Prefactor in the dynamically assisted Sauter-Schwinger effect

TL;DR

This paper investigates the subleading prefactor in the pair-creation probability of the dynamically assisted Sauter-Schwinger effect, finding that it does not significantly alter the main enhancement features dependent on the weaker field's shape.

Contribution

It extends the analysis of the dynamically assisted Sauter-Schwinger effect by calculating the prefactor using the worldline instanton method, confirming its negligible impact on the main enhancement mechanism.

Findings

Prefactor has minimal effect on the enhancement mechanism.

Main features depend primarily on the shape of the weaker field.

Numerical results agree with the instanton approximation.

Abstract

The probability of creating an electron-positron pair out of the quantum vacuum by a strong electric field can be enhanced tremendously via an additional weaker time-dependent field. This dynamically assisted Sauter-Schwinger effect has already been studied in several works. It has been found that the enhancement mechanism depends on the shape of the weaker field. For example, a Sauter pulse $1/\cosh(\omega t)^2$ and a Gaussian profile $\exp(-\omega^2 t^2)$ exhibit significant, qualitative differences. However, so far most of the analytical studies were focused on the exponent entering the pair-creation probability. Here, we study the subleading prefactor in front of the exponential using the worldline instanton method. We find that the main features of the dynamically assisted Sauter-Schwinger effect, including the dependence on the shape of the weaker field, are basically unaffected by the prefactor. To test the validity of the instanton approximation, we compare the number of produced pairs to a numerical integration of the full Riccati equation.