Population transfer to supercritical bound states during pair creation

Abstract

We study the electron-positron pair-creation process from the vacuum under a very strong electric field. The external field is so strong that discrete states can dive into the negative energy continuum (the Dirac sea). This process is simultaneously associated with the onset of pair creation as well as the possibility for capturing the created electrons. By varying the total spatial width of the potential well, we can shift these trapping states in and out of the negative energy continuum while keeping the associated electric force the same. We compute the population transfer in and out of these states by solving the corresponding quantum field theoretical equations for the field operator on a space-time grid. We compare the population of these states obtained by projecting the time-evolved states on instantaneous energy eigenstates with the kinetic-energy spectrum of the ejected positrons.