Pair Production and Optical Lasers

Electron-positron pair creation in a standing wave is explored using a parameter-free quantum kinetic equation. Field strengths and frequencies corresponding to modern optical lasers induce a material polarization of the QED vacuum, which may be characterized as a plasma of $e^{+}{e}^{-}$ quasiparticle pairs with a density of $\sim {10}^{20}{\mathrm{cm}}^{-3}$. The plasma vanishes almost completely when the laser field is zero, leaving a very small residual pair density $n_r$ which is the true manifestation of vacuum decay. The average pair density per period is proportional to the laser intensity but independent of the frequency $\nu$. The density of residual pairs also grows with laser intensity but $n_r\propto {\nu }^2$. With optical lasers at the forefront of the current generation, these dynamical QED vacuum effects can plausibly generate 5–10 observable two-photon annihilation events per laser pulse.

Figure 1

${\lambda }^{3}n(t)$ as a function of time, measured in units of the laser period $T$, i.e., the number of pairs produced within a volume ${\lambda }^3$ by the field in Eq. (8). Solid line: optical laser (weak-field case) [26]; $E_m^O=3\times {10}^{-5}{E}_{\mathrm{cr}}$ and ${\lambda }_O=795\mathrm{nm}$. Dotted line: XFEL (strong field) [7, 8, 21]; $E_m^X=0.24E_{\mathrm{cr}}$ and ${\lambda }_X=0.15\mathrm{nm}$. The value of the residual pair density $n_r$ is marked in both cases. N.B., $({\lambda }_O/{\lambda }_X{)}^3=1.5\times {10}^{11}$.

Figure 2

Single-particle momentum distribution function at an antinode of the electric field in Eq. (8) for optical laser parameters; viz., $E_m=3\times {10}^{-5}{E}_{\mathrm{cr}}$.

Figure 3

Solid line: $\lambda$ dependence of the mean quasiparticle number, ${\lambda }^3⟨n⟩$; dotted line: $\gamma \gamma$-production rate/laser period from the spot volume, ${\lambda }^3⟨d{N}_{e^{+}{e}^{-}}/dt/d^{3}x⟩$ [with the time-averaging procedure defined in Eq. (9)]. Both curves were calculated with $E_m=3\times {10}^{-5}{E}_{\mathrm{cr}}$ in Eq. (8).