décohérence dans une structure cubique contenant jusqu'à 40000 atomes. A partir d'atomes préparés dans un état de Rydberg bien défini, nous constatons l'apparition spontanée d'états de Rydberg voisins et le déclenchement d'un phénomène d'avalanche. Nous montrons que ce mécanisme émane de l'émission stimulée produite par le rayonnement du corps noir. Ce phénomène s'accompagne d'une diffusion induite par des interactions de type dipole-dipole résonant. Nous complétons ces observations avec un modèle de champ moyen en état stationnaire. Dans un second temps, l'étude de la dynamique du problème nous permet de mesurer les échelles de temps caractéristiques. La décohérence étant globalement néfaste pour la simulation quantique, nous proposons plusieurs solutions pour en atténuer les effets. Nous évaluons notamment la possibilité de travailler dans un environnement cryogénique, lequel permettrait de réduire le rayonnement du corps noir.Dans l'expérience du Laboratoire Charles Fabry à l'Institut d'Optique (France), nous analysons les limites d'un simulateur quantique générant des structures bi- et tridimensionnelles allant jusqu'à 70 atomes de Rydberg piégés individuellement dans des pinces optiques. Le système actuel étant limité par le temps de vie des structures, nous montrons que l'utilisation d'un cryostat permettrait d'atteindre des tailles de structures jusqu'à 300 atomes. Nous présentons les premiers pas d'une nouvelle expérience utilisant un cryostat à 4K, et en particulier les études amont pour le développement de composants optomécaniques placés sous vide et à froid. / Quantum simulation consists in engineering well-controlled artificial systems that are ruled by the idealized models proposed by the theorists. Such toy models can be produced with individual atoms, where laser beams control individual atomic states and interatomic interactions. In particular, exciting atoms into a highly excited state (called a Rydberg state) allows to control individual atoms and taylor interatomic interactions with light. In this thesis, we investigate experimentally two different types of Rydberg-based quantum simulators and identify some possible limitations.At the Joint Quantum Institute, we observe the decoherence of an ensemble of up to 40000 Rydberg atoms arranged in a cubic geometry. Starting from the atoms prepared in a well-defined Rydberg state, we show that the spontaneous apparition of population in nearby Rydberg states leads to an avalanche process. We identify the origin of the mechanism as stimulated emission induced by black-body radiation followed by a diffusion induced by the resonant dipole-dipole interaction. We describe our observations with a steady-state mean-field analysis. We then study the dynamics of the phenomenon and measure its typical timescales. Since decoherence is overall negative for quantum simulation, we propose several solutions to mitigate the effect. Among them, we discuss the possibility to work at cryogenic temperatures, thus suppressing the black-body induced avalanche.In the experiment at Laboratoire Charles Fabry (Institut d'Optique), we analyze the limitation of a quantum simulator based on 2 and 3 dimensional arrays of up to 70 atoms trapped in optical tweezers and excited to Rydberg states. The current system is limited by the lifetime of the atomic structure. We show that working at cryogenic temperatures could allow to increase the size of the system up to N=300 atoms. In this context, we start a new experiment based on a 4K cryostat. We present the early stage of the new apparatus and some study concerning the optomechanical components to be placed inside the cryostat.

