Theoretical study of double oscillating fields induced electron-positron pairs creation process

Abstract

<sec>We investigate an important aspect of electron-positron pair creation from vacuum in the presence of a strong background field, where the combined field plays a key role in the pair creation process. By utilizing computational quantum field theory, we explore electron-positron pair creation induced by double-located oscillating electric fields by numerically solving the Dirac equation in full spacetime dimensions. We demonstrate theoretically that computational quantum field theory is equivalent to the first-order time-dependent perturbation theory for single-photon transition pair creation in a spatially inhomogeneous and time-dependent electric field, and verify their equivalence through numerical simulations of pair creation in double-located oscillating fields. We show some interesting results about the periodic oscillation of the momentum spectrum structure of the created particle and the asymmetric multi-photon pair creation process due to the interference between two fields. By using first-order time-dependent perturbation theory, we find that the periodic oscillation in the momentum distribution of the created particle is affected by the field width, the field frequency and the distance between two fields. The period of the oscillation of momentum spectrum structure is changed by the distance between two fields, while the field width has an influence on both the difference between the peak and valley of the momentum spectra and the width of the momentum space available to the created particle. Increasing the frequency of the electric field results in larger momentum for the created particle pairs, while correspondingly reducing the coupling matrix element <inline-formula><tex-math id="M1">\begin{document}$ \langle p|V|n \rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M1.png"/></alternatives></inline-formula> and diminishing the probability of electron-positron pair creation.</sec><sec>The interference between two fields significantly enhances the yield of pair numbers for small distances between two fields. When the distance is too large, the number of pairs created by double oscillating fields is twice that created by a single field, and the enhancement is vanished. When the distance between two fields increases, the period of oscillation decreases. In turn, the creation of electron-positron pairs can become more monochromatic in momentum (energy), while the number of pairs created remains almost constant. As the electric field broadens, the yield of the created pairs decreases for constant potential height. Increasing the field width will reduce the number of particles for each momentum and narrow the momentum space of the created particle. Increasing the field frequency leads to the reduction of the coupling matrix element <inline-formula><tex-math id="M2">\begin{document}$ \langle p|V|n \rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M2.png"/></alternatives></inline-formula> and subsequently reduces the total number of electron-positron pairs created. The field profile parameters such as frequency, width, and distance between two fields can be utilized to select a specific momentum (energy) of particles in future electron-positron pair creation experiments.</sec>