Universität Stuttgart
Permanent URI for this communityhttps://elib.uni-stuttgart.de/handle/11682/1
Browse
6 results
Search Results
Item Open Access Application of machine learning to find exceptional points(2023) Egenlauf, PatrickIn open quantum systems, resonances can occur. These are quasi-bound states which can decay. By introducing a complex scaling, e.g. according to Reinhardt, and thus non-Hermitian operators, the complex energy eigenvalues of the resonances can be calculated. Here, the real part represents their energy, while the imaginary part unveils their lifetime. Resonances can degenerate, where a special case is the so-called exceptional point (EP) at which not only the eigenvalues but also the eigenvectors degenerate. Thus, the two resonances coalesce at the EP. An isolated EP can be described by a two-dimensional matrix model. A property of such an EP is that the two associated eigenvalues exchange their positions after one adiabatic orbit in parameter space around the EP. In 2007 the existence of these EPs was proven for the hydrogen atom in electric and magnetic fields by Cartarius. Due to limitations especially in magnetic field strengths, EPs in the hydrogen atom are not experimentally accessible. In 2014, a remarkable discovery by Kazimierczuk et al. revealed a mesmerizing hydrogen-like spectrum within cuprous oxide. This revelation stemmed from the resemblance between an exciton, a quasi-particle in a semiconductor consisting of electron and hole, and their atomic counterpart, the hydrogen atom. However, the fact that the excitons are environed by cuprous oxide necessitated consideration of the band structure to precisely describe the observed spectrum. This discovery kindled excitement as it provided a rare opportunity to bridge the realms of experimental and theoretical physics, inviting an enthralling dialogue between theory and experiment. For cuprous oxide the field strengths to observe EPs of resonances with small quantum numbers are much lower compared to the field strengths for the hydrogen atom, which is why it is favorable to find EPs in this system. This was already done for a hydrogen-like model, but to obtain experimentally comparable results the above mentioned band structure terms need to be considered. However, this increases the computational cost drastically for each diagonalization of the Hamiltonian due to its complexity. The existing methods to find EPs are based on a Taylor expansion around the EP. Due to the computational expensive diagonalizations of the Hamiltonian, these methods are inefficient or even not applicable. Hence, a new method is required to accurately and efficiently identify EPs in cuprous oxide. Inspired by the remarkable advances in machine learning, especially within the realm of physics, a novel method on the foundation of Gaussian process regression (GPR) is developed. As a prominent member of the supervised machine learning family, GPR serves as a powerful and innovative approach to predict the positions of EPs in cuprous oxide. The used data to train a GPR model is obtained by simulations. Hence, the error is only due to numerical inaccuracies, which can be neglected. Unlike neural networks, GPR offers the advantage of precisely passing through the provided training points, which is a key motivation for its utilization. Yet, the optimization of the searching process goes beyond the new method. An efficient algorithm is devised to enhance the search for EPs in cuprous oxide, which contributes to the discovery of promising EPs and thus enables a possible experimental verification of these data.Item Open Access Multi-fidelity Bayesian machine learning for global optimization(2022) Kuchelmeister, ManuelThe computational optimization and exploration of materials is a challenging task, due to the high dimensionality of the search space and the high cost of accurate quantum mechanical calculations. To reduce the number of costly calculations, the Bayesian Optimization Structure Search (BOSS) has been developed. BOSS combines sample-efficient active learning with Gaussian process regression. This work introduces several multi-fidelity approaches that can reduce the number of costly, accurate calculations even further by incorporating information from inexpensive but less accurate calculations. Using the intrinsic model of coregionalization, BOSS samples data from multiple atomistic calculations based on quantum chemistry (Gaussian16, using CCSD(T)), density-functional theory (FHI-aims, using a PBE-exchange correlation functional) and force fields (AMBER18). Multi-fidelity BOSS samples both, lower and higher-fidelity calculations, while maintaining CCSD(T) accuracy for the global minimum inference. We tested our new multi-fidelity approaches on a 4D alanine conformer search. There, multi-fidelity BOSS has reduced the computational cost, measured in CPU hours, by up to 90%. We found that the efficiency of the approaches depends mostly on the correlation and the computational cost difference between the fidelities. These tests serve as a benchmark for the great potential that multi-fidelity learning can have to reduce the cost of expensive structure-search problems.Item Open Access Quantum kernel methods and applications