Nuclei are objects made of nucleons, protons and neutrons. Several dynamical processes that occur in nuclei are of great interest for the scientific community and for possible applications. For example, nuclear fusion can help us produce a large amount of energy with a limited use of resources and environmental impact. Few-nucleon scattering is an essential ingredient to understand and describe the physics of the core of a star. The classical computational algorithms that aim to simulate microscopic quantum systems suffer from the exponential growth of the computational time when the number of particles is increased. Even using today's most powerful HPC devices, the simulation of many processes, such as the nuclear scattering and fusion, is out of reach due to the excessive amount of computational time needed. In the 1980s, Feynman suggested that quantum computers might be more efficient than classical devices in simulating many-particle quantum systems. Following Feynman's idea of quantum computing, a complete change in the computation devices and in the simulation protocols has been explored in the recent years, moving towards quantum computations. Recently, the perspective of a realistic implementation of efficient quantum calculations was proved both experimentally and theoretically. Nevertheless, we are not in an era of fully functional quantum devices yet, but rather in the so-called "Noisy Intermediate-Scale Quantum" (NISQ) era. As of today, quantum simulations still suffer from the limitations of imperfect gate implementations and the quantum noise of the machine that impair the performance of the device. In this NISQ era, studies of complex nuclear systems are out of reach. The evolution and improvement of quantum devices will hopefully help us solve hard quantum problems in the coming years. At present quantum machines can be used to produce demonstrations or, at best, preliminary studies of the dynamics of a few nucleons systems (or other equivalent simple quantum systems). These systems are to be considered mostly toy models for developing prospective quantum algorithms. However, in the future, these algorithms may become efficient enough to allow simulating complex quantum systems in a quantum device, proving more efficient than classical devices, and eventually helping us study hard quantum systems. This is the main goal of this work, developing quantum algorithms, potentially useful in studying the quantum many body problem, and attempting to implement such quantum algorithms in different, existing quantum devices. In particular, the simulations made use of the IBM QPU's , of the Advanced Quantum Testbed (AQT) at Lawrence Berkeley National Laboratory (LBNL), and of the quantum testbed recently based at Lawrence Livermore National Laboratory (LLNL) (or using a device-level simulator of this machine). The our research aims are to develop quantum algorithms for general quantum processors. Therefore, the same developed quantum algorithms are implemented in different quantum processors to test their efficiency. Moreover, some uses of quantum processors are also conditioned by their availability during the time span of my PhD. The most common way to implement some quantum algorithms is to combine a discrete set of so-called elementary gates. A quantum operation is then realized in term of a sequence of such gates. This approach suffers from the large number of gates (depth of a quantum circuit) generally needed to describe the dynamics of a complex system. An excessively large circuit depth is problematic, since the presence of quantum noise would effectively erase all the information during the simulation. It is still possible to use error-correction techniques, but they require a huge amount of extra quantum register (ancilla qubits). An alternative technique that can be used to address these problems is the so-called "optimal control technique". Specifically, rather than employing a set of pre-packaged quantum gates, it is possible to optimize the external physical drive (for example, a suitably modulated electromagnetic pulse) that encodes a multi-level complex quantum gate. In this thesis, we start from the work of Holland et al. "Optimal control for the quantum simulation of nuclear dynamics" Physical Review A 101.6 (2020): 062307, where a quantum simulation of real-time neutron-neutron dynamics is proposed, in which the propagation of the system is enacted by a single dense multi-level gate derived from the nuclear spin-interaction at leading order (LO) of chiral effective field theory (EFT) through an optimal control technique. Hence, we will generalize the two neutron spin simulations, re-including spatial degrees of freedom with a hybrid algorithm. The spin dynamics are implemented within the quantum processor and the spatial dynamics are computed applying classical algorithms. We called this method classical-quantum coprocessing. The quantum simulations using optimized optimal control methods and discrete get set approach will be presented. By applying the coprocessing scheme through the optimal control, we have a possible bottleneck due to the requested classical computational time to compute the microwave pulses. A solution to this problem will be presented. Furthermore, an investigation of an improved way to efficiently compile quantum circuits based on the Similarity Renormalization Group will be discussed. This method simplifies the compilation in terms of digital gates. The most important result contained in this thesis is the development of an algorithm for performing an imaginary time propagation on a quantum chip. It belongs to the class of methods for evaluating the ground state of a quantum system, based on operating a Wick rotation of the real time evolution operator. The resulting propagator is not unitary, implementing in some way a dissipation mechanism that naturally leads the system towards its lowest energy state. Evolution in imaginary time is a well-known technique for finding the ground state of quantum many-body systems. It is at the heart of several numerical methods, including Quantum Monte Carlo techniques, that have been used with great success in quantum chemistry, condensed matter and nuclear physics. The classical implementations of imaginary time propagation suffer (with few exceptions) of an exponential increase in the computational cost with the dimension of the system. This fact calls for a generalization of the algorithm to quantum computers. The proposed algorithm is implemented by expanding the Hilbert space of the system under investigation by means of ancillary qubits. The projection is obtained by applying a series of unitary transformations having the effect of dissipating the components of the initial state along excited states of the Hamiltonian into the ancillary space. A measurement of the ancillary qubit(s) will then remove such components, effectively implementing a "cooling" of the system. The theory and testing of this method, along with some proposals for improvements will be thoroughly discussed in the dedicated chapter.

