Pair Production in Laser Fields Oscillating in Space and Time

The production of electron-positron pairs from vacuum by counterpropagating laser beams of linear polarization is calculated. In contrast with the usual approximate approach, the spatial dependence and magnetic component of the laser field are taken into account. We show that the latter strongly affects the creation process at high laser frequency: the production probability is reduced, the kinematics is fundamentally modified, the resonant Rabi-oscillation pattern is distorted, and the resonance positions are shifted, multiplied, and split.

Figure 1

Pair creation in an OEF with $\omega =m/200$ and $E=E_c=m^2/|e|$. Three snapshots of the probability distribution are taken at times as indicated from the evolution of an initially negative-energy Gaussian wave packet at rest at the origin. The length is scaled in multiples of ${\lambda }_c=1/m$.

Figure 2

Disturbed Rabi oscillations: Pair production probability versus pulse length at $\xi =1$. (a) The red dashed line and the black solid line show the OEF case for $\omega =0.49072m$ and the CLP case for $\omega =0.4721m$, respectively, each corresponding to a 5-photon resonance. (b) CLP case for various frequencies on a logarithmic scale. The black solid curve coincides with the resonant case in part (a), while the others correspond to off resonant situations.

Figure 3

Resonant probability spectrum: Maximal value of the pair production probability during Rabi oscillation at $\xi =1$, varying the pulse length up to 200 cycles. The red crosses show the OEF spectrum; the peak labels denote the absorbed photon number. The black triangles show the CLP spectrum. Here, the labeling signifies the number of absorbed photons from the right-left propagating waves. A splitting occurs, as indicated by arrows for the example of the ($3-2$) peak. The frequency axis is plotted reciprocally [19].

Figure 4

Final positive-energy momentum distributions $W_{p^{\prime }}=|⟨{\Phi }_{{\mathbf{p}}^{\prime }}^{(+)}|\Psi (T)⟩{|}^2$ after the interaction with two counterpropagating laser pulses ($\xi =1$, $T=150\pi /\omega$). Because of its magnetic component, the field transfers longitudinal momentum to the wave packet. Shown are the results for four different frequencies corresponding to four peaks in the resonance spectrum in Fig. 3. Because of the symmetry of the spectra under momentum inversion $p_z^{\prime }\to -p_z^{\prime }$, we only show the positive half of them.

Figure 5

Coupling between the two upper states of the $V$-type system via Compton scattering for the ($2-1$) peak. (a) Population of the initially empty mirror state with $p_z^{\prime }=-p_{\mathrm{initial}}=-\omega$: (solid line) $\omega =0.766m$ and $\xi =0.5$, resulting in the Rabi frequency of ${\Omega }_C=0.018m$ due to Compton scattering; (dashed line) $\omega =0.812m$ and $\xi =1.0$ resulting in ${\Omega }_C=0.066m$. In both cases, $\Omega \ll {\Omega }_C$, where $\Omega$ is the associated Rabi frequency due to pair creation. (b) $\xi$ dependence of the peak splitting, $\Delta \omega \sim {\xi }^2$. (c) Level scheme.