to differential equations(2024) Flórez Ablan, RobertoQuantum computers have the potential to surpass classical computers in specific tasks, promising advantages in many fields. Machine Learning (ML), a domain with significant societal impact, is a key area of interest for exploring the applications of quantum computing. Here, we investigate two research directions aimed at understanding how current quantum computers can be used to solve ML problems. First, we study Quantum Kernels (QKs). By calculating inner products between quantum states, QKs can be used to define similarity measures between points. QKs are a promising approach to Quantum Machine Learning (QML) but, in general, they have not been shown to outperform classical ML methods. A key reason for this is that QKs suffer from the exponential concentration problem. As the number of qubits increases, the kernel matrices become similar to the identity matrix, preventing generalization. One strategy to alleviate the exponential concentration problem is to rescale the data points that enter the quantum model. This technique is known as bandwidth tuning and has been shown to allow generalization in QKs. However, it has been numerically demonstrated that using this method results in QKs that cannot provide a quantum advantage over classical methods. In this thesis, we propose an explanation for this phenomenon. We show that due to the size of the rescaling factors, the QKs become similar to polynomial and RBF kernels, which are classically tractable. Second, we implemented a Differential Equation (DE) solver based on variational quantum methods. A Quantum Neural Network (QNN) or QK, is used to represent an ansatz for the solution of a DE. The DE information is included into a loss function, which is minimized using a classical optimizer. In the case of a QK, the optimized parameters are the coefficients of a linear combination of QKs evaluated at the data points. In the case of a QNN, the optimized parameters are the phases of the quantum gates. The QNN implementation was included into the open-source QML python library sQUlearn. A preliminary hyperparameter study was conducted for QKs. Based on our limited investigation, we conclude that QKs leveraging the fidelity between quantum states, known as Fidelity Quantum Kernels (FQKs), demonstrate superior performance compared to those employing a semi-classical approach, referred to as Projected Quantum Kernels (PQKs).Item Open Access Wave functions and oscillator strengths in a two-band model for Rydberg excitons in cuprous oxide quantum wells(2024) Kühner, LeonRydberg physics is the study of systems involving highly excited states of atoms or molecules, known as Rydberg states. In these states, one or more electrons are far from the nucleus, giving the atom exaggerated properties such as large size, long lifetimes, and strong interactions with external fields and nearby particles. These unique features make Rydberg systems a valuable tool for exploring a range of phenomena in atomic physics, quantum optics, and condensed matter physics. They are particularly important for applications in quantum technologies, such as quantum simulation and computation and sensing. Another candidate for Rydberg physics are excitons. When an electron is excited from the valence band to the conduction band the electron in the conduction band and the positively charged hole in the valance band can form hydrogen-like states. Excitons in cuprous oxide, though with relatively low principal quantum numbers, have already been detected in the 1950s by Gross and Hayashi. In 2014 it was possible to measure exciton states with a principal quantum number up to n=25, since then the exciton Rydberg physics has attracted large attention. These states have radii in the range of microns. Rydberg excitons show a large variety of phenomena which do not occur in atomic physics, for example the structure of the valence band leads to a breaking of the spherical symmetry, the spin-orbit coupling leads to the occurrence of a green and yellow exciton series, and central-cell corrections have effects on even parity states. Other effects occur when Rydberg excitons are confined in quantum wells. Such effects have been experimentally observed in GaAs. Thin layers in cuprous oxide have already been produced. Therefore, the observation of excitons in cuprous oxide quantum wells is expected soon. Excitons in quantum wells allow one to investigate the dimensional crossover from three-dimensional systems with weak confinement to two-dimensional systems with strong confinement. For this system the energy spectra have already been computed and effects like overlapping Rydberg series and resonances have been discussed. The theoretical calculations have so far been restricted to the computation of eigenenergies in a hydrogen-like model ignoring the impact of the valence band. The aim of this thesis is to study the effects of Rydberg excitons which rely on the wave functions. Such effects are the behavior of wave functions from weak to strong confinement and the quenching behavior in these regions that are visualized in this thesis. Numerically the wave functions are expanded in a B-spline basis. Also resonances above the first