# Strong-field response of complex systems

**Principal investigator: **Prof. Dr. Stefanie Gräfe

**Project manager/Main research: **Dr. Martin Richter

**Researchers:** Prof. Dr. Stefanie Gräfe, Dr. Martin Richter

**Title of research project: **Strong-field response of complex systems

**Funding: **EU (European Research Council, Project QUEM-CHEM)

**Project partners: **FSU Jena, TU Wien

**Project endurance: **04.2020 – 04.2022

**Project area: **307-02

**Cluster: **Noctua Cluster at PC2

**Software: **Octopus, GPAW, Atomistic Simulation Environment (ASE)

**Introduction:**

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. 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] and 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] 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.

**Methods:**

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) as realized in the Octopus program package. The numerical propagation of time-dependent Kohn-Sham orbitals is done in short (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.

**Results:**

On the Noctua compute cluster, we have so far 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. Electron dynamics were propagated for >100 fs (17600 steps of about 6 as). A complex absorbing boundary at the periphery of the simulation box monitored electronic density leaving the nanoparticle. As the integrated electronic charge (i.e. number of electrons) of the system did not significantly change during simulation runs, we assured that the resulting HHG spectra originate from the current dynamics within the nanoparticles only. The resulting HHG spectrum of a 64-atom nanoparticle is shown in comparison to a bulk simulation of CdSe using peri-odic 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.

**Discussion:**

Higher harmonic generation is a process, in which atoms and molecules interacting with high intensity laser pulses emit radiation at frequencies that are multiples of the incident laser frequency. For small gas-phase systems in a time-dependent incident laser field, HHG is usually explained via the so-called three-step model, that includes (1.) tunneling ionization of an electron out of the potential well of the atom/molecule, (2.) acceleration of the electron due to interaction with the external field and (3.) recombination of the electron with the parent ion, which leads to emission. In solids, the HHG processes are much more complex since electrons do not freely propagate through space but in the conduction band(s), giving rise to inter- and intra-band currents. Although much more challenging for theoretical scientific efforts, solids provide a promising route towards bright and compact HHG sources since their electron density is much higher than that of gas phase systems. As computation of the spectra is extremely demanding, HPC facilities such as the PC² computer cluster are of utmost importance for our work.

**Outlook:**

Our goal is a systematic investigation of the effect of different laser and material parameters on the resulting HHG spectra using a rigorous state-of-the-art ab-initio approach based on the rtTDDFT.

[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).