Unified Strong-Field Dynamics Simulations from Atoms to Heterostructures

Simulating intense laser-matter interactions requires solving the time-dependent Schrödinger equation (TDSE) under extreme conditions. While homogeneous atomic systems use a standard Laplacian kinetic operator, semiconductor heterostructures feature spatially varying effective masses and sharp material interfaces. In these systems, standard operators fail to conserve probability current and generate unphysical interface reflections. Existing software packages typically specialize in either constant-mass atomic calculations or specific coordinate systems, leaving a gap for a unified, high-performance solver that rigorously handles the BenDaniel-Duke (BDD) effective-mass operator alongside arbitrary potentials and laser fields.

The authors present TDSE-Z, a framework built on a weak-form Galerkin discretization of the Hermitian BDD operator using geometry-adapted B-spline meshes. This approach naturally enforces the continuity of both the wavefunction and probability current across mass discontinuities without requiring explicit interface boundary conditions. To balance high resolution near Coulomb cusps and bound states with sparse allocation in the asymptotic continuum, the framework implements six non-uniform coordinate grading strategies. The architecture utilizes PETSc, SLEPc, and PetIGA, supporting GPU offloading for static eigensolvers and CPU-optimized parallel MPI execution for time propagation.

The authors validate the static position-dependent-mass eigensolver against the analytical Quesne PDM model and a realistic GaAs/Al0.3Ga0.7As double quantum well, where computed tunnel splittings follow Wentzel-Kramers-Brillouin theory at the sub-percent level. The time-propagation engine is validated on constant-mass systems by accurately reproducing high-harmonic generation spectra in atomic benchmarks and confirming strong-scaling efficiency across hundreds of CPU cores.