Schwinger pair production in inhomogeneous electric fields with symmetrical frequency chirp

Pair production in inhomogeneous electric fields with symmetrical frequency chirp is studied numerically using the Dirac-Heisenberg-Wigner formalism. We investigate high- and low-frequency modes and consider two carrier envelope phases. Momentum spectrum is sensitive to chirp causing different interference effect for different spatial scales as well as the carrier phase of the external field. The reduced particle number is in general enhanced with increasing chirp. The effect of spatial scale of the field on the reduced particle number is also examined. It is found that it is enhanced at small spatial scale but is almost unchangeable at large spatial scales for the considered field parameters. On the other hand, at small spatial scale, the reduced particle number is enhanced by one or two orders when chirp is applied with the exception of cosine low-frequency field which is only a few times larger. Moreover it is found that the reduced particle number is further increased by symmetrical chirp at about two times by comparing to the usual asymmetrical chirp in high frequency field.