We investigate the simulations of the the Schrödinger equation using the onedimensional quantum lattice Boltzmann (QLB) scheme and the irregular behaviour of solution. We isolate error due to approximation of the Schrödinger solution with the non-relativistic limit of the Dirac equation and numerical error in solving the Dirac equation. Detailed analysis of the original scheme showed it to be first order accurate. By discretizing the Dirac equation consistently on both sides we derive a second order accurate QLB scheme with the same evolution algorithm as the original and requiring only a one-time unitary transformation of the initial conditions and final output. We show that initializing the scheme in a way that is consistent with the non-relativistic limit supresses the oscillations around the Schrödinger solution. However, we find the QLB scheme better suited to simulation of relativistic quantum systems governed by the Dirac equation and apply it to the Klein paradox. We reproduce the quantum tunnelling results of previous research and show second order convergence to the theoretical wave packet transmission probability. After identifying and correcting the error in the multidimensional extension of the original QLB scheme that produced asymmetric solutions, we expand our second order QLB scheme to multiple dimensions. Next we use the QLB scheme to simulate Klein tunnelling of massless charge carriers in graphene, compare with theoretical solutions and study the dependence of charge transmission on the incidence angle, wave packet and potential barrier shape. To do this we derive a representation of the Dirac-like equation governing charge carriers in graphene for the one-dimensional QLB scheme, and derive a two-dimensional second order graphene QLB scheme for more accurate simulation of wave packets. We demonstrate charge confinement in a graphene device using a configuration of multiple smooth potential barriers, thereby achieving a high ratio of on/off current with potential application in graphene field effect transistors for logic devices. To allow simulation in magnetic or pseudo-magnetic fields created by deformation of graphene, we expand the scheme to include vector potentials. In addition, we derive QLB schemes for bilayer graphene and the non-linear Dirac equation governing Bose-Einstein condensates in hexagonal optical lattices.

La thèse traite de la dynamique d'un Condensat de Bose Einstein (CBE) dans un réseau optique modulé en phase et en amplitude. Dans un premier temps, je présente le dispositif expérimental permettant d'obtenir le CBE ainsi que le réseau optique, et décris les différents contrôles de la phase et de l'amplitude que nous avons mis en place. La première expérience que nous avons effectuée repose sur le changement brusque de la phase du réseau permettant de déplacer celui-ci de quelques dizaines de nm. Cette expérience nous a permis de mettre au point une méthode de calibration de la profondeur du potentiel périodique se basant sur la mesure de la période de la micro-oscillation de la chaîne de condensats induite par le déplacement soudain du potentiel. Il existe ainsi une bijection entre profondeur et période de l'oscillation faisant de cette dernière une candidate idéale comme méthode de calibration. Cette oscillation présente également de l'effet tunnel entre puits du réseau. Nous avons pu mesurer le temps tunnel i.e. le retard entre un paquet d'atomes ayant traversé une barrière de potentiel par effet tunnel et un paquet d'atomes ayant continué son oscillation. La dernière partie de ce manuscrit présente une étude de la dynamique du condensat dans un réseau dont la phase ou l'amplitude sont modulées sinusoïdalement. Nous avons étudié