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

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