This thesis describes aspects of dynamics of solid state systems which are relevant to quantum metrology and computation. It may be divided into three research directions (parts). For the first part, a new method to enhance precision measurements that makes use of a sensor’s environment to amplify its response to weak external perturbations is described. In this method a “central” spin is used to sense the dynamics of surrounding spins, which are affected by the external perturbations that are being measured. The enhancement in precision is determined by the number of spins that are coupled strongly to the central spin and is resilient to various forms of decoherence. For polarized environments, nearly Heisenberg-limited precision measurements can be achieved. The second part of the thesis focuses on the decoherence of Majorana fermions. Specializing to the experimentally relevant case where each mode interacts with its own bath we present a method to study the effect of external perturbations on these modes. We analyze a generic gapped fermionic environment (bath) interacting via tunneling with individual Majorana modes - components of a qubit. We present examples with both static and dynamic perturbations (noise), and derive a rate of information loss for Majorana memories, that depends on the spectral density of both the noise and the fermionic bath. For the third part of the thesis we discuss vortices in topological superconductors which we model as closed finite systems, each with an odd number of real fermionic modes. We show that even in the presence of many-body interactions, there are always at least two fermionic operators that commute with the Hamiltonian. There is a zero mode corresponding to the total Majorana operator [1] as well as additional linearly independent zero modes, one of which is continuously connected to the Majorana mode in the non-interacting limit. We also show that in the situation where there are two or more well separated vortices their zero modes have non-Abelian Ising statistics under braiding. / Physics

We study three different kinds of mesoscopic systems – in the intermediate region between macroscopic and microscopic scales consisting of many interacting constituents: We consider particle entanglement in one-dimensional chains of interacting fermions. By employing a field theoretical bosonization calculation, we obtain the one-particle entanglement entropy in the ground state and its time evolution after an interaction quantum quench which causes relaxation towards non-equilibrium steady states. By pushing the boundaries of the numerical exact diagonalization and density matrix renormalization group computations, we are able to accurately scale to the thermodynamic limit where we make contact to the analytic field theory model. This allows to fix an interaction cutoff required in the continuum bosonization calculation to account for the short range interaction of the lattice model, such that the bosonization result provides accurate predictions for the one-body reduced density matrix in the Luttinger liquid phase. Establishing a better understanding of how to control entanglement in mesoscopic systems is also crucial for building qubits for a quantum computer. We further study a popular scalable qubit architecture that is based on Majorana zero modes in topological superconductors. The two major challenges with realizing Majorana qubits currently lie in trivial pseudo-Majorana states that mimic signatures of the topological bound states and in strong disorder in the proposed topological hybrid systems that destroys the topological phase. We study coherent transport through interferometers with a Majorana wire embedded into one arm. By combining analytical and numerical considerations, we explain the occurrence of an amplitude maximum as a function of the Zeeman field at the onset of the topological phase – a signature unique to MZMs – which has recently been measured experimentally [Whiticar et al., Nature Communications, 11(1):3212, 2020]. By placing an array of gates in proximity to the nanowire, we made a fruitful connection to the field of Machine Learning by using the CMA-ES algorithm to tune the gate voltages in order to maximize the amplitude of coherent transmission. We find that the algorithm is capable of learning disorder profiles and even to restore Majorana modes that were fully destroyed by strong disorder by optimizing a feasible number of gates. Deep neural networks are another popular machine learning approach which not only has many direct applications to physical systems but which also behaves similarly to physical mesoscopic systems. In order to comprehend the effects of the complex dynamics from the training, we employ Random Matrix Theory (RMT) as a zero-information hypothesis: before training, the weights are randomly initialized and therefore are perfectly described by RMT. After training, we attribute deviations from these predictions to learned information in the weight matrices. Conducting a careful numerical analysis, we verify that the spectra of weight matrices consists of a random bulk and a few important large singular values and corresponding vectors that carry almost all learned information. By further adding label noise to the training data, we find that more singular values in intermediate parts of the spectrum contribute by fitting the randomly labeled images. Based on these observations, we propose a noise filtering algorithm that both removes the singular values storing the noise and reverts the level repulsion of the large singular values due to the random bulk.

Submitted by ANGEL EDUARDO OBISPO VASQUEZ null (signaux_fonce@hotmail.com) on 2016-03-10T21:30:19Z No. of bitstreams: 1 Tese final.pdf: 3148732 bytes, checksum: dc9e633bbfd74365e11b41baeb143eff (MD5) / Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-03-14T14:09:25Z (GMT) No. of bitstreams: 1 vasquez_aeo_dr_guara.pdf: 3148732 bytes, checksum: dc9e633bbfd74365e11b41baeb143eff (MD5) / Made available in DSpace on 2016-03-14T14:09:25Z (GMT). No. of bitstreams: 1 vasquez_aeo_dr_guara.pdf: 3148732 bytes, checksum: dc9e633bbfd74365e11b41baeb143eff (MD5) Previous issue date: 2016-02-17 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Desde aproximadamente o nal da década de 1970 efeitos quânticos e topológicos em sistemas da matéria condensada que são mostrados ocorrer a nível teórico em teoria quântica de campos têm atraído a atenção de físicos. Neste contexto, o grafeno representa uma das maiores vertentes de pesquisa dentro dos estudos das ciência dos materiais. O fato das excitações eletrônicas de baixa energia serem descritas por fermions de Dirac, estimulou uma relação frutífera entre a matéria condensada e a física de altas energias, fornecendo cenários propícios para o aparecimento de novos e exóticos fenômenos que são de grande interesse na física da matéria condensada atual. A presente tese aborda particularmente dois tópicos fundamentais da teoria quântica de campos: As Anomalias quânticas e o Fracionamento do número fermiônico. Especí camente, estamos interessados na realização de ambos fenômenos em redes de grafeno com deformações. No grafeno, um potencial vector de gauge axial surge como produto de deformações locais da rede, na forma de defeitos topológicos ou corrugações suaves. Analisaremos a in uência desses campos pseudomagnéticos nos estados eletrônicos para uma partícula, quando interagem com um campo magnético externo, considerando diferentes con gurações para esses campos. Estudamos o papel que desempenham os estados de modo-zero na indução de um número fermiônico fracionário e sua conexão com a anomalia de paridade. / Since approximately the late 1970s, topological quantum effects in condensed matter systems that are shown the occur at a theoretical level in quantum field theory have attracted the attention of physicists. In this context, the graphene is one of the major lines of research within the studies of materials science. The fact that the electronic excitations of low energy are described by Dirac fermions, stimulating a fruitful relationship between condensed matter and high energy physics, providing favorable scenarios for the arising of new and exotic phenomena which are of great interest in the current condensedmatter physics. This thesis addresses particularly two key topics of quantum field theory: Quantum anomalies and the fermion number fractionalization. Specifically, we are interested in performing both phenomena in deformed graphene lattice. In graphene, an axial vector potential arises as the result of local deformations on the lattice, as topological defects or soft corrugations. We analyze the ináuence of these pseudo-magnetic fields on the one-particle states, when interacting with a background magnetic field, for differents conÖguration for the fields. We study the role played by zero-mode states in fractional fermion number induced and its connection with the anomaly of parity.

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe1−xSex, intercalated FeSe materials, and monolayer FeSe and FeTe1−xSex on SrTiO3. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.

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