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 vacuum electron-positron pair production in strong classical background fields via slowly varying envelope approximation. It can provide momentum spectra with fully spin resolved components for all possible combined spin states of the particle and antiparticle simultaneously in multidimensional time-dependent electric fields. 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 antiparticle are parallel with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>S</a:mi><a:mo>=</a:mo><a:mn>1</a:mn></a:math>. 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. Significantly, we demonstrate that the generalized two level model is equivalent to the spin resolved quantum kinetic theory. In comparison to the equal-time Dirac-Heisenberg-Wigner and Feshbach-Villars-Heisenberg-Wigner methods, the two-level model is simpler and has the potential to deliver faster computational performance.