Imprint of the temporal envelope of ultra-short laser pulses on the longitudinal momentum spectrum of e+e− pairs

Abstract

The effect of the temporal pulse shape of intense pulses on the momentum distribution of ${e}^{+}{e}^{\ensuremath{-}}$ pairs is studied using the quantum kinetic equation. Two closely resembling temporal envelopes, namely, Gaussian and Sauter, keeping all the other pulse parameters the same, are considered to this end. Contrary to the common perception which can be gauged from the interchangeable use of these temporal profiles, the longitudinal momentum spectrum of the pairs created by the two pulses is found to differ significantly in all the temporal regimes. For the pulses having a few cycles of oscillations, the temporal profile of the pulse is revealed in the oscillatory interference pattern riding over the otherwise smooth longitudinal momentum spectrum at asymptotic times. The onset of the oscillation due to the quantum interference of reflection amplitudes from the scattering potential due to the pulses having a temporal structure of multiple barriers takes place for fewer-cycle oscillations for the Gaussian pulse compared to that for the Sauter pulse. Furthermore, the oscillation amplitude for the same number of oscillations within the pulse duration is larger for the Gaussian pulse. The presence of the carrier-envelope phase and the frequency chirping is found to magnify these differences. In the absence of any appreciable interference effect for the pulses having less than five oscillations, the longitudinal momentum spectrum has a higher peak value for the Sauter pulse at asymptotic times. On the other hand, before the transient stage of evolution, the peak of the spectrum shows the opposite trend.