Attosecond quantum dynamics as an optimization problem

The 2023 Nobel Prize for Physics was awarded to Agostini, Krausz, and L'Huillier for their seminal contributions to the development of attosecond laser pulses by means of high-harmonic generation. Attosecond laser pulses allow us to monitor electronic motion in atoms, molecules, and materials, providing insights into and potentially control the quantum dynamics that govern chemical processes. Moreover, attosecond spectroscopy gives new opportunities to study the structure and dynamics of short-lived matter-antimatter complexes, which may provide clues to fundamental research questions such as the nature of dark matter. Needless to say, simulations are crucial for understanding, interpreting, and predicting the quantum dynamics. However, accurate simulations are highly challenging since - ionization processes are almost unavoidable due to the inherently broad intensity distribution in the frequency domain - the population of numerous electronic states of neutral and potentially multiple ionized species necessitates computational models beyond the Born-Oppenheimer approximation - the ensuing coupled electronic-nuclear dynamics likely leads to bond breaking Highly adaptive computational models that do not rely on assumptions about the possible dynamics are needed to tackle these challenges. In this talk, I will present a novel approach developed at the Hylleraas Centre over the past $2$--$3$ years. It is based on recasting the time-dependent Schrödinger equation as an optimization problem with built-in wave-function error control and, thus, full adaptivity [1,2]. Using wave-function models expressed as linear combinations of Gaussians [3], it is demonstrated that high-harmonic generation processes and rovibrational dynamics can be simulated with high accuracy. [1] S. Kvaal, C. Lasser, T. B. Pedersen, and L. Adamowicz, No need for a grid: Adaptive fully-flexible gaussians for the time-dependent Schrödinger equation, arXiv:2207.00271 [2] S. E. Schrader, H. E. Kristiansen, T. B. Pedersen, and S. Kvaal, Time evolution as an optimization problem: The hydrogen atom in strong laser fields in a basis of time-dependent Gaussian wave packets, arXiv:2404.07699 \newline [3] A. P. Wozniak, L. Adamowicz, T. B. Pedersen, and S. Kvaal, Gaussians for Electronic and Rovibrational Quantum Dynamics, J. Phys. Chem. A 128, 3659-3671 (2024)