Uncertainty Estimates for Theoretical Atomic and Molecular Data

Sources of uncertainty are reviewed for calculated atomic and molecular data that are important for plasma modeling: atomic and molecular structure and cross sections for electron-atom, electron-molecule, and heavy particle collisions. We concentrate on model uncertainties due to approximations to the fundamental many-body quantum mechanical equations and we aim to provide guidelines to estimate uncertainties as a routine part of computations of data for structure and scattering.Comment: 65 pages, 18 Figures, 3 Tables. J. Phys. D: Appl. Phys. Final accepted versio

Microscopy of quantum many-body systems out of equilibrium

Quantensimulatoren können die Grenzen von analytischen und numerischen Methoden überwinden und detaillierte Informationen über stark korrelierte Vielteilchensysteme liefern. Für die experimentelle Erforschung komplexer Problemstellungen bieten Quantengase vielfältige Möglichkeiten und profitieren von der herausragenden Isolation von externen Störungen. Diese Promotionsarbeit befasst sich mit dem experimentellen Studium von Quantensystemen, die kontrolliert aus dem Gleichgewicht gebracht werden. Mit Einzelplatz aufgelöster Abbildung von bosonischen Rubidium Atomen in optischen Gittern wird die zeitliche Entwicklung festgehalten. Quantenmagnetismus ist der erste behandelte Schwerpunkt in dieser Arbeit. Zuerst zeigen wir, dass im Regime von starker Wechselwirkung,in welchem sich ein Mott Isolator bildet, ein zwei komponentiges Gas exzellent das Heisenberg Model simuliert. Hierzu vermessen wir die kohärente Ausbreitung eines Magnons mit der spinselektiven Abbildung nach einer lokalen Anregung eines einzelnen Spins. Spinprojektionen auf die $z$-Achse und den Äquator der Bloch-Kugel belegen die Entstehung und Propagation von verschränkten Zuständen. Detaillierte Informationen werden in diesem Experiment durch eine neu entwickelte Abbildung gewonnen, welche an Stern-Gerlach Messungen angelehnt ist. Bei der Anregung zweier benachbarter Spins wird des Weiteren die Entstehung gebundener Zustände beobachtet und deren Ausbreitungsgeschwindigkeit sowie Zerfallszeit charakterisiert. In weiterführenden Messungen erzeugen wir hochangeregte Spiralzustände, die in einen homogenen Gleichgewichtszustand zerfallen und keine kohärente Zeitentwicklung aufweisen. Die Geschwindigkeit der beobachteten Zerfälle ist abhängig von der Windungsstärke und weist in eindimensionalen Systemen auf ein diffusives Verhalten hin. Im Gegensatz dazu deuten die Ergebnisse in zweidimensionalen Systemen auf ein sub-diffusive Propagation hin. Der zweite Schwerpunkt dieser Arbeit behandelt die Thermalisierung von hoch angeregten Systemen. Wir ermitteln wie stark eine zusätzlich eingestrahlte computergenerierte zufällige Potentiallandschaft sein muss, um zu einer Lokalisierung der Atome zu führen. Von diesen entstehenden lokalisierten Vielteilchenzustände wird die Zerfallslänge der Dichteverteilung bestimmt, welche am Phasenübergang eine Divergenz zeigt. Die in dieser Arbeit beschriebenen Experimente demonstrieren unterschiedliche Realisierungen von Quantensimulationen. Viele weitere Effekte im Bereich der Quantenmechanik können mit der hier dargelegten Technik untersucht werden. Weitere Messungen profitieren insbesondere von der nachgewiesenen präzisen Anfangszustandspräparation, basierend auf der Kontrolle jedes einzelnen Atomes in wechselwirkenden Vielteilchensystemen, und der ortsaufgelösten Erfassung von einzelnen Atomen. Dieses wird in Zukunft einen wesentlichen Beitrag zur Informationsgewinnung über komplexe verschränkte Systeme liefern können.Quantum simulators can overcome the limits of analytical and numerical methods and deliver detailed information about strongly correlated many-body systems. For the experimental exploration of complex problems, quantum gases offer versatile possibilities and profit from the outstanding isolation from external disturbances. This doctoral thesis deals with the experimental study of quantum systems, which are controllably moved out of equilibrium. The temporal evolution is recorded with single-site resolved imaging of bosonic Rubidium atoms in optical lattices. Quantum magnetism is the first examined main topic of this thesis. At first, we reveal that a two component gas is well suited to simulate the Heisenberg model in the regime of strong interaction and under the formation of a Mott insulating state. Therefore, we survey, after a local excitation of a single spin, the coherent expansion of a magnon with spin selective imaging. Utilizing spin projections on the $z$-axis and the equator of the Bloch sphere, the creation and propagation of entangled states is observed. In this experiment, detailed information are extracted with the newly developed Stern-Gerlach like imaging. Furthermore, the emergence and expansion velocity of bound states after the excitation of two neighboring spins is surveyed. The experiments are extended to highly excited spiral states, which decay to homogeneous equilibrium states and do not indicate coherent evolution. The determined decay rate depends on the winding strength and manifests a diffusive behavior in one dimensional systems. In contrast, measurements in two dimensional systems point towards a sub-diffusive evolution. The second main focus of this theses is the thermalization of highly excited states. We investigate how strong an additional computer generated random potential needs to be in order to lead to localization of the atoms. The decay length of the corresponding density distribution of the arising many-body localized states is quantified, which diverges at the phase transition. The experiments characterized in this thesis demonstrate different realizations of quantum simulation. Several further effects in the field of quantum mechanics can be studied with the here demonstrated techniques. Further research will in particular benefit from the precise initial state manipulation, based on the control of every single atom within the many-body interacting system, and the spin selective spatial resolved detection of single atoms. In the future, this will yield a substantial contribution to the acquisition of information on complex entangled systems

