Chirp-wave Expansion of the Electron Wavefunctions in Atoms

The description of the electron wavefunctions in atoms is generalized to the fractional Fourier series. This method introduces a continuous and infinite number of chirp basis sets with linear variation of the frequency to expand the wavefunctions, in which plane-waves are a special case. The chirp characteristics of each basis set can be adjusted through a single parameter. Thus, the basis set cutoff can be optimized variationally. The approach is tested with the expansion of the electron wavefunctions in atoms, and it is shown that chirp basis sets substantially improve the convergence in the description of the electron density. We have found that the natural oscillations of the electron core states are efficiently described in chirp-waves

Attosecond chirp-encoded dynamics of light nuclei Attosecond chirp-encoded dynamics of light nuclei

International audienceWe study the spectral phase of high-order harmonic emission as an observable for probing ultrafast nuclear dynamics after the ionization of a molecule. Using a strong-field approximation theory that includes nuclear dynamics, we relate the harmonic phase to the phase of the overlap integral of the nuclear wavefunctions of the initial neutral molecule and the molecular ion after an attosecond probe delay. We determine experimentally the group delay of the high harmonic emission from D 2 and H 2 molecules, which allows us to verify the relation between harmonic frequency and the attosecond delay. The small difference in the harmonic phase between H 2 and D 2 calculated theoretically is consistent with our experimental results

Attosecond Coherent Control of Symmetry Breaking and Restoration in Atoms and Molecules

Symmetry is a fundamental phenomenon in science, and symmetry breaking is often the origin of subsequent processes which are important in chemistry, physics and biology. As is well-known, a laser pulse can break the electronic symmetry in atoms and molecules by creating a superposition of electronic eigenstates with different irreducible representations, which typically initiates attosecond ultrafast charge migration. In the first part of this dissertation, an original theory of coherent laser control is proposed to induce the symmetry restoration of the electronic structure in atoms and molecules after symmetry breaking, with application to the oriented benzene molecule and to the ^{87}Rb atom. Four different strategies are proposed and corresponding sufficient conditions for symmetry restoration are derived analytically. The numerical and analytical results agree perfectly with each other. Meanwhile, the theoretical predictions for the ^{87}Rb atom have been confirmed by experimental partners in Japan, by means of high contrast Ramsey interferometry with a precision of about three attoseconds. The second part is devoted to the electronic flux during charge migration in oriented benzene molecule. Two different patterns of adiabatic attosecond charge migration are investigated by laser induced preparation of two different non-aromatic superposition states. From the knowledge of the time-dependent many-body wave functions as a linear combination of many-electron wave functions obtained from conventional quantum chemistry calculations, we derive expressions for the time-evolution of the one-electron density and the electronic flux. This allows to specify the number of electrons flowing during a given charge migration process, together with the mechanism of charge migration. In conclusion, this dissertation shows, for the first time, that the symmetry of electronic structure in atoms and molecules can not only be broken but also be restored by means of simple laser pulses. The coherent control strategies require strict control over the time-dependent phases of electronic wave functions. In practice, the precision required is few attoseconds - much shorter than the timescale of charge migration in such systems. The analysis of charge migration indicates that similar superposition states may lead to quantitative differences in the number of electrons flowing.Symmetrie ist ein fundamentales Phänomen in der Naturwissenschaft, und Symmetriebrechung kann bedeutende Folgeprozesse in der Chemie, Physik und Biologie auslösen. Insbesondere kann die elektronische Symmetrie von Atomen und Molekülen bekanntlich durch einen Laserpuls gebrochen werden, und zwar durch die Erzeugung einer Superposition von elektronischen Zuständen mit verschiedenen irreduziblen Darstellungen - dies bewirkt dann typischerweise ultraschnelle Ladungsmigration auf der Attosekundenzeit-skala. Der erste Teil dieser Dissertation entwickelt eine grundlegende Theorie der kohärenten Laserpuls-Kontrolle mit dem Ziel der Wiederherstellung der elektronischen Symmetrie in Atomen und Molekülen nach Symmetriebrechung, mit Anwendungen auf das orientierte Benzolmolekül sowie auf das ^{87}Rb Atom. Es werden insgesamt vier Strategien zur Wiederherstellung der Symmetrie vorgestellt, wobei hinreichend zielführende Bedingungen analytisch hergeleitet werden. Die analytischen Ergebnisse stimmen exzellent mit numerischen Quantendynamiksimulationen überein. Die theoretischen Vorhersagen für das ^{87}Rb Atom wurden inzwischen mit Hilfe der hoch-kontrastreichen Ramsey Interferometrie von experimentellen Partnern in Japan mit einer Genauigkeit von drei Attosekunden bestätigt. Der zweite Teil untersucht den Elektronenfluss während der Ladungsmigration in orientierten Benzolmolekülen. Dabei werden für zwei unterschiedliche nicht-aromatische elektronische Superpositionszustände verschiedene Typen der adiabatischen Ladungsmigration auf der Attosekundenzeitskala aufgezeigt. Aus der Kenntnis der zeitabhängigen Viel-Elektronen-Wellenfunktion als Linearkombination elektronischer Eigenfunktionen, die mit Hilfe konventioneller Verfahren der Quantenchemie berechnet werden, werden Ausdrücke für die Zeit-Evolution der Ein-Elektronen-Dichte und des Elektronenflusses hergeleitet. Daraus ergibt sich die jeweilige Zahl der Elektronen, die zur Ladungsmigration beitragen, sowie der Mechanismus der Ladungsmigration. Zusammenfassend zeigt diese Dissertation erstmals, dass die Symmetrie der Elektronenstruktur von Atomen und Molekülen mit Hilfe von einfachen Laserpulsen nicht nur gebrochen, sondern auch wiederhergestellt werden kann. Die Strategien der kohärenten Laserkontrolle verlangen dazu die strenge Kontrolle der zeitabhängigen Phasen der elektronischen Wellenfunktionen. Praktische Anwendungen erfordern dafür eine zeitliche Genauigkeit von wenigen Attosekunden - also noch viel genauer als die ohnehin schon ultrakurze Zeitskala der Ladungsmigration. Untersuchungen der Ladungsmigration zeigen, dass vergleichbar ähnliche Superpositionen elektronischer Wellenfunktionen zu quantitativ verschiedenen Elektronenflusszahlen führen können

