Breit-Wheeler process in intense short laser pulses

Energy-angular distributions of electron-positron pair creation in collisions of a laser beam and a nonlaser photon are calculated using the $S$-matrix formalism. The laser field is modeled as a finite pulse, similar to the formulation introduced in our recent paper in the context of Compton scattering [Phys. Rev. A 85, 062102 (2012)]. The nonperturbative regime of pair creation is considered here. The energy spectra of created particles are compared with the corresponding spectra obtained using the modulated plane-wave approximation for the driving laser field. A very good agreement in these two cases is observed, provided that the laser pulse is sufficiently long. For short pulse durations, this agreement breaks down. The sensitivity of pair production to the polarization of a driving pulse is also investigated. We show that in the nonperturbative regime, the pair-creation yields depend on the polarization of the pulse, reaching their maximal values for the linear polarization. Therefore, we focus on this case. Specifically, we analyze the dependence of pair creation on the relative configuration of linear polarizations of the laser pulse and the nonlaser photon. Lastly, we investigate the carrier-envelope phase effect on angular distributions of created particles, suggesting the possibility of phase control in relation to the pair-creation processes.

Figure 1

The Feynman diagrams for the laser-induced (top diagram) and the laser-modified (bottom diagrams) Breit-Wheeler processes [30]. The fermion lines (double solid lines) represent the Volkov states for electrons and positrons in the background laser field.

Figure 2

An arbitrary laboratory geometry (up to the space rotation) for the laser-induced Breit-Wheeler process.

Figure 3

Comparison of the positron energy-angular distributions for a single laser pulse (blue solid line) and for a train of pulses (green dots) [Eqs. (43) and (54), respectively], in the case when a different number of laser-field oscillations, $N_{\mathrm{osc}}$, is contained in the pulse. The positron polar and azimuthal angles are ${\theta }_{e^{+}}=\pi /2$ and ${\phi }_{e^{+}}=0$, respectively. The results are for the parameters of the laser pulse such that $\mu =1$ and ${\omega }_L=0.1m_e{c}^2$, and for the energy of the $\gamma$ photon ${\omega }_{\mathit{K}}=2m_e{c}^2$. Both the $\gamma$ photon and the laser field are linearly polarized, with ${\mathit{\varepsilon }}_{\mathit{K}\sigma }={\mathit{\varepsilon }}_1={\mathit{e}}_x$.

Figure 4

The same as in Fig. 3, but the linear polarization vectors of the colliding $\gamma$ photon and the laser field are perpendicular to each other, i.e., ${\mathit{\varepsilon }}_{\mathit{K}\sigma }=-{\mathit{e}}_y$ and ${\mathit{\varepsilon }}_1={\mathit{e}}_x$.

Figure 5

The same as in Fig. 3, but the laser field is circularly polarized ($\delta =\pi /4$) whereas the $\gamma$ photon is linearly polarized along the $x$ axis, i.e., ${\mathit{\varepsilon }}_{\mathit{K}\sigma }={\mathit{e}}_x$.

Figure 6

The angular distributions of positrons produced with momentum $|{\mathit{p}}_{e^{+}}|=m_{e}c$ by a single laser pulse including 32 field oscillations ($N_{\mathrm{osc}}=32$). The other parameters are $\mu =1$, ${\omega }_L=0.1m_e{c}^2$, ${\omega }_{\mathit{K}}=2m_e{c}^2$, ${\phi }_{e^{+}}=0$ for ${\Theta }_{e^{+}}⩽\pi$ (or, ${\phi }_{e^{+}}=\pi$ for ${\Theta }_{e^{+}}>\pi$), and $\chi =0$. The upper panel relates to the case when the $\gamma$ photon is linearly polarized such that ${\mathit{\varepsilon }}_{\mathit{K}\sigma }={\mathit{e}}_x$, whereas the lower panel is for ${\mathit{\varepsilon }}_{\mathit{K}\sigma }=-{\mathit{e}}_y$. The peaks appear when $N_{\mathrm{eff}}$ changes by multiples of $N_{\mathrm{osc}}$. The spectra are symmetric with respect to the propagation direction of the incident $\gamma$ photon.

Figure 7

The same as in Fig. 6, but for $N_{\mathrm{osc}}=2$. The angular spectra are asymmetric with respect to the propagation direction of the colliding $\gamma$ photon.

Figure 8

The same as in Fig. 7, but for a carrier-envelope phase of the driving laser pulse $\chi =\pi /2$. This time, the angular distributions are symmetric with respect to the propagation direction of the $\gamma$ photon.