Efficient Split-Lanczos propagator for strong-field ionization of atoms

Area of Science:

• Atomic Physics
• Quantum Mechanics
• Computational Chemistry

Background:

• High angular momentum partial waves are crucial for accurate numerical solutions of the time-dependent Schrödinger equation (TDSE).
• The standard Lanczos propagator requires very small time steps for convergence when dealing with strong laser-atom interactions, limiting computational efficiency.

Purpose of the Study:

• To develop a more efficient numerical method for solving the TDSE in strong-field atomic physics.
• To reduce the computational cost associated with high angular momentum partial waves in TDSE calculations.

Main Methods:

• The study introduces a modified Lanczos propagator, termed the Split-Lanczos propagator.
• This method involves separating the centrifugal potential from the Hamiltonian.
• The modified approach aims to mitigate the stiffness of the TDSE.

Main Results:

• The Split-Lanczos propagator successfully reduces the stiffness of the TDSE.
• This reduction allows for significantly larger time steps compared to the standard Lanczos propagator.
• Efficiency improvements exceeding 100 times were observed for large angular momentum calculations.

Conclusions:

• The Split-Lanczos propagator offers a substantial advancement in the numerical simulation of atom-laser interactions.
• This method provides a more computationally efficient alternative for problems involving high angular momentum partial waves.
• The findings pave the way for more complex and accurate simulations in strong-field physics.