Adiabatic Formation of Rydberg Crystals with Chirped Laser Pulses

Ultracold atomic gases have been used extensively in recent years to realize textbook examples of condensed matter phenomena. Recently, phase transitions to ordered structures have been predicted for gases of highly excited, 'frozen' Rydberg atoms. Such Rydberg crystals are a model for dilute metallic solids with tunable lattice parameters, and provide access to a wide variety of fundamental phenomena. We investigate theoretically how such structures can be created in four distinct cold atomic systems, by using tailored laser-excitation in the presence of strong Rydberg-Rydberg interactions. We study in detail the experimental requirements and limitations for these systems, and characterize the basic properties of small crystalline Rydberg structures in one, two and three dimensions.Comment: 23 pages, 10 figures, MPIPKS-ITAMP Tandem Workshop, Cold Rydberg Gases and Ultracold Plasmas (CRYP10), Sept. 6-17, 201

Vibrational interference of Raman and high-harmonic generation pathways

Experiments have shown that the internal vibrational state of a molecule can affect the intensity of high harmonic light generated from that molecule. This paper presents a model which explains this modulation in terms of interference between different vibrational states occurring during the high harmonic process. In addition, a semiclassical model of the continuum electron propagation is developed which connects with rigorous treatments of the electron-ion scattering

Attosecond pulse characterization with coherent Rydberg wavepackets

We propose a new technique to fully characterize the temporal structure of extreme ultraviolet pulses by ionizing a bound coherent electronic wavepacket. The populated energy levels make it possible to interfere different spectral components leading to quantum beats in the photoelectron spectrum as a function of the delay between ionization and initiation of the wavepacket. The influence of the dipole phase, which is the main obstacle for state-of-the-art pulse characterization schemes, can be eliminated by angle integration of the photoelectron spectrum. We show that particularly atomic Rydberg wavepackets are ideal and that wavepackets involving multiple electronic states provide redundant information which can be used to cross-check the consistency of the phase reconstruction.Comment: 12 pages, 8 figure