trois régimes de fréquences de modulation présentant des comportements très différents. Les régimes de fréquences sont définies par rapport à la fréquence résonante entre la bande fondamentale du réseau et la première bande excitée. Pour la modulation à basse fréquence, le taux tunnel intersite est renormalisé et peut atteindre des valeurs effectives négatives. Ce phénomène engendre une instabilité dynamique qui est à l'origine d'une transition de phase quantique. Nous avons effectué une étude théorique, numérique et expérimentale qui nous a permis de déterminer le rôle des fluctuations quantiques et thermiques dans la cinétique de cette transition. Pour le régime de modulation haute fréquence, la profondeur du potentiel du réseau est renormalisée par une fonction de Bessel. Nous nous sommes servis de cet effet pour placer les atomes dans une situation très loin de l'équilibre avec un grand contrôle. Enfin, en nous plaçant dans le régime où la fréquence de modulation est de l'ordre de la fréquence résonante entre la bande fondamentale du réseau et la première bande excitée, nous induisons des transitions interbandes. Nos données révèlent les règles de sélection qui sont différentes pour la modulation de phase et d'amplitude, et le rôle des interactions dans les excitations résonantes. / The subject of this thesis is the study of the dynamics of a Bose Einstein condensate in a phase and amplitude modulated optical lattice. First, I present the experimental setup allowing us to produce the BEC as well as the optical lattice. I describe the different means of control on the phase and on the amplitude of the lattice that we implemented. The first experiment we performed is based on the sudden shift of the phase of the lattice that induces a displacement of a few tenth of nm. This experiment allowed us to develop a new method to calibrate the depth of the lattice using the period of the micro-oscillation of the BEC chain triggered by the phase shift. There is a bijection between the depth of the lattice and the oscillation period giving the period the ideal profile to be a calibration method. The dynamic of the oscillation shows tunnel effect between adjacent wells of the lattice. We have been able to measure directly the tunneling time which is the delay between an atoms packet which passed through a potential barrier by tunnel effect and a packet of atoms which continued its oscillation. The last part of the manuscript presents a study of the dynamics of the BEC inside a lattice which phase or amplitude is modulated with a sine function. We study three ranges of modulation frequencies showing different behaviors. The frequency is compared with the resonant frequency between the fundamental band of the lattice band structure and the first excited band. When we modulate with low frequencies the phase of the lattice, the tunnel rate between adjacent wells is renormalized. This yields a dynamical instability which triggers a quantum phase transition. We performed a theoretical study, a numerical study and an experimental study that allowed us to define the role of quantum and thermal fluctuations in the system on the kinetics of this transition. For the high modulation frequency regime, the potential depth is renormalized with a Bessel function. We used this effect to put the atoms in a far-out of equilibrium position in a well- controlled manner. Lastly, by choosing the modulation frequency to be of the order of the resonant frequency between the fundamental band and the first excited band, we induce interband transitions. Our data reveal the selection rules which are different for phase and amplitude modulation, and the role of two-body interactions in the excitation process.

