Pulse shape dependence in the dynamically assisted Sauter-Schwinger effect

TL;DR

This paper investigates how the shape of a weak, fast electric pulse influences the enhancement of electron-positron pair creation in the Sauter-Schwinger effect, revealing shape-dependent thresholds for the effect's onset.

Contribution

It demonstrates that the pulse shape critically affects the threshold frequency for pair creation enhancement, with different behaviors observed for Sauter, Gaussian, oscillating, and standing wave profiles.

Findings

Threshold frequency is shape-dependent.

Sauter profile's threshold is independent of weak pulse magnitude.

Other profiles show a logarithmic dependence on the weak-to-strong field ratio.

Abstract

While the Sauter-Schwinger effect describes nonperturbative electron-positron pair creation from vacuum by a strong and slowly varying electric field $E_{\mathrm{strong}}$ via tunneling, the dynamically assisted Sauter-Schwinger effect corresponds to a strong (exponential) enhancement of the pair-creation probability by an additional weak and fast electric or electromagnetic pulse $E_{\mathrm{weak}}$. Using the WKB and worldline instanton method, we find that this enhancement mechanism strongly depends on the shape of the fast pulse. For the Sauter profile $1/\cosh^2(\omega t)$ considered previously, the threshold frequency $\omega_{\mathrm{crit}}$ (where the enhancement mechanism sets in) is basically independent of the magnitude $E_{\mathrm{weak}}$ of the weak pulse---whereas for a Gaussian pulse $\exp(-\omega^2t^2)$, an oscillating profile $\cos(\omega t)$ or a standing wave $\cos(\omega t)\cos(kx)$, the value of $\omega_{\mathrm{crit}}$ does depend (logarithmically) on $E_{\mathrm{weak}}/E_{\mathrm{strong}}$.