Geração de números verdadeiramente aleatórios baseados em ruído quântico

Quantum Random Number Generators (QRNGs) promise information-theoretic security by exploring the intrinsic probabilistic properties of quantum mechanics. In practice, their security frequently relies on a number of assumptions over physical devices. In this thesis, a randomness generation framework that explores the amplitude quadrature fluctuations of a vacuum state was analyzed. It employs a homodyne measurement scheme, which can be implemented with low-cost components, and shows potential for high performance with remarkable stability. A mathematical description of all necessary stages was provided as security proof, considering the quantization noise introduced by the analog-to-digital converter. The impact of experimental limitations, such as the digitizer resolution or the presence of excess noise due to an unbalanced detection, was characterized. Moreover, we propose a framework to estimate the excess entropy introduced by an unbalanced detection, and its high impact within the Shannon entropy model was experimentally verified. Furthermore, a real-time dedicated QRNG scheme was implemented and validated. The variance characterization curve of the homodyne detector was measured, and the quantum fluctuations were determined to be preponderant for an impinging power PLO < 45.7mW. By estimating the worst-case min-entropy conditioned on the electronic noise, approximately 8.39 true random bits can be extracted from each sample, yielding a maximum generation rate of 8.23 Gbps. With a lengthcompatible Toeplitz-hashing algorithm, these can be extracted at 75 Mbps with an upper security bound of 2−105, which illustrates the quality of this implementation. Moreover, the generation scheme was validated and verified to pass all the statistical tests of the NIST, DieHarder, and TestU01’s SmallCrush batteries, as well as most of TestU01’s Crush evaluations. Finally, we propose a framework for time-interleaving the entropy source within a classical communication channel, which removes the need for a dedicated generation device. After assessing the conditions where quantum noise is dominant, support for generation rates up to 1.3 Gbps was observed. The random bitstream was subjected to the NIST randomness test suite and consistently passed all evaluations. Moreover, a clean quadrature phase shift keying constellation was recovered, which supports the multi-purpose function of the scheme.Geradores quânticos de números aleatórios (QRNGs) prometem sistemas informação-teoricamente seguros explorando as propriedades intrinsecamente probabilísticas da mecânica quântica. No entanto, experimentalmente, um conjunto de pressupostos é tipicamente imposto sobre os dispositivos experimentais. Nesta dissertação, analisou-se uma abordagem para geração de números aleatórios que explora as flutuações de amplitude em quadratura de um estado vácuo. Para tal, recorre-se a um esquema de deteção homodina que permite um elevado desempenho e estabilidade, requerendo apenas dispositivos de baixo custo. Um modelo matemático das diferentes etapas do gerador foi desenvolvido de forma a fornecer uma prova de segurança, e contabilizou-se o ruído de discretização introduzido pelo conversor analógico-digital. Adicionalmente, caracterizou-se o impacto de imperfeições experimentais como a resolução do conversor analógico-digital e a presença de ruído em excesso como consequência de uma deteção não balanceada. Uma abordagem para estimar esta contribuição no modelo de entropia de Shannon foi também proposta e experimentalmente verificada. Adicionalmente, uma implementação em tempo-real foi caracterizada. A curva de caracterização do detetor homodino foi experimentalmente verificada, e uma preponderância de ruído quântico observado para potências óticas inferiores a 45.7mW. Através de uma estimativa da min-entropy condicionada ao ruído eletrónico, aproximadamente 8.39 bits por medição podem ser extraídos, o que corresponde a uma taxa de geração máxima de 8.23 Gbps. Estes podem ser extraídos a uma taxa de 75 Mbps com um parâmetro de segurança de 2−105, ilustrativo da qualidade desta implementação, através de um algoritmo eficiente de multiplicação de matrizes de Toeplitz. Posteriormente, o esquema foi validado, passando todos os testes estatísticos das baterias NIST, DieHarder, e SmallCrush, assim como a maioria das avaliações contidas na bateria Crush. Por último, foi proposta uma abordagem para integrar esta fonte de entropia num canal de comunicação clássico, removendo desta forma a necessidade de uma implementação dedicada. Após avaliação das condições de preponderância do ruído quântico, foram observadas taxas de geração até 1.3 Gbps. Os números obtidos foram também submetidos à bateria de testes do NIST, passando consistentemente todas as avaliações. Adicionalmente, a constelação de modulação de amplitude em quadratura obtida viabiliza a operação multifuncional do sistema.Mestrado em Engenharia Físic