Les circuits supraconducteurs sont parmi les technologies de l'information quantique les plus avancées. Ils ont aujourd'hui atteint la maturité qui offre un grand degré de contrôle et une large gamme d'interactions qui peuvent être précisément réalisées sur mesure. Le mixeur Josephson est un exemple de circuit supraconducteur qui effectue le mixage à trois ondes aux fréquences micro-ondes. Dans cette thèse, trois expériences, où le mixeur Josephson est utilisé pour trois applications différentes sont décrites. D'abord, nous avons réalisé le couplage ultrafort effectif entre deux modes bosoniques afin d'étudier les propriétés de l'état fondamental de ce système, tels que le squeezing à un mode et à deux modes du champ radié. Ensuite, nous avons construit un nœud quantique, capable de créer et distribuer de l'intrication sur un réseau quantique micro-onde, alors que de stocker et relâcher de l'information quantique à demande. Nous avons intégré un qubit de mesure dans ce dispositif pour augmenter le degré de contrôle sur son état quantique. Finalement, nous avons poussé le mixeur Josephson au delà du seuil de l'oscillation paramétrique, où nous avons démontré une technique inhabituelle de verrouillage par injection en conversion de fréquence dans ce dispositif non-dégénéré. / Superconducting circuits stand among the most advanced quantum information processing platforms. They have nowadays reached a maturity that offers a high level of controllability and a large variety of interactions that can be precisely designed on demand. The Josephson mixer is one such superconducting device that performs three-wave mixing at microwave frequencies. In this thesis, we describe three experiments in which the Josephson mixer was used for different applications. First, we have realized an effective ultrastrong coupling of two bosonic modes that allowed us to study the ground state properties of this system, such as the single mode and the two mode squeezing of the emitted radiation. Second, we have built a quantum node, able to generate and distribute entanglement over a microwave quantum network, as well as to store and release quantum information on demand. We have integrated an ancilla qubit to this device in order to increase the degree of control over the quantum state of the system. Finally, we have pushed the Josephson mixer beyond the parametric oscillation instability threshold, where we have demonstrated an atypical injection locking technique that relies on coherent frequency conversion in this non-degenerate device.

Title: Optimizing quantum simulations and the DMRG method Author: Jan Brandejs Department: Department of Chemical Physics and Optics Supervisor: doc. Dr. rer. nat. Jiří Pittner, DSc., J. Heyrovský Institute of Physical Chemistry of the Czech Academy of Sciences Abstract: In this work, we explore the quantum information theoretical aspects of simulation of quantum systems on classical computers, in particular the many- electron strongly correlated wave functions. We describe a way how to reduce the amount of data required for storing the wavefunction by a lossy compression of quantum information. For this purpose, we describe the measures of quantum entanglement for the density matrix renormalization group method. We imple- ment the computation of multi-site generalization of mutual information within the DMRG method and investigate entanglement patterns of strongly correlated chemical systems. We present several ways how to optimize the ground state calculation in the DMRG method. The theoretical conclusions are supported by numerical simulations of the diborane molecule, exhibiting chemically interest- ing electronic structure, like the 3-centered 2-electron bonds. In the theoretical part, we give a brief introduction to the principles of the DMRG method. Then we explain the quantum informational...

Lattice gauge theories are crucial for our understanding of many physical phenomena ranging from fundamental particle interactions in high-energy physics to frustration and topological order in condensed matter. Hence, many equilibrium aspects of these theories have been studied intensively over the past decades. Recent developments, however, have shown that the study of nonequilibrium dynamics in lattice gauge theories also provides a very fertile ground for interesting phenomena. This thesis is devoted to the study of two particular dynamical processes in lattice gauge theories and related quantum spin models. First, we show that an interacting two-dimensional lattice gauge theory can exhibit disorder-free localization: a mechanism for ergodicity breaking due to local constraints imposed by gauge invariance. This result is particularly remarkable as the stability in two dimensions of the more conventional (disorder-induced) many-body localization is still debated. Concretely, we show this type of nonergodic behavior in the quantum link model. Our central result is based on a bound on the localization-delocalization transition, which is established through a concomitant classical percolation problem. Further, we develop a numerical method dubbed “variational classical networks”, to study the quantum dynamics in this system. This technique provides an efficient and perturbatively controlled representation of the wave