Comparison of wave-mixing processes in rarefied gas and QED vacuum using numerical simulations

We study the conditions required to distinguish laser-induced nonlinear quantum electrodynamics (QED) effects in vacuum from competing signals due to interactions of laser pulses with ionized residual gas. The latter is inevitably present in vacuum chambers where experiments are performed because the vacuum is never perfect and there is always some residual pressure. The rarefied gas contribution is modeled statistically using the 1D-1V Vlasov-Maxwell system, while vacuum nonlinearities are described within the weak-field expansion of the Heisenberg-Euler effective action. In both cases, photon spectra from wave-mixing processes are evaluated by solving numerically the resulting partial differential equations using a semi-Lagrangian scheme. We consider short pulses in co- and counter-propagating configurations, allowing us to identify the laser intensities and vacuum pressures for which the vacuum signal dominates. These results provide quantitative guidance for future all-optical experiments aiming to detect light-by-light scattering in vacuum.