Scanning tunneling microscopy of Bi₂Se₃ and CuxBi₂Se₃

textRecently, Bi₂Se₃ was added to a new class of materials known as topological insulators. While several studies have provided tantalizing hints towards novel physical properties, such as backscatter suppression and spin-polarized transport, several concerns remain in actual materials. In particular, high defect densities, strong surface band bending, and potential fluctuations have been observed. Here, scanning tunneling microscopy and spectroscopy are used to reveal surface effects in Bi₂Se₃ and CuxBi₂Se₃. First, a detailed examination of defects in bulk-grown samples is described. Then, I provide an analysis of molecular beam epitaxy results, done in collaboration with colleague Yuxuan Chen. Following this, I provide a detailed study of individual point defects in Cu-doped Bi₂Se₃ and examine how Cu is incorporated into the Bi₂Se₃ lattice. Finally, through spectroscopic analysis, a novel depth-sensitive measurement of the local band bending field is developed. Furthermore, for the first time, fluctuations of the Dirac point can be correlated to specific near-surface defects, namely Se vacancies. These analyses provide valuable insights into the preparation of future samples for the investigation of topological insulators.Materials Science and Engineerin

Nuclear Lattice Investigations of Fundamental Symmetries

Fundamental symmetries (and their violations) play a significant role in active experimental searches of Beyond the Standard Model (BSM) signatures. An example of such phenomena is the neutron Electric Dipole Moment (EDM), a measurement of which would be evidence for Charge-Parity (CP) violation not attributable to the basic description of the Standard Model (SM). Another example is the strange scalar quark content of the nucleon and its coupling to Weakly Interacting Massive Particles (WIMPs), which is a candidate model for Dark Matter (DM). The theoretical understanding of such processes is fraught with uncertainties and uncontrolled approximations. On the other hand, methods within nuclear physics, such as Lattice Quantum Chromodynamics (LQCD) and Effective Field Theories (EFT), are emerging as powerful tools for calculating non-perturbatively various types of nuclear and hadronic observables. This research effort will use such tools to investigate phenomena related to BSM physics induced within light nuclear systems. As opposed to LQCD which deal with quarks and gluons, in Nuclear Lattice Effective Field Theory (NLEFT) individual nucleons – protons and neutrons – form the degrees of freedom. From the symmetries of Quantum Chromodynamics (QCD), one can derive the most general interaction-structures allowed on the level of these individual nucleons. In general, this includes an infinite number of possible interactions. Utilizing the framework of EFTs, more specifically for this work Chiral Perturbation Theory (χPT), one can systematically expand the nuclear behavior in a finite set of relevant nuclear interactions with a quantifiable accuracy. Fundamental parameters of this theory are related to experiments or LQCD computations. Using this set of effective nuclear interaction-structures, one can describe many-nucleon systems by simulating the quantum behavior of each involved individual nucleon. The 'ab initio' method NLEFT introduces a spatial lattice which is finite in its volume (FV) and allows to exploit powerful numerical tools in the form of statistical Hybrid Monte Carlo (HMC) algorithms. The uncertainty of all three approximations – the statistical sampling, the finite volume and the discretization of space – can be analytically understood and used to make a realistic and accurate estimation of associated uncertainty. In the first part of the thesis, χPT is used to derive nuclear interactions with a possible BSM candidate up to Next-to-Leading Order (NLO) in the specific case of scalar interactions between DM and quarks or gluons. Following this analysis, Nuclear Matrix- Elements (NMEs) are presented for light nuclei (2H, 3He and 3H), including a complete uncertainty estimation. These results will eventually serve as the benchmark for the many-body computations. In the second part of this thesis, the framework of NLEFT is briefly presented. It is shown how one can increase the accuracy of NLEFT by incorporating few-body forces in a non-perturbative manner. Finite-Volume (FV) and discretization effects are investigated and estimated for BSM NME on the lattice. Furthermore, it is displayed how different boundary conditions can be used to decrease the size of FV effects and extend the scope of available lattice momenta to the range of physical interest

Numerical Analyses on Ultra-Lean Si Engine Integrated In a Hybrid Powertrain to Reduce Noxious Emissions

The topic of the research activity, presented in this Ph.D. thesis, is the numerical investigation, through a hierarchical simulation-level approach, of innovative SI engines, possibly suitable for hybrid powertrains and featured by a reduced CO2 impact. For this purpose, firstly a conventional naturally aspirated small Spark Ignition (SI) engine has been analyzed, assessing the model predictivity of engine performance, combustion, and pollutant emissions. In the second stage, several engine architectures working in ultra-lean conditions have been numerically investigated, with particular emphasis on unburned hydrocarbon emission estimation. Then, an innovative 4-cylinder SI engine, equipped with an active pre-chamber (PC) ignition system and operating with an ultra-lean mixture, has been studied. Finally, this last engine has been virtually embedded into a hybrid electric vehicle (HEV), belonging to the C segment, to estimate CO2 and pollutant emissions along the worldwide harmonized light vehicles test cycle (WLTC) and Real Driving Emission (RDE)-compliant cycles and to verify the EU regulation fulfillment