Numerical simulations of the nonlinear quantum vacuum in the Heisenberg-Euler weak-field expansion

Abstract

The nonlinear Heisenberg-Euler theory is capable of describing the dynamics of vacuum polarization, a key prediction by quantum electrodynamics. Due to vast progress in the field of laser technology in recent years vacuum polarization can be triggered in the lab by colliding high-intensity laser pulses, leading to a variety of interesting novel phenomena. Since analytical methods for highly nonlinear problems are generally limited and since the experimental requirements for the detection of the signals from the nonlinear quantum vacuum are high, the need for numerical support is apparent. The paper presents a highly-accurate, efficient numerical scheme for solving the nonlinear Heisenberg-Euler equations in weak-field expansion up to six-photon interactions. Properties of the numerical scheme are discussed and an implementation accurate up to order thirteen in terms of spatial resolution is given. Simulations are presented and benchmarked with known analytical results. The versatility of the numerical solver is demonstrated by solving problems in complicated configurations.