Spin resolved momentum spectra for vacuum pair production via a generalized two level model

We have formulated a generalized two level model for studying the pair production in multidimensional time-dependent electric fields. It can provide momentum spectra with fully spin resolved components for all possible combined spin states of the particle and anti-particle simultaneously. Moreover, we have also investigated the validity of the two level model for fermions (scalar particles) by comparing the results with those by equal-time Dirac-Heisenberg-Wigner (Feshbach-Villars-Heisenberg-Wigner) formalism in different regimes of pair creation, i.e., multiphoton and tunneling dominated mechanisms. It is found that the results are consistent with each other, indicating the good approximation of the two level model. In particular, in terms of the two level model, we found that the contribution of the particle momentum spectra is the greatest when the spin states of the particle and anti-particle are parallel with $S=1$. It is believed that by this two level model one can extend researches on pair production for more different background fields, such as a slowly varying spatial-temporal one. Many other interesting phenomena may also be revealed, including the spin-resolved vortex structure that is contained in the phase feature of the distribution function of the created pairs.