scattering threshold as well as bound states in the continuum above this threshold are visualized. Further, wave functions that undergo an avoided crossing are investigated. Another aspect is the influence of electrostatic effects for exciton states in quantum wells. These lead to the appearance of surface excitons, which can be seen in the visualization of these states. Oscillator strengths are investigated and rely on the behavior of the wave function. In our system the oscillator strengths are no longer translational invariant. Ultimately, this work provides a comprehensive exploration of Rydberg exciton wave functions, which could be instrumental in advancing the use of these systems in emerging quantum applications.Item Open Access Relation between ionized gas kinematics and Lyman-alpha observables in galaxies(2023) Schaible, Anna LenaIn the early universe, galaxies can be detected via their Lyman-alpha emission, which is redshifted in the optical wavelength range (1215:7 Å, 2p to 1s transition of hydrogen). However, not all galaxies in the early universe show Ly-alpha emission. The reasons for this are only partly understood. Neutral hydrogen has a high absorption cross-section for Ly-alpha photons. In galaxies, this leads to a spatial and spectral random walk of the Ly-alpha photons in the interstellar-medium (ISM), which increases the absorption probability by interstellar dust of the Ly-alpha photons and is a main reason that not all galaxies show Ly-alpha emission. The random walk of the photons leads to a diffusion spatially and spectrally, which makes it harder to detect the Ly-alpha radiation. The study of spatially resolved observations with samples of galaxies with and without Ly-alpha emission can give important insights in the prevailing ISM conditions for promoting Ly-alpha escape. Such studies can be performed well on a sample of nearby galaxies, which resemble galaxies from the early universe. For nearby galaxies multi-wavelength observations can be obtained, which allow a detailed study of the ISM conditions influencing the Ly-alpha escape. This thesis uses integral field spectroscopic data obtained from the Potsdam Multi Aperture Spectrophotometer at the Calar Alto 3.5 m telescope to investigate the kinematics of ionized gas in 42 nearby galaxies with young stellar populations and active star formation. We use the Balmer-alpha line (6562:8 Å, 3 to 2 transition) as a tracer for the intrinsic Ly-alpha radiation field in the galaxies. Additionally, we use photometric observations from the Hubble Space Telescope for the Lyman-alpha Reference Sample (LARS) and Extended Lyman-alpha Reference Sample (eLARS) galaxies to obtain the Ly-alpha observables. Turbulent kinematics may shift emitting and absorbing material out of resonance, increasing the likelihood of Ly-alpha escaping from galaxies. To test this hypothesis, we perform a global analysis of the kinematic properties of the LARS and eLARS sample, along with their Ly-alpha observables. We derive velocity fields and velocity dispersion maps from the H-alpha observations, and then we focus on the relation between integrated kinematic quantities and the Ly-alpha observables (luminosity, equivalent width and escape fraction). Prior to the analysis, we apply a newly introduced gradient method to correct our data for point spread function smearing. Our results from Kendall tau statistic tests between ionized gas kinematics and Ly-alpha observables support the hypothesis that galaxies dominated by turbulent kinematics, rather than ordered motions, favor the escape of Ly-alpha. Furthermore, we apply a multivariate linear regression method on the Ly-alpha observables luminosity, equivalent width and escape fraction to asses the importance of the integrated kinematic parameters. Again, we find that intrinsic velocity dispersion is an important parameter in affecting the emergence of Ly-alpha emission. We therefore suggest that dispersion dominated ionized gas kinematics may be a necessary, but not a sufficient, condition for facilitating Ly-alpha escape.Item Open Access Excitons in cuprous oxide quantum wells : computation of spectra in consideration of the valence band structure(2025) Scheuler, NiklasIn finite-sized crystals, quantum confinement causes excitons to exhibit properties that differ significantly from those in bulk systems. Recent studies on excitons in bulk cuprous oxide have demonstrated that an accurate description requires accounting for the material's complex valence-band structure. By contrast, existing work on excitons in quantum wells has largely relied on simplified hydrogen-like models that neglect these band-structure effects. The aim of this thesis is to bridge this gap. Using the Luttinger-Kohn model, we derive the complete Hamiltonian for excitons in cuprous oxide quantum wells, fully incorporating the band structure. The symmetry properties of the resulting system are analyzed. Numerical results obtained from diagonalizing the Hamiltonian using B-spline basis functions reveal energy shifts and the lifting of degeneracies arising from the coupling terms of the complex valence band. Furthermore, we compute relative oscillator strengths of excitonic transitions induced by circularly polarized light.