We investigate the creation of electron-positron pairs (EPPs) in a sequence of alternating-sign, time-dependent electric field pulse trains by solving the quantum Vlasov equations. Specifically, we focus on Sauter-like pulse trains with random time delays between successive pulses, drawn from a Gaussian distribution wherein the extent of fluctuations is controlled by the standard deviation σ T of the distribution. We find that increasing σ T leads to a dramatic transformation in the longitudinal momentum spectrum. The well-known fringe pattern, akin to that in the multi-slit interference, gets significantly modified. The averaged spectra exhibit a robust Gaussian-like envelope with residual oscillations, which are much more prominent in the central momentum region. Notably, we find that in certain cases, stochastic time delays lead to a pronounced enhancement in the central peak of the distribution function for pulse train containing N pulses. For example, for N = 20 pulses, σ T ≈ 31 m − 1 (about 17% of the mean time delay) yields nearly a tenfold increase in the central peak, which for σ T ≈ 50 m − 1 (about 27% of the mean time delay), scales up to 10 3 . This may open up new possibilities for optimizing multi-pulse field configurations and guides future experimental designs aimed at maximizing EPPs creation.
Sah et al. (Sun,) studied this question.