Electron-positron pair production in strong electric fields, i.e., the Sauter-Schwinger effect, is studied using the real-time Dirac-Heisenberg-Wigner formalism. Hereby, the electric field is modeled to be a homogeneous, single-pulse field with subcritical peak field strength. Momentum spectra are calculated for four different polarizations—linear, elliptic, near-circular elliptic or circular—as well as a number of linear frequency chirps. With details depending on the chosen polarization, the frequency chirps lead to strong interference effects and thus quite substantial changes in the momentum spectra. The resulting produced pairs’ number densities depend nonlinearly on the parameter characterizing the polarization and are very sensitive to variations of the chirp parameter. For some of the investigated frequency chirps, this can provide an enhancement of the number density by 3 to 4 orders of magnitude.

In the quantum kinetic framework, we investigate the momentum spectrum and the number density of created electron-positron pairs from vacuum in the combined electric fields composed of two sets of alternating-sign electric field pulse trains, a strong but slowly varying one and a weak but rapidly changing one. It is found that the pair production can be strongly enhanced by combining the multiple-slit interference effect with the dynamically assisted Schwinger mechanism. By considering the contribution of the transverse momentum, we find that the number density of created particles depends linearly on the electric field pulse number, i.e., a power law with index 1. Moreover, we study the effect of interpulse time delay on pair production and find that the number density is very sensitive to the interpulse time delay. The symmetry of the momentum spectrum for an $N$-pulse electric field and the difference of the multiple-slit interference effect between the nonperturbative Schwinger mechanism and the perturbative multiphoton electron-positron pair creation are also studied. Some possible explanations for observed results of momentum spectrum and number density are also given and discussed.

The momentum signatures of created pairs in the multiphoton regime in strong fields are investigated and obvious vortex patterns that are constituted of the quasi-Archimedian spirals are found when considering two opposite-handedness circularly polarized fields. Distinguished from the familiar Ramsey interference fringes with the concentric rings under two identical-handedness fields, however, the finding vortices are associated to the interference between the pair production amplitudes of these two opposite-handedness fields. Moreover, the sensitive dependence of vortex patterns on the relative carrier envelope phase, the time delay, and the handedness between two fields imply also a new way to detect the applied laser field characteristics.

Electron-positron pair production from vacuum in external electric fields with space and time dependencies is studied numerically using real time Dirac-Heisenberg-Wigner formalism. The influence of the spatial focusing scale of the electric field on momentum distribution and the total yield of the particles is investigated by considering space-time dependent electric fields in $1+1$ dimensions with various temporal configurations. With the decrease of the spatial extent of the external field, signatures of the temporal field are weakened in the momentum spectrum. Moreover, in the extremely small spatial extent, novel features emerge due to the combined effects of both temporal and spatial variations. We also find that for dynamically assisted particle production, while the total particle yield drops significantly in small spatial extents, the assistance mechanism tends to increase in these highly inhomogeneous regimes, where the slow and fast pulses are affected differently by the overall spatial inhomogeneity.

The effects of electric field polarizations on pair production from a vacuum are investigated numerically by employing the real-time Dirac-Heisenberg-Wigner formalism. For few-cycle fields, it is found that the interference pattern in momentum spectra is absent and the circular distortion of the momentum distribution becomes more apparent with an increase of the polarization. For multicycle fields, it is found that the interference effects in momentum spectra are obvious. And as the polarization increases, the momentum distribution is split into two parts in the momentum $q_y$ direction first and then two separated parts are connected into a ring. The effects of polarizations on the number density of created particles exhibits two different characteristics. For a small laser frequency, the particle number density decreases with the polarization, while for a large laser frequency, the relation between them is sensitive to the field frequency nonlinearly. Some interpretations for the results obtained in this study are provided, which are expected to be valuable for understanding pair production in complex fields and also helpful for the study of strong-field ionization.

Spirals in multiphoton pair production are revisited by two counterrotating fields with time delay for different cycles in pulse. Novel findings include that for subcycle fields; the remarkable spiral structure in the momentum spectrum can be still caused by a large time delay compared to the previous study for the supercycle case where it is easier to be generated by a small time delay. Also there exist a range of critical polarization values for the spirals’ appearance corresponding to the different cycle numbers. The relative phase difference between two fields causes not only severe symmetry breaking of the momentum spectra pattern and spiral but also a significant change for the shape and the number of spiral arms. The number density is found to be more sensitive to the cycle number; in particular, it is enhanced by more than one order of magnitude for a small cycle pulse, while it is increased a few times when the time delay is small. These results provide an abundant theoretical testbed for the possible experimental observation of the multiphoton pair production in the future. Meanwhile, it is applicable to use the particles’ momentum signatures as a new way to probe the laser field information.