Dissertationenhttps://kobra.uni-kassel.de:443/handle/123456789/2006022270452021-10-25T17:58:05Z2021-10-25T17:58:05ZMolecular-Frame Angular Distributions of Electrons Emitted by Photoionization and Interatomic Coulombic DecayMhamdi, Abirhttps://kobra.uni-kassel.de:443/handle/123456789/124002021-06-23T14:24:18Z2020-01-01T00:00:00ZThe continuous refinement of the experimental and theoretical methods to study the electron angular emission distributions, and particularly in a molecule frame of reference, have contributed to a keen understanding of the structure of molecules and have provided deeper insight into fundamental physical phenomena.
Revealing many details of the ionization dynamics, the molecular-frame angular distributions (MFADs) of emitted electrons have been an appealing research topic for the last two decades. Owing to the interesting physics taking place within few tens of electron volts above the ionization thresholds of molecules, the MFADs have mainly been studied in the low-energy regime. In addition, a broad interest has been devoted to the interatomic Coulombic decay (ICD) since its prediction in the late 1990s. This process appears to prevail everywhere as an ultrafast mechanism by which energy can be transferred from a given center to its environment. Presently, few studies have explored the MFADs of the ICD electrons, and thus very little is known about their angle-resolved spectra.
The present work aims at theoretically investigating the MFADs of electrons emitted by photoionization and interatomic Coulombic decay from small linear molecules. To this end, the electron discrete and continuum spectra in the investigated molecules were computed using the stationary Single Center method which is known to be a powerful tool for studying the angle-resolved ionization of molecules. The first part of this work concerns the examination of the quantum nature of valence holes in Ne2, and the core holes in CO2. Furthermore, smooth transformations of the MFADs in CO and N2 for photoelectron energies ranging between 10 and 1000 eV are studied. The second part is devoted to the investigation of the MFADs of ICD electrons in four noble gas dimers.
In Ne2, the influence of a spectator electron on the MFADs of resonant ICD electrons is examined. For HeNe, the present theoretical study provides unambiguous assignments of two different decay channels. Lastly, in He2 and NeAr, the present theory explores the strong dependence of the MFADs of ICD electrons on the electronic properties of the decaying states. This research work is the fruit of a close collaboration between theory and experiment.
2020-01-01T00:00:00ZMhamdi, AbirThe continuous refinement of the experimental and theoretical methods to study the electron angular emission distributions, and particularly in a molecule frame of reference, have contributed to a keen understanding of the structure of molecules and have provided deeper insight into fundamental physical phenomena.
Revealing many details of the ionization dynamics, the molecular-frame angular distributions (MFADs) of emitted electrons have been an appealing research topic for the last two decades. Owing to the interesting physics taking place within few tens of electron volts above the ionization thresholds of molecules, the MFADs have mainly been studied in the low-energy regime. In addition, a broad interest has been devoted to the interatomic Coulombic decay (ICD) since its prediction in the late 1990s. This process appears to prevail everywhere as an ultrafast mechanism by which energy can be transferred from a given center to its environment. Presently, few studies have explored the MFADs of the ICD electrons, and thus very little is known about their angle-resolved spectra.
The present work aims at theoretically investigating the MFADs of electrons emitted by photoionization and interatomic Coulombic decay from small linear molecules. To this end, the electron discrete and continuum spectra in the investigated molecules were computed using the stationary Single Center method which is known to be a powerful tool for studying the angle-resolved ionization of molecules. The first part of this work concerns the examination of the quantum nature of valence holes in Ne2, and the core holes in CO2. Furthermore, smooth transformations of the MFADs in CO and N2 for photoelectron energies ranging between 10 and 1000 eV are studied. The second part is devoted to the investigation of the MFADs of ICD electrons in four noble gas dimers.
