Rydberg Excitation in Infrared-Laser-Pulses Using a Stiffness Reducing Spectral Approach (Contemporary Mathematics, 2025)
An effective spectral method based on square-integrable (L2) functions is presented to solve the Time- Dependent Schröedinger Equation (TDSE) of an atom in the presence of a strong, rapidly oscillating laser field. The corresponding system of differential equations is extremely stiff. To reduce this problem, the wave function is expanded in an eigenvector basis to the unperturbed atomic Hamiltonian operator and highly oscillating eigenvectors are excluded. An explicit solution method is used for the time propagation, which significantly reduces the demands on Information Technology (IT) resources compared to implicit methods. To avoid numerical reflections due to a finite eigenvector basis, a Complex Absorbing Potential (CAP) is implemented, which is adapted to the L2 function space. The absorption properties of the CAP are investigated. The method is applied to the ionization and excitation of atomic H in few cycle laser fields. The Rydberg excitation spectrum after the passage of a laser pulse is calculated and discussed. The results show a pronounced dependence of the Rydberg occupation probabilities on the laser parameters and allow selective control.
Keywords: TDSE; stiffness; Coulomb-Sturmians; L2expansion; tunnel ionization