Electron rearrangement upon removal of one electron occurs on very fast – attosecond – time scales. Ultrafast dynamics of this process determines the shape of the hole after ionization, its further evolution and is largely unknown. In this project, we develop theoretical and computational methods that will allow one to use high harmonic spectroscopy to get insight into dynamics of electron rearrangement in molecules during ionization in strong laser fields.

High harmonic emission occurs when an electron, liberated from a molecule by an incident intense laser field, gains energy from the field and recombines with the hole left in the molecule. The emission provides a snapshot of the structure and dynamics of the recombining system, encoded in the amplitudes, phases and polarization of the harmonic light.

High harmonic spectroscopy combines sub-Angstrom spatial and attosecond temporal resolution. Spatial resolution comes from Angstrom wave-length of the recombining electron and temporal resolution comes from the attosecond duration of the recombination event.

In the language of pump-probe spectroscopy, strong-field ionization acts as a 'pump' and recombination acts as a 'probe'. Recombination occurs within a fraction of the laser cycle after ionization. The time of ionization is linked to the time of recombination, the latter is mapped onto the harmonic number. The shape of the hole at the time of recombination determines harmonic amplitudes, phases and polarizations. Thus, each harmonic makes a snapshot of the hole dynamics for a different 'pump-probe' delay, providing a 'frame' for the attosecond 'movie'. The time interval between the frames, which is about 100 asec, determines temporal resolution.

By looking at harmonic amplitudes and phases for different intensities of the laser field we reconstruct the initial shape of the hole upon strong field ionization and its further dynamics for different molecules, gaining insight into the attosecond dynamics of multielectron rearrangement in strong laser fields. Our long-term goal is to develop solid theoretical foundation that will turn HHG spectroscopy from exotic method into a quantitative spectroscopic tool.

Theoretical ambitions include understanding and modeling of intense-field ionization of molecules, including polarization of the core. This requires analysis of

• Laser-induced non-adiabatic multi-electron excitations in the neutral, including excitation of charge transfer and autoionizing states, which open new ionization pathways;
• Coupling of multiple ionization continua in atoms and molecules during ionization; Electron-molecule scattering in strong laser field
• Modeling and reconstructing multi-electron dynamics on the sub optical cycle time-scale
• Decoupling temporal and spatial information in harmonic spectra