In Ne2, the influence of a spectator electron on the MFADs of resonant ICD electrons is examined. For HeNe, the present theoretical study provides unambiguous assignments of two different decay channels. Lastly, in He2 and NeAr, the present theory explores the strong dependence of the MFADs of ICD electrons on the electronic properties of the decaying states. This research work is the fruit of a close collaboration between theory and experiment.Electron Dynamics Driven by Intense Coherent Femtosecond Laser Pulses: Dynamic Interference in Atoms and Photoelectron Circular Dichroism in Chiral MoleculesMüller, Anne Dorotheehttps://kobra.uni-kassel.de:443/handle/123456789/110172020-01-28T09:51:09Z2018-12-01T00:00:00ZSince humans have begun to explore nature, they came up with new ways and tools, which
have been permanently improved. At some point, those tools allowed to look into the
microworld and to study the quantum nature of matter. One of such tools to explore the
quantum world is the light amplification by stimulated emission of radiation (laser). Since the
first lasers were built almost 60 years ago, their capabilities improved permanently, allowing
the study of hitherto-unknown physical phenomena. Two of such phenomena, the dynamic
interference and the multiphoton photoelectron circular dichroism (PECD), are the subjects of
the present theoretical work.
The dynamic interference appears when matter is exposed to intense coherent laser pulses.
It is an analogy of the double-slit experiment in time, when two photoelectron wave packets
of the same kinetic energy emitted at different moments in time along the pulse superimpose.
The resulting interference patterns in the electron spectra are well understood theoretically,
but an experimental verification of this effect is still absent. In this work, two open tasks
relevant for the theoretical description of the dynamic interference are studied. The first task
is to investigate the dynamic interference for systems, which are amenable to experiments at
modern laser facilities. The second task is to reinvestigate available theoretical results, which
were obtained with simple models, by numerically exact methods. For this purpose, a new
method, the time-dependent single center method (TDSC), was developed and tested as a
part of this work.
The TDSC method solves the time-dependent Schrödinger equation in spherical coordinates
for single-active-electron or two-electron wave packets driven in an ionic potential by a laser
pulse. It is also used in this work to study the multiphoton PECD in the electron spectra of
chiral molecules in the single-active-electron approximation. The PECD is the difference of
the angular emission distributions of electrons emitted by chiral molecules ionized by right-
and left-handed circularly polarized light, and it consists in the forward/backward asymmetry
in the photoelectron emission. The PECD is extensively studied in the one-photon ionization
regime, both, experimentally and theoretically. For the multiphoton ionization, many new
experiments are available, but a reliable quantitative theoretical interpretation of those
observations is still missing. In order to explain available experimental results, in this work,
the TDSC method is first tested on the model methane-like chiral system and then applied to
study the three- and four-photon PECD in real chiral molecules Camphor and Fenchone.
2018-12-01T00:00:00ZMüller, Anne DorotheeSince humans have begun to explore nature, they came up with new ways and tools, which
have been permanently improved. At some point, those tools allowed to look into the
microworld and to study the quantum nature of matter. One of such tools to explore the
quantum world is the light amplification by stimulated emission of radiation (laser). Since the
first lasers were built almost 60 years ago, their capabilities improved permanently, allowing
the study of hitherto-unknown physical phenomena. Two of such phenomena, the dynamic
interference and the multiphoton photoelectron circular dichroism (PECD), are the subjects of
the present theoretical work.
The dynamic interference appears when matter is exposed to intense coherent laser pulses.
It is an analogy of the double-slit experiment in time, when two photoelectron wave packets
of the same kinetic energy emitted at different moments in time along the pulse superimpose.
The resulting interference patterns in the electron spectra are well understood theoretically,
but an experimental verification of this effect is still absent. In this work, two open tasks
relevant for the theoretical description of the dynamic interference are studied. The first task
is to investigate the dynamic interference for systems, which are amenable to experiments at
modern laser facilities. The second task is to reinvestigate available theoretical results, which
were obtained with simple models, by numerically exact methods. For this purpose, a new
method, the time-dependent single center method (TDSC), was developed and tested as a
part of this work.
