Dirac Vacuum as a Transport Medium for Information

Usually, the transport of information requires either an electromagnetic field or matter as a carrier. It turns out that the Dirac vacuum modes could be exploited as a potentially loss-free carrier of information between two distant locations in space. At the first location, a spatially localized electric field is placed, whose temporal shape is modulated, for example, as a binary sequence of distinguishable high and low values of the amplitude. The resulting distortion of the vacuum state reflecting this information propagates then to a second location, where this digital signal can be read off sequentially by a static electric field pulse. If this second field is supercritical, it can create electron-positron pairs from the manipulated vacuum state. The original information transported by the vacuum mode is then imprinted on the temporal behavior of the created particle yield for a selected energy.

Figure 1

Sketch of the setup for a vacuum mode as a carrier of information. In the left inset, we show the time dependence of an electric pulse that is spatially localized at a distant $L$ from the receiver. The receiver contains a spatially localized supercritical field that creates $e^{-}-e^{+}$ pairs from the (modulated) vacuum.

Figure 2

The open circles show the growth of the number density of created positrons $N(E,t)$ as the vacuum mode is temporally modulated by the sender’s electric field of magnitude $F_S(t)$ shown below. For comparison, the solid line is the prediction according to Eq. (3). The displayed pulse durations of the sender’s field are in ${10}^{-3}$ atomic units [$L=1.5\mathrm{a}.\mathrm{u}.$, $V_S=0.35m{c}^2$, $w_S=2.2\times {10}^{-2}\mathrm{a}.\mathrm{u}.$, $V_R=2.5m{c}^2$, $w_R=2.2\times {10}^{-3}\mathrm{a}.\mathrm{u}.$], the electric fields have the spatial shape $-V_S\mathrm{sech}{[(x+L)/w_S]}^2/(2w_S)$ and $V_R$$\mathrm{sech}{(x/w_R)}^2/(2w_R)$ and positron energy $E=1.2m{c}^2$, the slope of the graph is $\mathrm{\Gamma }(E)=0.732$ with $T(E)=0.268$ and delay $\tau =1.71\times {10}^{-3}\mathrm{a}.\mathrm{u}.$, and numerical box $B=32\mathrm{a}.\mathrm{u}.$ with 32 768 spatial and 10 000 temporal grid points to solve the Dirac equation.

Figure 3

Impact of the electron echoes on the growth of the number density of created positrons $N(E,t)$ as the vacuum is blocked by the sender’s electric field $F_S(t)$ shown below. For comparison, the solid line is the prediction according to Eq. (4). [All field and numerical parameters are as in Fig. 2, except the positron energy $E=1.25m{c}^2$, leading to $\mathrm{\Gamma }(E)=0.700$ with $T(E)=0.272$ and delay $\tau =1.824\times {10}^{-3}\mathrm{a}.\mathrm{u}.$]