The main goal of the project is the development of an efficient numerical code that serves to calculate the high-harmonic generation (HHG) spectrum of a molecular system that interacts with a XUV/x-ray attosecond/femtosecond pulse. One may think in this final goal as two connected approaches: a numerical method to calculate HHG for molecules and a numerical method to simulate the time-dynamics of the system after interacting with a XUV/x-ray pulse. Here we are interested in investigating with high-harmonic spectroscopy (HHS) core-hole excitations, but the developed numerical tools are general and can be applied to a wide range of physical scenarios. In the following, we describe some applications we have been working on during the progress of this project.

 

Development of a time-dependent approach for core-shell excitations: ultrafast x-ray spectroscopy

For describing the excitations of XUV/x-ray pulses with a physical system, one needs first to calculate the electronic structure of highly excited states with holes in core shells, the so-called core-hole states. We are investigating the possibility to implement a multi-center Gaussian-basis quantum chemistry code, which allows the calculation of core-hole states, into a time-dependent Schrödinger equation (TDSE) in order to be able to describe ultrafast x-ray spectroscopy experiments.

 

Time-dependent SFA and HHG in molecules

In HHS, an intense infrared source is used to probe the system via measuring the emitted HHG spectrum. The non-linear interaction with the IR field results in a complex harmonic spectrum that encodes the transient dynamics of the target system. This technique has been proven to resolve nuclear structure and dynamics in molecules with attosecond resolution. The strong-field approximation (SFA) is a successful theory that has been used to calculate the HHG emission. Here, we are investigating the possibility to create a general time-dependent code, within the SFA theory, in which a second pulse (e.g. an attosecond x-ray pulse) creates a particular dynamics and then the HHG emission provides information of the dynamics.

 

Charge migration and electron transfer coherence with core electrons

Charge migration refers to the fast motion of electrons driven purely by electron effects right after photo-excitation, occurring between hundreds of attoseconds to few femtoseconds. In first theoretical papers, charge migration was conceived as a non-equilibrium charge distribution in the molecular cation after sudden ionization of an electron in the valence shell. Here, we are investigating the possibility to induce charge migration but when a core electron is removed. This may create an electron transfer that could be followed via HHS.

 

Two-dimensional materials: HHG in graphene

Another interesting avenue is the possibility to induce HHG in two-dimensional materials. If the laser is polarized perpendicular to the thin material layer, one should expect that the behavior is not so different to the atomic case. However, if the polarization is parallel to the thin layer, then we should expect that the electronic structure complexity of the material starts to play a major role. In particular, we are studying the possibility to generate HHG in graphene with mid-IR ultrashort pulses and investigate the underlying mechanism of the nonlinear response of the thin-layer material.