Phase effect on and symmetry of pair production in inhomogeneous electric fields with chirping

The effect of the carrier envelope phase on electron-positron pair production is studied in a spatially inhomogeneous electric field with symmetrical frequency chirp. In both high- and low-frequency fields, we find periodic variations in the momentum spectrum and in the reduced particle number induced by the phase. In particular, the changes are more sensitive in the case of a low-frequency field. Under certain conditions, the reduced particle number can increase by over one order of magnitude, induced by the phase. Some different types of symmetries for two correlated phases and an interesting individual self-symmetry are revealed in the momentum spectrum. The combined roles of phase and chirping in the periodic and symmetrical behaviour of the momentum spectrum and the reduced particle number provide a more flexible parameter choice to control and optimise the pair production.