Pulse shape dependence in the dynamically assisted Sauter-Schwinger effect

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 $1/\cosh^2(ωt)$ considered previously, the threshold frequency $ω_{\mathrm{crit}}$ (where the enhancement mechanism sets in) is basically independent of the magnitude $E_{\mathrm{weak}}$ of the weak pulse---whereas for a Gaussian pulse $\exp(-ω^2t^2)$, an oscillating profile $\cos(ωt)$ or a standing wave $\cos(ωt)\cos(kx)$, the value of $ω_{\mathrm{crit}}$ does depend (logarithmically) on $E_{\mathrm{weak}}/E_{\mathrm{strong}}$.