Objectives:

• Testing and improving the strong-field approximation for atoms
• Above-threshold ionization into states with very low energy, especially for long wavelengths of the driving laser
• Formulating and testing the strong-field approximation for simple molecules

The interaction of atoms, let alone of molecules and clusters, with intense laser fields poses a problem of tremendous complexity: the many-electron dynamics, which by themselves already exceed the capabilities of presently available computers for all but the simplest atoms, are completely modified by the highly nonlinear interaction with the time-dependent laser field. An ab-initio approach via the solution of the time-dependent Schroedinger equation will remain restricted to the case of helium. In view of this, the strong-field approximation (SFA) in combination with the single-active-electron approximation provides a viable approach, which combines comparative simplicity with intuitive understanding and high predictive power. Briefly, the SFA neglects the interaction of the electron with the laser field while the electron is bound within the atom, and the interaction with the binding potential as soon as it is liberated.

The very simplest version of the SFA has been improved by

(i) allowing the liberated electron to interact once again (first-order Born approximation) with its parent ion, which allows for rescattering and especially backscattering.

(ii) replacing the single interaction of the liberated electron with the ion core by the (field-free) ion-specific T matrix (the so-called low-frequency approximation). This makes it possible to calculate atom-specific angle-resolved above-threshold ionization (ATI) spectra. Conversely, the analysis of experimentally observed spectra allows one to deduce the electron-ion cross section.

(iii) introducing the action of the Coulomb potential for the liberated electron along its way towards the detector.

The effect of the above improvements is still not completely satisfactory, not even for rare-gas atoms (D. B. Milosevic et al., J. Phys. B 43, 015401 (2010)). Future work will introduce a more realistic description of the final state of the liberated electron. The formalism will be applied to a variety of experimental observations: rescattering effects in photodetachment of negative ions, ionization into states with very low energy including negative energy (Rydberg states as final states), low-energy effects in ATI by long-wavelength lasers. For molecules, the theory will be compared with the results of alternative theoretical approaches and available experimental data, with and without fixed molecular orientation.

Fig. 1: False-color plot of the ionization rate of argon in the energy-angle plane (the energy is in multiples of the ponderomotive energy of the laser field; zero angle corresponds to emission in the direction of the laser polarization) calculated from the SFA in fisrt-order Born approximation (left-hand panel) and the low-frequency approximation (LFA) (right-hand panel). Only the LFA reproduces the zeroes in the angle-resolved spectrum. From Cerkic et al., Phys. Rev. A 79, 043413 (2009).

Fig. 2: Angle-resolved ATI spectra forN2 (left) and O2 (right) for fixed orientation of the molecular axis with respect to the laser polarization at angles 0° (1° for O2), 30°, 45°, 60°, and 90° (89° for O2) from top to bottom (the energy is in multiples of the ponderomotive energy of the laser field; zero angle corresponds to emission in the direction of the laser polarization). The broad depression that dominates most of the spectra is due to a destructive interference of four different quantum orbits that start from and return to either the same or different centers. For O2, it remains visible if the molecules are not aligned, and this has been experimentally observed. From M. Okunishi et al., Phys. Rev. Lett. 103, 043001 (2009).