# Dynamically assisted Sauter-Schwinger effect - non-perturbative versus perturbative aspects

## TL;DR

This paper investigates how a weaker, time-dependent electric field can enhance the electron-positron pair creation in a strong electric field, analyzing the effects through perturbative and non-perturbative methods to understand the influence of pulse shape.

## Contribution

It introduces a perturbative approach to compare the effects of different pulse shapes on pair creation, clarifying when low-order approximations are sufficient and when higher orders are necessary.

## Key findings

- First-order perturbation often suffices for certain pulse shapes.
- Higher-order contributions dominate for Gaussian and sinusoidal profiles.
- Numerical simulations confirm the perturbative analysis and clarify the role of pulse shape.

## Abstract

The Sauter-Schwinger effect predicts the creation of electron-positron pairs out of the quantum vacuum by a strong and slowly varying electric field. This effect can be dynamically assisted by an additional weaker time-dependent field, which may drastically enhance the pair-creation probability. In previous studies, it has been found that the enhancement may crucially depend on the temporal shape of this weaker pulse, e.g., a Gaussian profile $\exp\{-(\omega t)^2\}$ or a Sauter pulse $1/\cosh^2(\omega t)$ behave quite differently. In order to understand this difference, we make a perturbative expansion in terms of the weaker field while treating the strong electric field non-perturbatively. For a large class of profiles including the Sauter pulse, already the sum of the zeroth-order and the first-order amplitudes of this perturbative expansion yields good agreement. For other cases, such as a Gaussian or sinusoidal profile, this is not true in general and higher orders can yield the dominant contribution - where the dominant order depends on the chosen parameters. Our findings are confirmed by numerical simulations and help us to sort previous results into a bigger picture.