Condensed-matter analogs of the Sauter--Schwinger effect

The Sauter--Schwinger effect predicts the creation of electron--positron pairs from the vacuum due to a quasiconstant electric field $E_{\mathrm{strong}}$. The pair-creation yield can be exponentially enhanced without destroying the tunneling-like nature of this mechanism by adding a weaker temporal Sauter pulse $E_{\mathrm{weak}}/\cosh^{2}(\omega t)$ with $\omega$ above a certain threshold $\omega_{\mathrm{crit}}$. In this original form of the so-called dynamically assisted Sauter--Schwinger effect, $\omega_{\mathrm{crit}}$ is independent of $E_{\mathrm{weak}}\ll E_{\mathrm{strong}}$. Via the semiclassical solution (contour integral) of the Riccati equation in 1+1 spacetime dimensions, we find that a Gaussian-shaped pulse $E_{\mathrm{weak}}\exp[-(\omega t)^{2}]$ assists tunneling in a similar way but with $\omega_{\mathrm{crit}}$ depending on $E_{\mathrm{weak}}$. This remarkable sensitivity to the pulse shape arises due to the different pole structures of the vector potentials for complex times. We also study dynamical assistance by an oscillation $E_{\mathrm{weak}}\cos(\omega t)$ as a model for counterpropagating laser beams and find another dependence $\omega_{\mathrm{crit}}(E_{\mathrm{weak}})$. The largeness of the Schwinger limit $E_{\mathrm{crit}}^{\mathrm{QED}}\approx 10^{18}\,\mathrm{V/m}$ has rendered the observation of this nonperturbative pair-creation mechanism impossible so far. In order to facilitate a better understanding of this effect and its dynamical assistance via experiments, we propose an analog of the many-body Dirac Hamiltonian in direct-bandgap semiconductors. The nonrelativistic Bloch-electron Hamiltonian is restricted to the valence and conduction bands in reciprocal space, which correspond to the two relativistic energy continua. Similar models have been considered before---but mainly for constant external fields. [...]