Enhanced vacuum pair production by combination of two spatially separated electric fields

The effective enhancement of the pair production rate using a subcritical electromagnetic field is an active area of interest in quantum electrodynamics. Enhanced pair production was investigated using the Dirac-Heisenberg-Wigner (DHW) formalism with spatially separated electric fields. Symmetric and asymmetric combinations of two separate electric fields with the same temporal shape were considered. The interplay and dynamical assistance between the fields were examined from a numerical perspective to elucidate the effects of the spatial distance and asymmetry of the field on the pair production efficiency. For the symmetric combination, the total particle number was reduced with an increase in the distance between the two fields up to one Compton length and then remained constant with distance. For the asymmetric combination, the total number of created pairs increased significantly up to a distance of one Compton length. It was also determined that not only was the separation distance crucial for enhancing pair production, but the spatial field asymmetries were also important, both of which had nontrivial effects on the particle momentum distribution. Finally, we have studied the validity of the DHW and analytical approximation in the spatially separated two electric fields. We found that the analytical approximation could almost estimate the DHW results.