Electron-positron pair creation induced by multi-pulse train of electric fields: effect of randomness in time-delay

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 $\sigma_T$ of the distribution. We find that increasing $\sigma_T$ 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, $\sigma_T \approx 31$ $[m^{-1}]$(about $17\%$ of the mean time delay) yields nearly a tenfold increase in the central peak, which for $\sigma_T \approx 50$ $[m^{-1}]$ (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 guide future experimental designs aimed at maximizing EPPs creation.