Pulse shape dependence in the dynamically assisted Sauter-Schwinger effect

While the Sauter-Schwinger effect describes nonperturbative electron-positron pair creation from vacuum by a strong and slowly varying electric field Estrong 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 Eweak. 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/cosh²(ωt) considered previously, the threshold frequency ωcrit (where the enhancement mechanism sets in) is basically independent of the magnitude Eweak of the weak pulse---whereas for a Gaussian pulse exp(-ω²t²), an oscillating profile cos(ωt) or a standing wave cos(ωt)cos(kx), the value of ωcrit does depend (logarithmically) on Eweak/Estrong.