function in terms of networks of classical spins akin to artificial neural networks. This allows us to identify distinguishing transport properties in the localized and ergodic phases, respectively. In the second problem, we study the dynamics of string breaking, a key process in confining gauge theories, where a string connecting two charges decays due to the creation of new particle-antiparticle pairs. Our main result here is that string breaking can also be observed in quantum Ising chains, in which domain walls get confined either by a symmetry-breaking field or by long-range interactions. We identify, in general, two distinct stages in this process. While at the beginning the initial charges remain stable, the string can exhibit complex dynamics with strong quantum correlations. We provide an effective description of this string motion, and find that it can be highly constrained. In the second stage, the string finally breaks at a timescale that depends sensitively on the initial separation of domain walls. We observe that the second stage can be significantly delayed as a consequence of the dynamical constraints appearing in the first stage. Finally, we discuss the generalization of our results to low-dimensional confining gauge theories. As a general aspect of this work, we discuss how the phenomena studied here could be realized experimentally with current and future technologies in quantum simulation. Furthermore, the methods developed in this thesis can also be applied to other lattice gauge theories and constrained quantum many-body models, not only to address purely theoretical questions but also to provide a theoretical description of experiments in quantum simulators. / Gittereichtheorien sind ein wichtiger Bestandteil im Verständnis vieler physikalischer Phänomene und Grundlage verschiedener Theorien, welche sich von der elementaren Wechselwirkungen in der Hochenergiephysik, Frustration in Spinmodellen bis hin zu topologischer Ordnung in der Festkörperphysik erstrecken. Die Eigenschaften von Eichtheorien im Gleichgewicht waren in den letzten Jahrzehnten ein zentraler Punkt der Forschung. Obwohl sich Untersuchungen der Dynamik jenseits des Gleichgewichs als eine große Herausfordung dargestellt haben, haben kürzliche Erkenntnisse gezeigt, dass die Dynamik in Gittereichtheorien überraschende und interessante Entdeckungen bereithält. Diese Dissertation behandelt zwei zentrale dynamische Prozesse in Gittereichtheorien und verwandten Spinmodellen. Einerseits soll die Dynamik von zweidimensionalen und wechselwirkenden Gittereichtheorien untersucht werden im Falle des sogenan- nten Quanten-Link-Modells untersucht werden. Entgegen der Ergodenhypothese zeigt das System Lokalisierung ohne Unordnung aufgrund lokaler Zwangsbedingungen durch Eininvarianz. Dieses Ergebnis ist insofern bemerkenswert, als die gewöhnliche, durch Unordnung induzierte, Vielteilchenlokalisierung in zwei Dimensionen umstritten ist. Als ein Hauptergebnis finden wir einen Übergang zwischen einer lokalisierten und ergodischen Phase, dessen Existenz durch ein zugehöriges klassisches Perkolationsproblem gezeigt werden konnte. Die quantenmechanischen Transporteigenschaften, elementar verschieden in der lokalisierten und ergodischen Phase, werden charakterisiert und untersucht. Die Lösung der quantenmechanischen Zeitentwicklung wird durch eine methodische Weiterentwicklung der sogenannten „variationellen klassischen Netzwerke“ erreicht Diese Methode stellt eine perturbative, aber kontrollierte Repräsentation von zeitentwickelten quantenmechanischen Wellenfunktionen dar in Form von Netzwerken klassischer Spins, ähnlich wie bei einem künstlichen neuronalen Netz. Im zweiten Teil untersuchen wir die Dynamik eines Schlüsselprozesses in Eichtheorien mit Confinement, welcher als „String-Breaking“ bezeichnet wird In diesem Prozess zerfällt der der Strang, der zwei elementare Ladungen verbindet, durch die Bildung neuer Teilchen-Antiteilchen-Paare. Ein Hauptresultat dieser Arbeit ist die Beobachtung dieses dynamischen Phänomens in Quantum-Ising-Ketten und damit in Systemen ohne Eichinvarianz. Das Confinement entsteht dabei zwischen Domänenwänden entweder durch eine langreichweitige Wechselwirkung zwischen den beteiligten Spins oder durch symmetriebrechende Magnetfelder. Es wird gezeigt, dass während des „String-breaking“ Prozesses das Modell zwei Phasen durchläuft: Während zu Beginn die Anfangsladungen stabil bleiben, weist der Strang eine komplexe Dynamik mit starken Quantenkorrelationen auf. Für diese erste Phase wird eine effektive Beschreibung eingeführt, um die verschiedenen Aspekte zu analysieren und zu verstehen. Die Zeitskalen zur Destabilisierung des Strangs innerhalb einer zweiten Phase zeigen eine starke Abhängigkeit von der anfänglichen Trennung der Domänenwände. Es wird gezeigt, dass die zweite Phase als Konsequenz der dynamischen Beschränkungen der ersten Phase signifikant verzögert werden kann. Diese Resultate können in niedrigdimensionalen Eichtheorien verallgemeinert werden. Weiterführend sollen die Ergebnisse als Grundlage einer experimentellen Realisierung durch Quantensimulationen dienen. Die entwickelten Methoden können auf andere Eichtheorien und verwandten Vielteilchenmodellen angewendet werden und bieten eine Plattform für weitere Ansätze.

