Nonperturbative Treatment of Double Compton Backscattering in Intense Laser Fields

The emission of a pair of entangled photons by an electron in an intense laser field can be described by two-photon transitions of laser-dressed, relativistic Dirac–Volkov states. In the limit of a small laser field intensity, the two-photon transition amplitude approaches the result predicted by double Compton scattering theory. Multiexchange processes with the laser field, including a large number of exchanged laser photons, cannot be described without the fully relativistic Dirac–Volkov propagator. The nonperturbative treatment significantly alters theoretical predictions for future experiments of this kind. We quantify the degree of polarization correlation of the photons in the final state by employing the well-established concurrence as a measure of the entanglement.

Figure 1

The Feynman diagrams for perturbative (a), and nonperturbative (b) double Compton scattering. In (a), an electron with initial momentum $p_i$ absorbs one laser photon (four-momentum $\varkappa$), emits two photons with wave vectors $k_b$ and $k_c$ and ends with final momentum $p_f$. Instead in (b), the laser-dressed initial state with average four momentum $q_i$, decays to the final state with average four momentum $q_f$ under emission of two photons. In the intermediate state the momenta are labeled by $p_b$ and $p_c$, respectively. The nonperturbative interaction with the laser field is depicted by dressing the electron lines with a zigzag line.

Figure 2

Comparison of the perturbative and nonperturbative approach. Shown is the laboratory frame rate $d\dot{W}/d{\omega }_{b}d{\Omega }_{b}d{\Omega }_c$, in units of ${\mathrm{s}}^{-1}{\mathrm{sr}}^{-2}{\mathrm{MeV}}^{-1}$, for the nonperturbative [(a),(c)] and perturbative [(b),(d)] case. The parameters employed are $E_i={10}^{3}m$, $\omega =2.5\mathrm{eV}$, $\xi =1$, ${\omega }_b=1\mathrm{MeV}$, and ${\theta }_b={\theta }_c={10}^{-3}$. The photon polarizations are given by ${ϵ}_{b,c}={ϵ}_{b,c}^1$ in (a) and (b), and ${ϵ}_{b,c}={ϵ}_{b,c}^2$ in (c) and (d).

Figure 3

The integrated and polarization-summed lab-frame rate $d\dot{W}/d{\theta }_c=\sin {\theta }_{c}d\dot{W}/d\cos {\theta }_c$, differential only in the angle ${\theta }_c$. Shown are results for the perturbative and the nonperturbative calculations, for $E_i={10}^{3}m$, $\omega =2.5\mathrm{eV}$, $\xi =1$.

Figure 4

In panel (a) we show the concurrence $C({\rho }_f)$ [see Eq. (4)], using the nonperturbative expression for the matrix element, which should be compared to panel (c), where the concurrence is shown for the perturbative case. The parameters employed are $E_i={10}^{3}m$, $\omega =2.5\mathrm{eV}$, $\xi =1$, ${\omega }_b=1\mathrm{MeV}$, and ${\psi }_b={\psi }_c=0$. As a reference, we also display in the right column the logarithm of the polarization-summed differential rate ${log}_{10}(d\dot{W}/d{\omega }_{b}d{\Omega }_{b}d{\Omega }_c)$, in units of ${\mathrm{s}}^{-1}{\mathrm{sr}}^{-2}{\mathrm{MeV}}^{-1}$, for the nonperturbative [(b)] and perturbative [(d)] case.