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Electron-positron pair production is investigated in spatial inhomogeneous electric fields with high or/and low central frequency as well as sinusoidal phase modulation. It is found that the momentum spectrum (the reduced particle number) is more sensitive to the modulated amplitude (modulated frequency) of the phase. The stronger the modulation parameters are applied, the more remarkable the interference effect in momentum spectrum occur. In particular, for high central frequency field, an extremely good symmetry in momentum spectrum is found while it is destroyed severely when the modulated amplitude becomes large. The reduced particle number can be also enhanced greatly at about a few times or/and one order by the modulation parameters. Moreover, the effect of spatial scales on the reduced particle number are examined carefully and found that it increases rapidly at small spatial scales, while it tends to be a constant at large spatial scales. Two interesting features are revealed for the reduced particle number, i.e., the optimal modulation parameters are found and the same particle number can be got through different set of modulation parameters. The latter findings is important because one can choose different ways of phase modulation to realize the required pair number even if for the optimal pair production., 26 pages, 10 figures

Chirped dynamically assisted pair production in spatial inhomogeneous electric fields is studied by the Dirac-Heisenberg-Wigner formalism. The effects of the chirp parameter on the reduced momentum spectrum, the reduced total yield of the created pairs for either low or high frequency one-color field and two-color dynamically assisted combinational fields are investigated in detail. Also, the enhancement factor is obtained in the later two-color field case. It is found that for the low frequency field, no matter whether it is accompanied by the other high frequency field, its chirping has a little effect on the pair production. For the one-color high frequency field or/and two-color fields, the momentum spectrum exhibits incomplete interference and the interference effect becomes more and more remarkable as chirp increases. We also find that in the chirped dynamically assisted field, the reduced total yield is enhanced significantly when the chirps are acting on the two fields, compared with that the chirp is acting only for the low frequency strong field. Specifically, by the chirping, it is found the reduced pair number is increased by more than one order of magnitude in the field with a relative narrow spatial scale, while it is enhanced at least two times in other case of field with larger spatial scales or even in the quasi-homogeneous region. We also obtain some optimal chirp parameters and spatial scales for the total yield and enhancement factor in different scenarios of the studied external field. These results may provide a theoretical basis for possible experiments in the future., 30 pages, 16 figures, 1 Table

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., Comment: 20 pages, 8 figures, 4 tables