Manipulation of the Vacuum to Control Its Field-Induced Decay

It has long been predicted that permanent electron-positron pairs can be created from the quantum vacuum at those spatial regions where an external electric field exceeds a supercritical value. By solving the Dirac equation numerically, we show that the yield of the created positrons at targeted energies can be controlled via a second (subcritical) electric field that is placed far outside the creation zone. This is a clear indication of the nonlocal character of the pair-creation process, as the second field can be placed at distant spatial regions that are never visited by the created positrons. This counterintuitive phenomenon can be understood in terms of a dressing of the vacuum state long before the particles are actually created. We present an analytical expression for the spectrum of the created particles that describes all quantitative features of this dressing and predicts how the second field can be used to increase as well as decrease the electron-positron yield for desired energies.

Figure 1

Sketch of the electric field configuration based solely on a supercritical field at $x=0$ (top panel). In the bottom panel, a second (control) field at $x=-d$ is added. Electron-positron pairs are created from the vacuum solely by the supercritical field, and the particles’ energy is detected. Positrons are ejected to the right and therefore cannot interact with the control field.

Figure 2

The (normalized) energy spectra $N(E,t)(2\pi /t)$ of the created electrons (left) and positrons (right). For comparison, the dashed lines are the corresponding spectra without the second field. The open circles denote the numerical data obtained from the simulation, while the solid line is the analytical expressions according to Eq. (2). The potential energy is given by $V(x)=V_c\{1-\tan h[(x+d)/w]\}/2+V_s[1-\tanh (x/w)]/2$, where $V_s=2.5m{c}^2$, $V_c=0.25m{c}^2$, $w=0.075\hslash /(\alpha mc)$, $d=0.2\hslash /(\alpha mc)$, the interaction time was $t=0.045\hslash /({\alpha }^{2}m{c}^2)$, and $\alpha$ is the fine structure constant.

Figure 3

The spatial probability density of the created electrons (continuous line) and positrons (dashed line) after time $t=0.024\hslash /({\alpha }^{2}m{c}^2)$. Other parameters are identical as in Fig. 2.