Control of the laser-induced vacuum decay by electronic phases

We examine the laser-assisted electron-positron pair-creation process from the quantum vacuum in the presence of a binding potential with one optically active bound electron. If this core electron is initially prepared in a coherent superposition state of two resonant bound states, the electronic phase properties between both state excitations can be transferred to the positron during the pair-creation process. For example, the periodic Rabi population exchange between both electronic states modulates the temporal growth of the pair-creation probability and also leads to an Autler-Townes split positron energy spectra. Even more astonishing, for the case of different phases, for which the internal electronic dynamics (in the absence of pair creation) is identical, the positron's creation probability is different, suggesting that the vacuum decay process can “sense” the phase and not just the occupation number of the core electron. The field theoretical model of the laser assisted pair-creation process with subsequent electron capture can be mapped exactly onto two mutually independent (single-electron) ionization-like processes. This mathematical equivalency permits us to derive analytical solutions for the time evolution of the vacuum decay process under the rotating-wave approximation.

Figure 1

The relevant continuum and discrete energy levels describing the laser field-induced electron-positron creation process from the quantum vacuum in the presence of a nuclear potential, which supports two bound states. While the created positron (hole in the Dirac sea) can escape to infinity, the associated created electron (green circle) is captured by the nucleus, which binds already one resonantly driven core electron (black circle). The parameters in our numerical simulations are $E_1=–0.9m{c}^2, E_2=–0.4m{\mathrm{c}}^2$ and the laser's time dependence is given by $\mathrm{\Omega }\left(t\right)={\mathrm{\Omega }}_0\sin \left(\omega t\right)$ with (scaled) amplitude ${\mathrm{\Omega }}_0=0.005m{c}^2/\hslash$ and frequency $\omega =0.5m{c}^2/\hslash$.

Figure 2

The time evolution of the probability $|C_1\left(t\right){|}^2$ to find the core electron in state $|1\rangle$. For the initial excitation amplitudes we chose $C_1\left(t=0\right)=\exp \left(i\varphi \right)/2^{1/2}$ and $C_2\left(t=0\right)=1/2^{1/2}$, with the four phases $\varphi =0, \pi /2$, π, and $3\pi /2$. The predictions based on the rotating-wave approximation are indicated by the open circles. The time is in units of the laser period $T=2\pi /\omega$ with all parameters as in Fig. 1.

Figure 3

The time dependence of the created positrons as a function of time (in units of the laser period $T=2\pi /\omega$) $N\left(e^{+},t\right)=N\left(e^{–},1,t\right)+N\left(e^{–},2,t\right)–1$. Here the initially bound electron was in the superposition state $\left[\exp \left(i\varphi \right)\right|1\rangle +|2\rangle ]/2^{1/2}$ with four different initial phases ϕ. All other parameters as in Fig. 1, except that ${\kappa }_0=0.1m^{1/2}c$. The open circles represent the predictions based on the rotating-wave approximation and the crosses are the analytical predictions based on Fermi golden rule given by Eqs. (6) and (9), where the vacuum decay constant is $\mathrm{\Gamma }\equiv 2\pi {[\kappa \left(E_r\right)/2]}^2/\hslash$, with $E_r=–1.4m{c}^2$.