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Ultrafast coherent electron dynamics in solids
Ultrafast coherent electron dynamics in solids
Due to recent developments in high-field laser systems, intense sub-cycle pulses can be generated on a routine basis in laser laboratories around the world. The electric fields originating from such few-femtosecond laser pulses can be on the same order of magnitude as the internal electric fields in bulk, crystalline solids. Due to the short duration of the pulses the laser fluence can remain below the damage threshold of the material. This paves the way for exploring strong-field effects in solids in a non-destructive regime experimentally, and hence motivates theoretical investigations in this field. This thesis is about numerical studies of strong-field effects in insulators and semiconductors. In particular, calculations are performed at a quantum mechanical level in order to examine the importance of quantum coherence in light-matter interactions in the strong-field regime. The dynamics of electrons in one-dimensional spatially periodic potentials excited by laser pulses was simulated. Upon introducing phenomenological decoherence into the dynamical equations, it was found that the optical responses calculated from geometric phases of mixed quantum system were in excellent agreement with conventional approaches for evaluating the optically induced current and polarization response. The excellent agreement even extended to highly non-linear, strong-field regimes, and motivated the development of a numerical method to simulate open quantum mechanical systems governed by spatially periodic Hamiltonians subject to perturbations with broken translation symmetry. Density functional theory was also employed to obtain wave functions from first principles for a number of materials, for which time-resolved optical responses were calculated. Field-induced intraband motion was found to modify the interband transitions significantly at high field strengths for transitions that would otherwise be resonant at low field strengths. For semiconducting materials like GaAs, where the transition elements are strongly peaked at the centre of the Brillouin zone, a step-like excitation mechanism was revealed at field strengths on the order of 0.5 V/Å. Similar ab initio methods were used to model the optical Faraday effect in the insulating, wide band gap material Al2O3 for few-cycle pulses. The magnitude of the effect was predicted using non-perturbative methods. Time-dependent calculations confirmed that a near-instantaneous response is to be expected., Es wurde die Dynamik von Elektronen in Festkörpern, die durch intensive, Subzykluslaserpulse erregt werden numerisch untersucht. Die Berechnungen wurden auf der quantenmechanischen Ebene und in verschiedenen, unabhängigen elektromagnetischen Eichungen ausgeführt. Zuerst wurde die Dynamik der Elektronen in eindimensionalen periodischen Potentialen berechnet um die Gültigket von neuen numerischen Verfahren zu bestätigen. Eines dieser Verfahren ermöglicht Simulationen von räumlich periodischen, gemischten Quantensystemen mit Hamilton-Operatoren mit gebrochener Translationssymmetrie. Durch Anwendung der Dichtefunktionaltheorie wurden Wellenfunktionen für Halbleiter und Insulatoren hergeleitet. Danach konnt der zeitliche Verlauf des optisch induzierten Strom nach ersten Prinzipien bestimmt werden. Die Bedeutung von intraband Bewegungen für Elektronen im halbleitenden Material GaAs wurde ebenfalls untersucht. Bei Erregung mit resonanten Pulsen konnte ein stufenförmiger Anregungsmechanismus beobachtet werden. Ähnliche Methoden wurden verwendet, um die Größe des optischen Faraday-Effektes in einem Insulator mit einer Bandlücke, grösser der Fotonenergie beider Pulse, zu bestimmen. Diese Berechnungen deuten darauf hin, dass ultraschnelle Kontrolle der optisch induzierten Chiralität möglich ist.
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Wismer, Michael Sejer
2018
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Wismer, Michael Sejer (2018): Ultrafast coherent electron dynamics in solids. Dissertation, LMU München: Faculty of Physics
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Abstract

Due to recent developments in high-field laser systems, intense sub-cycle pulses can be generated on a routine basis in laser laboratories around the world. The electric fields originating from such few-femtosecond laser pulses can be on the same order of magnitude as the internal electric fields in bulk, crystalline solids. Due to the short duration of the pulses the laser fluence can remain below the damage threshold of the material. This paves the way for exploring strong-field effects in solids in a non-destructive regime experimentally, and hence motivates theoretical investigations in this field. This thesis is about numerical studies of strong-field effects in insulators and semiconductors. In particular, calculations are performed at a quantum mechanical level in order to examine the importance of quantum coherence in light-matter interactions in the strong-field regime. The dynamics of electrons in one-dimensional spatially periodic potentials excited by laser pulses was simulated. Upon introducing phenomenological decoherence into the dynamical equations, it was found that the optical responses calculated from geometric phases of mixed quantum system were in excellent agreement with conventional approaches for evaluating the optically induced current and polarization response. The excellent agreement even extended to highly non-linear, strong-field regimes, and motivated the development of a numerical method to simulate open quantum mechanical systems governed by spatially periodic Hamiltonians subject to perturbations with broken translation symmetry. Density functional theory was also employed to obtain wave functions from first principles for a number of materials, for which time-resolved optical responses were calculated. Field-induced intraband motion was found to modify the interband transitions significantly at high field strengths for transitions that would otherwise be resonant at low field strengths. For semiconducting materials like GaAs, where the transition elements are strongly peaked at the centre of the Brillouin zone, a step-like excitation mechanism was revealed at field strengths on the order of 0.5 V/Å. Similar ab initio methods were used to model the optical Faraday effect in the insulating, wide band gap material Al2O3 for few-cycle pulses. The magnitude of the effect was predicted using non-perturbative methods. Time-dependent calculations confirmed that a near-instantaneous response is to be expected.

Abstract

Es wurde die Dynamik von Elektronen in Festkörpern, die durch intensive, Subzykluslaserpulse erregt werden numerisch untersucht. Die Berechnungen wurden auf der quantenmechanischen Ebene und in verschiedenen, unabhängigen elektromagnetischen Eichungen ausgeführt. Zuerst wurde die Dynamik der Elektronen in eindimensionalen periodischen Potentialen berechnet um die Gültigket von neuen numerischen Verfahren zu bestätigen. Eines dieser Verfahren ermöglicht Simulationen von räumlich periodischen, gemischten Quantensystemen mit Hamilton-Operatoren mit gebrochener Translationssymmetrie. Durch Anwendung der Dichtefunktionaltheorie wurden Wellenfunktionen für Halbleiter und Insulatoren hergeleitet. Danach konnt der zeitliche Verlauf des optisch induzierten Strom nach ersten Prinzipien bestimmt werden. Die Bedeutung von intraband Bewegungen für Elektronen im halbleitenden Material GaAs wurde ebenfalls untersucht. Bei Erregung mit resonanten Pulsen konnte ein stufenförmiger Anregungsmechanismus beobachtet werden. Ähnliche Methoden wurden verwendet, um die Größe des optischen Faraday-Effektes in einem Insulator mit einer Bandlücke, grösser der Fotonenergie beider Pulse, zu bestimmen. Diese Berechnungen deuten darauf hin, dass ultraschnelle Kontrolle der optisch induzierten Chiralität möglich ist.