Des atomes individuels piégés dans des matrices de pinces optiques et excités vers des états de Rydberg forment une plateforme expérimentale prometteuse pour la simulation quantique de modèles de spins. Lors de cette thèse, nous avons d’abord résolu le problème du chargement aléatoire des pièges, seulement 50 % d’entre eux étant chargés avec un atome. Nous avons développé une technique pour préparer des matrices 2D, puis 3D, d’atomes de 87Rb en les déplaçant un par un avec une pince optique mobile contrôlée par ordinateur. Nous avons ensuite réalisé le modèle d’Ising en excitant de manière cohérente les atomes depuis leur état électronique fondamental vers un niveau de Rydberg. Après avoir trouvé un régime optimal où l’interaction dipolaire entre deux atomes de Rydberg se réduit à une énergie de van der Waals, nous avons tenté de préparer adiabatiquement l’état de Néel qui minimise l’énergie d’interaction. Nous avons montré que l’efficacité de préparation étaitlimitée par la décohérence induite par les lasers d’excitation. Nous avons ensuite utilisé un autre régime d’interaction, le couplage dipolaire résonant, pour étudier des modèles de spins de type XY, dont le modèle Su-Schrieffer-Heeger, connu pour sa phase fermionique topologique protégée par une symétrie chirale. Ici, nous avons remplacé les fermions par des particules effectives de type `boson de cœur dur’, ce qui modifie les propriétés de cette phase. Nous avons d’abord retrouvé les propriétés à une particule, comme l’existence d’états de bords à énergie nulle. Nous avons ensuite préparé l’état fondamental à N corps pour un remplissage moitié, et observé sa dégénérescence causée par les états de bords, même en présence d’une perturbation qui lèverait cette dégénérescence dans le cas fermionique. Nous avons expliqué ce résultat par l’existence d’une symétrie plus générale, qui protège la phase bosonique. / Single atoms trapped in arrays of optical tweezers and excited to Rydberg states are a promising experimental platform for the quantum simulation of spin models. In this thesis, we first solved a long-standing challenge to this approach caused by the random loading of the traps, with only 50% of them filled with single atoms. We have engineered a robust and easy-to-use method to assemble perfectly filled two-dimensional arrays of 87Rb atoms by moving them one by one with a moveable optical tweezers controlled by computer, a technique further enhanced to trap, image and assemble three-dimensional arrays. We then implemented the quantum Ising model by coherently coupling ground-state atoms to a Rydberg level. After finding experimental parameters where the dipole-dipole interaction takes the ideal form of a van der Waals shift, we performed adiabatic preparation of the Néel state. We showed that the coherence time of our excitation lasers limited the efficiency of this technique. We then used a different type of interaction, a resonant dipolar coupling, to implement XY spin models and notably the Su-Schrieffer-Heeger model, known for its fermionic topological phase protected by the chiral symmetry. Here, we used effective hard-core bosons, which modify the properties of the topological phase. We first recovered known properties at the single particle level, such as the existence of localized zero-energy edge-states. Then, preparing the many-body ground state at half-filling, we observed a surprising robustness of its four-fold degeneracy upon applying a perturbation. This result was explained by the existence of a more general symmetry protecting the bosonic phase.

No description available.