The TDSC method solves the time-dependent Schrödinger equation in spherical coordinates
for single-active-electron or two-electron wave packets driven in an ionic potential by a laser
pulse. It is also used in this work to study the multiphoton PECD in the electron spectra of
chiral molecules in the single-active-electron approximation. The PECD is the difference of
the angular emission distributions of electrons emitted by chiral molecules ionized by right-
and left-handed circularly polarized light, and it consists in the forward/backward asymmetry
in the photoelectron emission. The PECD is extensively studied in the one-photon ionization
regime, both, experimentally and theoretically. For the multiphoton ionization, many new
experiments are available, but a reliable quantitative theoretical interpretation of those
observations is still missing. In order to explain available experimental results, in this work,
the TDSC method is first tested on the model methane-like chiral system and then applied to
study the three- and four-photon PECD in real chiral molecules Camphor and Fenchone.Finite-Elemente-Mehrgitter von MolekülenBeck, Oliverhttps://kobra.uni-kassel.de:443/handle/123456789/20140519454302021-06-23T14:24:24Z2014-05-19T00:00:00ZIm Rahmen der Dichtefunktionaltheorie wurden Orbitalfunktionale wie z.B. B3LYP entwickelt. Diese lassen sich mit der „optimized effective potential“ – Methode selbstkonsistent auswerten. Während sie früher nur im 1D-Fall genau berechnet werden konnte, entwickelten Kümmel und Perdew eine Methode, bei der das OEP-Problem unter Verwendung einer Differentialgleichung selbstkonsistent gelöst werden kann. In dieser Arbeit wird ein Finite-Elemente-Mehrgitter-Verfahren verwendet, um die entstehenden Gleichungen zu lösen und damit Energien, Dichten und Ionisationsenergien für Atome und zweiatomige Moleküle zu berechnen. Als Orbitalfunktional wird dabei der „exakte Austausch“ verwendet; das Programm ist aber leicht auf jedes beliebige Funktional erweiterbar.
Für das Be-Atom ließ sich mit 8.Ordnung –FEM die Gesamtenergien etwa um 2 Größenordnungen genauer berechnen als der Finite-Differenzen-Code von Makmal et al. Für die Eigenwerte und die Eigenschaften der Atome N und Ne wurde die Genauigkeit anderer numerischer Methoden erreicht. Die Rechenzeit wuchs erwartungsgemäß linear mit der Punktzahl. Trotz recht langsamer scf-Konvergenz wurden für das Molekül LiH Genauigkeiten wie bei FD und bei HF um 2-3 Größenordnungen bessere als mit Basismethoden erzielt. Damit zeigt sich, dass auf diese Weise benchmark-Rechnungen durchgeführt werden können. Diese dürften wegen der schnellen Konvergenz über der Punktzahl und dem geringen Zeitaufwand auch auf schwerere Systeme ausweitbar sein.
2014-05-19T00:00:00ZBeck, OliverIm Rahmen der Dichtefunktionaltheorie wurden Orbitalfunktionale wie z.B. B3LYP entwickelt. Diese lassen sich mit der „optimized effective potential“ – Methode selbstkonsistent auswerten. Während sie früher nur im 1D-Fall genau berechnet werden konnte, entwickelten Kümmel und Perdew eine Methode, bei der das OEP-Problem unter Verwendung einer Differentialgleichung selbstkonsistent gelöst werden kann. In dieser Arbeit wird ein Finite-Elemente-Mehrgitter-Verfahren verwendet, um die entstehenden Gleichungen zu lösen und damit Energien, Dichten und Ionisationsenergien für Atome und zweiatomige Moleküle zu berechnen. Als Orbitalfunktional wird dabei der „exakte Austausch“ verwendet; das Programm ist aber leicht auf jedes beliebige Funktional erweiterbar.
Für das Be-Atom ließ sich mit 8.Ordnung –FEM die Gesamtenergien etwa um 2 Größenordnungen genauer berechnen als der Finite-Differenzen-Code von Makmal et al. Für die Eigenwerte und die Eigenschaften der Atome N und Ne wurde die Genauigkeit anderer numerischer Methoden erreicht. Die Rechenzeit wuchs erwartungsgemäß linear mit der Punktzahl. Trotz recht langsamer scf-Konvergenz wurden für das Molekül LiH Genauigkeiten wie bei FD und bei HF um 2-3 Größenordnungen bessere als mit Basismethoden erzielt. Damit zeigt sich, dass auf diese Weise benchmark-Rechnungen durchgeführt werden können. Diese dürften wegen der schnellen Konvergenz über der Punktzahl und dem geringen Zeitaufwand auch auf schwerere Systeme ausweitbar sein.Entanglement analysis of atomic processes and quantum registersRadtke, Thomashttps://kobra.uni-kassel.de:443/handle/123456789/20080924240742021-06-23T14:24:24Z2008-09-24T13:00:32ZDuring recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise.
Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register.
Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments.
To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations.
As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement.
Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.
2008-09-24T13:00:32ZRadtke, ThomasDuring recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise.
Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register.
Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments.
To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations.
As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement.
Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.