Imprint of temporal envelope of ultrashort laser pulses on longitudinal momentum spectrum of $e^+e^-$ pairs

TL;DR

This study investigates how the temporal shape of ultrashort laser pulses, specifically Gaussian and Sauter profiles, significantly influences the longitudinal momentum spectrum of electron-positron pairs produced, revealing distinct interference effects.

Contribution

It demonstrates that the pulse shape critically affects pair momentum spectra, highlighting differences overlooked by common assumptions and emphasizing the role of pulse parameters like carrier-envelope phase and chirping.

Findings

Gaussian and Sauter pulses produce significantly different momentum spectra.

Interference patterns depend on pulse duration and shape, especially for few-cycle pulses.

Carrier-envelope phase and chirping amplify spectral differences.

Abstract

The effect of the temporal pulse shape of intense pulses on the momentum distribution of $e^+e^-$ 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 few-cycle oscillations for the Gaussian pulse than 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 hand, before the transient stage of evolution, the peak of the spectrum shows the opposite trend.