Computational modelling of the semi-classical quantum vacuum in 3D

Abstract The global commissioning of multi-Petawatt laser systems provides unprecedented access to ultra-high electromagnetic fields for probing the quantum vacuum. However, current analytical models are limited, necessitating large-scale simulations for experimental validation. Here, we present real-time three-dimensional simulations of two quantum vacuum effects, using a semi-classical numerical solver based on the Heisenberg-Euler Lagrangian. The simulation model is benchmarked against vacuum birefringence analytical results with a counter-propagating setup. Simulations results of both plane-wave and Gaussian pulses are consistent with theoretical predictions. The solver is then applied to four-wave mixing using three Gaussian pulses with real-time information on the harmonic evolution. We provide quantitative explanations for the astigmatism in the output and produce precise estimates of the interaction time and size. Results are compared with the plane-wave model and previous numerical results. This solver paves the way for in-depth investigations of a broad spectrum of quantum vacuum effects in any arbitrary laser setup.