eTraj.jl: Trajectory-based simulation for strong-field ionization

Abstract

The dynamics of light-matter interactions in the realm of strong-field ionization has been a focal point and has attracted widespread interest. We present the eTraj.jl program package, designed to implement established classical/semiclassical trajectory-based methods to determine the photoelectron momentum distribution resulting from strong-field ionization of both atoms and molecules. The program operates within a unified theoretical framework that separates the trajectory-based computation into two stages: initial-condition preparation and trajectory evolution. For initial-condition preparation, we provide several methods, including the Strong-Field Approximation with Saddle-Point Approximation (SFA-SPA), SFA-SPA with Non-adiabatic Expansion (SFA-SPANE), and the Ammosov-Delone-Krainov theory (ADK), with atomic and molecular variants, as well as the Weak-Field Asymptotic Theory (WFAT) for molecules. For trajectory evolution, available options are Classical Trajectory Monte-Carlo (CTMC), which employs purely classical electron trajectories, and the Quantum Trajectory Monte-Carlo (QTMC) and Semi-Classical Two-Step model (SCTS), which include the quantum phase during trajectory evolution. The program is a versatile, efficient, flexible, and out-of-the-box solution for trajectory-based simulations for strong-field ionization. It is designed with user-friendliness in mind and is expected to serve as a valuable and powerful tool for the community of strong-field physics.

Program summary

Program title: eTraj.jl

CPC Library link to program files: https://doi.org/10.17632/33fm297cz4.1

Developer's repository link: https://github.com/TheStarAlight/eTraj.jl

Licensing provisions: Apache-2.0

Programming language: Julia

Nature of problem: Atoms and molecules exposed in an intense laser field go through complex processes of ionization through mechanisms such as multi-photon ionization and tunneling ionization. The trajectory-based methods are powerful tools for simulating these processes, and have considerable advantages over the time-dependent Schrödinger equation (TDSE) and the strong-field approximation (SFA). However, the community lacks a unified theoretical framework for trajectory-based methods, and there are no public-available code that implements the schemes.

Solution method: We developed a general, efficient, flexible, and out-of-the-box solution for trajectory-based simulation program named after eTraj.jl using the Julia programming language. This program conducts trajectory-based classical/semiclassical simulations of photoelectron dynamics under the single-active-electron approximation and the Born-Oppenheimer approximation. It supports multiple methods, including the SFA-SPA, SFA-SPANE, ADK and WFAT for initial condition preparation. Additionally, it incorporates the CTMC, QTMC and SCTS methods for trajectory evolution. The program is written in a clear and concise manner, and features versatility, extensibility, and usability.

Additional comments including restrictions and unusual features: A detailed documentation is available at https://thestaralight.github.io/eTraj.jl/stable/. The package has been tested for compatibility with Julia versions 1.9 to 1.11 and is expected to remain compatible with newer Julia versions released after the test date.