## Bachelor theses

### Quantum dynamics in a strong laser field

The interaction between a model atom and an intense laser pulse can be investigated by solving numerically the one-dimensional Schrödinger equation. Typical workflows of these quantum mechanical calculations consist of three steps, first, the computation of the initial groundstate via time-independent Schrödinger eq., second, the propagation of this electron wave packet in the electric field of the laser pulse and third the extraction of measurable observables from the final wave packet like electron spectra, High Harmonics and ionization probabilities. Possible key aspects could be the investigation of laser frequency dependent excitation and ionization of atoms, attosecond laser pulses, ionization from combined infrared and short-wavelength laser pulses and specific laser field driven electron acceleration processes with connection to the classical three-step model.

### Cluster ionization dynamics (IR, XUV, X-ray)

The interaction of clusters with intense ultrashort laserpulses show a fundamental difference in the ionization process when switching from infrared pulses to short-wavelength free-electron-laser based XUV (extrem-ultraviolet) radiation. In the infrared regime the ionization is initiated by tunnel ionization with subsequent very efficient laser heating e.g. by inverse bremsstrahlung and resonant collective energy deposition. For XUV-pulses single photon absorption governs the ionization of the clusters whereas ponderomotive effects are suppressed. In short, the field-dominated cluster dynamics at optical frequencies becomes photon-dominated in the XUV domain.

For both regimes there are multitude of interesting questions for the bachelor thesis, regarding to the ionization and expanding of the cluster and the development of a transient nanoplasma inside the system. Furthermore pump-probe szenarios provide the time-dependent investigation of the cluster evolution and open the room for a lot of interesting analyses.

For metal clusters the investigation of the many-particle dynamics can be numerically done with a semiclassical approach of a Thomas-Fermi-Vlasov molecular dynamics simulation.

Another possibiltity is a fully classical molecular dynamics simulation where quantum effects like photon-absorption and tunnelionization are considered by rate equations. The latter is usually used for rare gas clusters.

### FEL single-shot imaging

The availibility of intense femtosecond pulses at short wavelength from free electron lasers (FELs) has enabled the experimental investigation of structure and dynamics of nanosystems via coherent single shot diffractive imaging. Corresponding theoretical analyses of light scattering and diffraction from nanosystems are typically done with Mie theory. However this method is limited to spherical and homogeneous objects.

This limitation can be avoided by using the Green‘s function theory, a microscopic approach to describe singleshot diffractive imaging. Via solving numerically the corresponding Dyson equation systems of any shape can be treated and further effects can be incorporated like plasma wave dynamics and absorption, which becomes important for large, opaque matter.

Possible topics of the bachelor thesis can be a systematic study how the initial cluster geometry and the absorption effect change the resulting scattering image.

### Quantum confinement in clusters

Systems in the range of only a few nanometers show often features which change strongly with the actual size and exhibit a quantized character where every single atom in the system counts. As an example sodium clusters show enhanced stability and therefore higher detection probability for specific constituent counts, the so-called magic numbers, which can be traced back to closed electronic shells. These quantum-size-effects can be investigated numerically in the bachelor thesis via simulation of a spherical jellium model for metal clusters. The aim of the work is to acquire experience in calculating the quantum mechanical groundstate of a many-particle system with density functional theory and to apply these calculations to basic problems in the field of cluster physics.