Fig. 3: Dirac particle in electric fields.
From: Experimental simulation of Dirac equation in superconducting qubits
a The rapid ramping of the momentum induces an electric field (purple pulse), which is strong enough to depolarize the vacuum and produce the electron-positron pair. A negative energy electron (blue ball) in the Dirac sea is stimulated to a positive energy state (red ball), leaving a hole in the Dirac sea (violet ball). b Schematic of Schwinger effect. The system can be viewed as a two-fold degenerate Landau-Zener model, with no interaction between degenerate states. The electric field depolarizes the vacuum and creates electrons and positrons (holes in the Dirac sea). The minimal gap of 2m determines the minimal chirp rate(electric field) to observe the Schwinger effect. c Experimental results of the populations of four states in the chirping process are demonstrated for different masses, and they are in accord with numerical simulations in (d). In (c) and (d), The colour bar represents the population (shared across all panels). e The remaining population in \(\{\left\vert 0\right\rangle ,\left\vert 1\right\rangle \}\) manifold characterizes the pair production, and it decreases with increasing mass. At large mass, the initial state is not far from the anti-crossing for the finite momentum compared with the gap. Therefore, the deviation from the Landau-Zener transition rate formula in the pink regime is caused by the finite max effective coupling strength.
