Field-induced decay of the quantum vacuum: Visualizing pair production in a classical photonic system

The phenomenon of vacuum decay, that is, electron-positron pair production due to the instability of the quantum electrodynamics vacuum in an external field, is a remarkable prediction of Dirac theory whose experimental observation is still lacking. Here a classic wave optics analog of vacuum decay, based on light propagation in curved waveguide superlattices, is proposed. This photonic analog enables a simple and experimentally accessible visualization in space of the process of pair production as breakup of an initially negative-energy Gaussian wave packet, representing an electron in the Dirac sea, under the influence of an oscillating electric field.

Figure 1

(a) and (b) Schematic of a binary superlattice, made of two interleaved lattices $A$ and $B$ of waveguides with high (${\mathit{dn}}_1$) and low (${\mathit{dn}}_2$) refractive index changes, equally spaced by $a$ (a) and with a periodically curved axis (b). The array is excited by a broad beam tilted at angle $\theta$. (c) Dispersion curves (minibands) of the tight-binding binary superlattice [Eq. (3)] for the straight binary array (solid curves), and corresponding electron and positron dispersion curves of the Dirac equation (7) (in the absence of the ac field) near the Brillouin zone edge $q=\pi /(2a)$ (dotted curves).

Figure 2

Transition probability $P=|r_{+}(z)|{}^2$ vs propagation distance $z$, normalized to the ac oscillation period $\Lambda$, in a tight-binding binary lattice with a sinusoidally curved axis for parameter values $\sigma =2$, $\delta =1.817$, $\mathit{qa}=\pi /4$, and ${\Phi }_0=0.4$ and for two values of modulation period $\Lambda$: (a) $\Lambda =2.8556$, and (b) $\Lambda =2.7196$. In (a) the multiphoton resonance condition (22) is satisfied for $n=3$, and Rabi flopping is clearly observed. In (b) the modulation period is slightly decreased by $5\%$ from the $n=3$ resonance value.

Figure 3

Transition probability $P$ in a tight-binding binary lattice with a single-cycle sinusoidally curved axis for parameter values $\sigma =2$, $\delta =1.817$, $\mathit{qa}=\pi /4$, and $\Lambda =0.6676$, and for increasing values of amplitude ${\Phi }_0$. Points A, B, and C in the figure correspond to the values ${\Phi }_0=4$, ${\Phi }_0=6$ and ${\Phi }_0=0$, respectively. Also shown is the detailed behavior of $|r_{+}(z)|{}^2$ vs propagation distance $z$ in the single-cycle modulation period corresponding to points A (b) and B (c) of Fig. 3a.

Figure 4

(a) Refractive index profile of the binary superlattice used in numerical simulations, and (b) corresponding band diagram. Parameter values are given in the text.

Figure 5

Beam propagation in a 6-cm-long one-dimensional binary waveguide array (snapshot of $|E(x,z)|{}^2$), comprising a first section with a single-cycle sinusoidally curved axis of period $\Lambda =6.67\hspace{0.5em}\mathrm{mm}$ and amplitude $A$ and a second section with a straight axis: (a) $A=0$ (straight array), (b) $A=30\hspace{0.5em}\mu$m, and (c) $A=45\hspace{0.5em}\mu$m. The array is excited by a Gaussian beam tilted at half of the Bragg angle. (Parameter values are given in the text.)