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 · doi:10.1063/5.0213576
Abstract
Recent advances in attosecond science have made it increasingly important to develop stable, reliable and accurate algorithms and methods to model the time evolution of atoms and molecules in intense laser fields. A key process in attosecond science is high-harmonic generation, which is challenging to model with fixed Gaussian basis sets, as it produces high-energy electrons, with a resulting rapidly varying and highly oscillatory wave function that extends over dozens of ångström. Recently, Rothe's method, where time evolution is rephrased as an optimization problem, has been applied to the one-dimensional Schrödinger equation. Here, we apply Rothe's method to the hydrogen wave function and demonstrate that complex-valued Gaussian wave packets with time-dependent width, center, and momentum parameters are able to reproduce spectra obtained from essentially exact grid calculations for high-harmonic generation with only 50-181 Gaussians for field strengths up to W/cm. This paves the way for the inclusion of continuum contributions into real-time, time-dependent electronic-structure theory with Gaussian basis sets for strong fields, and eventually accurate simulations of the time evolution of molecules without the Born-Oppenheimer approximation.
arXiv comment20 pages, 10 figures
References in corpus (20)
- SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
- Deep neural network solution of the electronic Schrödinger equation
- Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
- Multiconfiguration Time-Dependent Hartree-Fock Treatment of Electronic and Nuclear Dynamics in Diatomic Molecules
- Modeling electron dynamics coupled to continuum states in finite volumes
- A general approach to few-cycle intense laser interactions with complex atoms
- Gaussian continuum basis functions for calculating high-harmonic generation spectra
- Theory of projections with non-orthogonal basis sets: Partitioning techniques and effective Hamiltonians
- Local-in-time error in variational quantum dynamics
- On the mathematical treatment of the Born-Oppenheimer approximation
- Ab initio lifetime correction to scattering states for time-dependent electronic-structure calculations with incomplete basis sets
- Functional Tensor-Train Chebyshev Method for Multidimensional Quantum Dynamics Simulations
- A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation
- Quantum dynamics and spectroscopy of dihalogens in solid matrices. I. Efficient simulation of the photodynamics of the embedded cluster using the G-MCTDH method
- An optimized absorbing potential for ultrafast, strong-field problems
- Gaussians for Electronic and Rovibrational Quantum Dynamics
- Transient spectroscopy from time-dependent electronic-structure theory without multipole expansions
- Two-particle coalescence conditions revisited
- No need for a grid: Adaptive fully-flexible gaussians for the time-dependent Schrödinger equation
- Pseudospectral discretization of the time-dependent Schrödinger equation