Strong-field Response of complex Systems

The interaction of light with matter covers a large number of physical phenomena that we literally see in our everyday life, as it is responsible (amongst other things) for the vision process. Early scientists mostly focused on investigations of electromagnetic radiation in the visible range and at low intensities, where material polarization responds linearly to incident electromagnetic fields. With the advent of tunable, high-intensity light sources, the investigation of nonlinear effects, where the material polarization changes in a nonlinear fashion with electric field of incident light, became accessible. The interactions of intense light and matter give rise to a plethora of interesting phenomena such as multiphoton absorption/ionization, laser induced electron diffraction [1,2] or second-, third or higher-order harmonic generation. Spectral signatures however, become increasingly complex when investigating quantum systems and their dynamics in strong fields. So far, most of our understanding of strong-field effects is based on the simplest atoms and molecules such as H2 and H2+ or simple model systems. [3,4]

Goals and Methods
This project aims at simulating and interpreting the strong-field dynamics of real molecules and larger systems in a rigorous real-space real-time approach including non-linear strong-field effects such as photoionization and high-order harmonic generation (HHG) of systems ranging from small (chiral) molecules over nano-systems to the condensed phase. Our goal is to advance the theoretical description of light-driven dynamics of multi-electron systems. To this end, we employ a state-of-the-art numerical description of the strong-field response of solids and molecules based on the real-time real-space time-dependent density functional theory (rtTDDFT). The numerical propagation of time-dependent Kohn-Sham orbitals is done in attosecond time steps, typically requiring several ten-thousand consecutive propagation steps for covering a short excitation pulse of about 50-100 fs duration. This comprehensive microscopic description of light-matter interaction allows for a detailed investigation of non-linear effects such as high harmonic generation (HHG) or photo electron emission. As computation of the spectra is extremely demanding (up to 100,000 CPU hours per simulation run), HPC facilities such as the computer clusters at PC2 are of utmost importance for our work.

Results
On the Noctua 1 compute cluster at the Paderborn Center for Parallel Computing (PC2), we have performed simulations of CdSe nanoparticles with different particle sizes (4-64 atoms, corresponding to about 0.5-1.5 nm diameter). Figure 1 shows the different employed structures including spherical boxes of varying size that were discretized with an equidistant grid with more than 7 million mesh points. The resulting HHG spectrum of a 64-atom nanoparticle is shown in comparison to a bulk simulation of CdSe using periodic boundary conditions in Figure 2. The simulation of bulk CdSe clearly shows peaks for low orders (1st – the fundamental – and the 3rd harmonic order). From 5th to 9th order the signal is rather noisy, which might be due to a high joint density of states in this energy window. For higher energies, clear peaks of odd harmonics are visible up to the 17th harmonic. In contrast to this, the HHG spectrum of 1.5 nm (64 atom) CdSe nanoparticles looks very different. Clearly, the confinement significantly reduces the contribution of high orders (>5) to the spectrum.

References:
•    [1] K Amini, M Sclafani, T Steinle, AT Le, A Sanchez, C Müller, J Steinmetzer, L Yue, JRM Saavedra, M Hemmer, N Lewenstein, R Moshammer, T Pfeifer, MG Pullen, J Ullrich, B Wolter, R Moszynski, FJ García de Abajo, CD Lin, S Gräfe, J Biegert «Imaging the Renner–Teller effect using laser-induced electron diffraction», PNAS 116 (17), 8173 (2019).
•    [2] B Wolter, MG Pullen, AT Le, M Baudisch, K Doblhoff-Dier, A Senftleben, M Hemmer, CD Schröter, J Ullrich, T Pfeifer, R Moshammer, S Gräfe, O Vendrell, CD Lin, J Biegert «Ultrafast electron diffraction imaging of bond breaking in acetylene"», Science 354, 308 (2016).
•    [3] L Yue, P Wustelt, AM Sayler, F Oppermann, M Lein, GG Paulus and S Gräfe «Strong-field polarizability-enhanced dissociative ionization», Phys. Rev. A 98(4), 043418 (2018).
•    [4] M Paul and S Gräfe «Strong-field ionization dynamics of asymmetric equilateral triatomic model molecules in circularly polarized laser fields», Phys. Rev. A 99(5), 053414 (2019).