Semiclassical picture for electron-positron photoproduction in strong laser fields

The nonlinear Breit-Wheeler process is studied in the presence of strong and short laser pulses. We show that for a relativistically intense plane-wave laser field many features of the momentum distribution of the produced electron-positron pair like its extension, region of highest probability and carrier-envelope phase effects can be explained from the classical evolution of the created particles in the background field. To this end an intuitive semiclassical picture based on the local constant-crossed field approximation applied on the probability-amplitude level is established and compared with the standard approach used in QED-PIC codes. The main difference is the substructure of the spectrum, which results from interference effects between macroscopically separated formation regions. In order to compare the predictions of the semiclassical approach with exact calculations, a very fast numerical scheme is introduced. It renders the calculation of the fully differential spectrum on a grid which resolves all interference fringes feasible. Finally, the difference between classical and quantum absorption of laser four-momentum in the process is pointed out and the dominance of the former is proven. As a self-consistent treatment of the quantum absorption is not feasible within existing QED-PIC approaches, our results provide reliable error estimates relevant for regimes where the laser depletion due to a developing QED cascade becomes significant.

Figure 1

Leading-order Feynman diagram for electron-positron photoproduction inside a plane-wave background field (nonlinear Breit-Wheeler process). The double lines represent Volkov states (solutions of the interacting Dirac equation, which take the plane-wave background field into account exactly [36, 37]), the wiggly line the incoming photon. As long as the total pair-production probability is much smaller than unity, the spectrum for the final particles is determined to a good accuracy by simply evaluating this diagram and neglecting radiative corrections [38].

Figure 2

Momentum distribution for the created electron-positron pair [see Eq. (8)] for the parameters $\chi =1$, $\xi =5$, $N=5$ and ${\varphi }_0=\pi /2$ [the longitudinal momentum characterized by $R$ is integrated numerically and the incoming photon has parallel polarization (${\epsilon }^{\mu }={\mathrm{\Lambda }}_1^{\mu }$)]. The parameters $\xi =5$ and $\chi =1$ could be obtained by colliding 17 GeV photons head-on with optical ($\omega =1.55\mathrm{eV}$) laser pulses having an intensity of ${10}^{20}\mathrm{W}/{\mathrm{cm}}^2$ (note that few-cycle laser pulses are envisaged, e.g., at the petawatt field synthesizer (PFS) in Garching [116]). (a) Full numerical calculation of the spectrum [see Eq. (15)]. (b) Local constant-crossed field approximation applied on the amplitude level [see Eq. (26)]. The inset shows that the interference pattern is lost if the local constant-crossed field approximation is applied on the probability level. (c) Outline for $t_2=0$. Solid line: full numerical calculation; dotted (dashed) line: local constant-crossed field approximation applied on the amplitude (probability) level.

Figure 3

Left side: Numerically calculated differential pair-production probability as a function of the transversal momentum parameters $t_1$ and $t_2$ (the longitudinal momentum characterized by $R$ is integrated numerically). The incoming photon has parallel polarization (${\epsilon }^{\mu }={\mathrm{\Lambda }}_1^{\mu }$), the laser pulse $N=2$ cycles (such short pulses are envisaged, e.g., at the PFS in Garching [116]) and $\chi =1$. We compare two different CEPs and two different intensities: (a) ${\varphi }_0=0$, $\xi =10$; (b) ${\varphi }_0=0$, $\xi =5$; (c) ${\varphi }_0=\pi$, $\xi =10$; (d) ${\varphi }_0=\pi$, $\xi =5$. The solid white lines confine the phase-space region where the pair can be produced at a phase $\varphi$ with $|{\psi }^{\prime }(\varphi )|\ge 0.5$ and the dashed white lines indicate the transverse momenta for which the pair can be produced at a local field peak. After integrating over $t_1$ and $t_2$ we obtain for the total pair-production probability $W_{\parallel }=0.09\%$ ($\xi =10$) and $W_{\parallel }=0.045\%$ ($\xi =5$), up to this precision it is independent of the CEP. Right side: Plot of the laser pulse shape [solid line: ${\psi }^{\prime }(\varphi )$, dashed line: $\psi (\varphi )$].

Figure 4

Differential probability with respect to the parameters $t_2$ and $R$ for $\chi =1$, $\xi =10$, $N=5$ and ${\varphi }_0=\pi /2$ [full numerical calculation, $t_1$ is integrated numerically and the incoming photon has parallel polarization (${\epsilon }^{\mu }={\mathrm{\Lambda }}_1^{\mu }$)]. The inset shows $d^3{W}_{\parallel }/(dRd{t}_{1}d{t}_2)$ for $t_1=0$ [in arb. units, see Eq. (8)]. The pronounced interference pattern vanishes after the integral in $t_1$ is taken. Note that the (spin-summed) differential probability does not depend on the sign of $R$ and $t_2$.