Pumping Electron-Positron Pairs from a Well Potential

In the presence of very deep well potential, electrons will spontaneously occupy the empty embedded bound states and electron-positron pairs are created by means of a non-perturbative tunneling process. In this work, by slowly oscillating the width or depth, the population transfer channels are opened and closed periodically. We find and clearly show that by the non-synchronous ejections of particles, the saturation of pair number in a static super-critical well can be broken, and electrons and positrons can be pumped inexhaustibly from vacuum with a constant production rate. In the adiabatic limit, final pair number after a single cycle has quantized values as a function of the upper boundary of the oscillating, and the critical upper boundaries indicate the diving points of the bound states.