Symmetries in the nonlinear Bethe-Heitler process

The nonlinear Bethe-Heitler process in a bichromatic laser field is investigated using strong-field quantum electrodynamics formalism. The symmetry properties of the angular distributions of the created $e^{-}{e}^{+}$ pairs are analyzed. These properties are shown to be governed by a behavior of the vector potential characterizing the laser field, rather than by the respective electric-field component.

Figure 1

In the upper panel, we show shape functions for the four-vector potential $f\left(\phi \right)$ (blue solid line) and for the electric field $f^{\prime }\left(\phi \right)$ (red dashed line), describing a bichromatic laser field defined by Eqs. (1) and (2). The laser-field parameters are such that $\omega =m_{\mathrm{e}}{c}^2$ and $\mu =1$. The lower panel presents coarse-grained angular distributions of probability rates of created electrons, which have been projected onto the $xy$ plane.

Figure 2

Same as in Fig. 1 but for the bichromatic laser field described by Eqs. (3) and (4).

Figure 3

Angular maps of $R_4({\mathit{q}}_{\mathrm{f}},{\widehat{\mathit{p}}}_{{\mathrm{e}}^{-}})$ (left column) and $R_7({\mathit{q}}_{\mathrm{f}},{\widehat{\mathit{p}}}_{{\mathrm{e}}^{-}})$ (right column) in the case when ${\mathit{q}}_{\mathrm{f}}=-2m_{\mathrm{e}}c{\mathit{e}}_z$. The parameters of the laser field have been chosen such that $\omega =m_{\mathrm{e}}{c}^2$ and $\mu =1$. While the upper panels refer to the vector potential specified by Eqs. (1) and (2), the lower panels are for the vector potential described by Eqs. (3) and (4). For visual purposes, the rates have been raised to power 1/5.

Figure 4

Angular maps of $R_{183}({\mathit{q}}_{\mathrm{f}},{\widehat{\mathit{p}}}_{{\mathrm{e}}^{-}})$ (left column) and $R_{186}({\mathit{q}}_{\mathrm{f}},{\widehat{\mathit{p}}}_{{\mathrm{e}}^{-}})$ (right column) in the case when ${\mathit{q}}_{\mathrm{f}}=-2m_{\mathrm{e}}c{\mathit{e}}_z$. The parameters of the laser field are $\omega =m_{\mathrm{e}}{c}^2$ and $\mu =10$. The upper panels correspond to the case specified by Eqs. (1) and (2), whereas the lower panels are for the vector potential described by Eqs. (3) and (4). For visual purposes, the rates have been raised to power 1/10.