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Via the worldline instanton method, we study electron-positron pair creationby a strong electric field of the profile $E/\cosh^2(kx)$ superimposed by aweaker pulse $E'/\cosh^2(\omega t)$. If the temporal Keldysh parameter$\gamma_\omega=m\omega/(qE)$ exceeds a threshold value $\gamma_\omega^{\rmcrit}$ which depends on the spatial Keldysh parameter $\gamma_k=mk/(qE)$, wefind a drastic enhancement of the pair creation probability -- reporting onwhat we believe to be the first analytic non-perturbative result for theinterplay between temporal and spatial field dependences $E(t,x)$ in theSauter-Schwinger effect.

Dynamically assisted Sauter-Schwinger effect in inhomogeneous electric fields