Dirac proposed the negative energy sea theory in 1931 and predicted the existence of positrons. He suggested that an electron removed from a filled negative energy state would leave a particle called an “anti-electron” in its place, which we now know as the positron. It has the same mass as the electron but carries a positive charge. Currently, two mechanisms are recognized for generating positrons in a vacuum: the Schwinger tunneling mechanism and the multi-photon absorption mechanism. Traditionally, there have been at least two main methods for manipulating outfields to generate superior results. The first method involves generating a strong external field through the superposition of two Coulomb fields. The first method involves generating a strong external field through the superposition of two Coulomb fields. The second method explores the properties of the vacuum by using a very powerful laser to provide an excitation field. However, pure laser energy fields have not been observed to generate positrons from the vacuum in laboratory experiments, due to the insufficient laser intensity and photon energy required to produce observable positrons. Currently, it is not feasible to achieve electric field intensities at the critical value in the laboratory. Given this research status, our study arranges multiple subcritical laser beams in a specific sequence to create a supercritical step potential, thereby lowering the threshold for positron generation. The results show that increasing the number of steps significantly boosts positron production, with each step formed between two laser beams transmitted in the same direction.

In this study, we apply the computational quantum field theory (CQFT) method, based on the numerical solution of the time-dependent Dirac equation, to study the positron generation process in a spatially and temporally varying laser field. This approach allows visualization of positron production dynamics and addresses conceptual issues related to negative energy states. In the process of energy-to-mass conversion, positrons are created and annihilated. Meanwhile, the probability of finding particles in the entire space is not conserved. Hence, it is not appropriate to describe this process using quantum mechanical theory. To delineate the creation and annihilation of particles, quantum field theory is employed, wherein the evolution of operators is derived from Heisenberg’s equations of motion. By utilizing the Hamiltonian of quantum field theory and neglecting the interactions among internal fermions, the resulting operator Ψ(x, t) can be described by the Dirac equation. This operator Ψ(x, t) enables the calculation of spatial density distributions and the total number of positrons created.

For the static step well formed by multiple strongest laser beams, we find that arranging subcritical laser beams of equal intensity can achieve supercritical potential well effects and improve energy utilization rates. Increasing the number of laser beams, despite their individual low electric field intensity, leads to positron generation via a supercritical effect. However, more beams also extend the tunneling distance for positrons, reducing the generation rate compared to a single supercritical laser beam in localized space (Fig. 2). Investigating positron production under tunneling and photon absorption mechanisms revealed that a synergistic effect enhances the generation rate further (Fig. 4). The supercritical potential overlaps positive and negative energy levels, allowing virtual state particles to absorb photon energy during tunneling and produce positrons. With the same number of laser beams, oscillation step well excitation generates more positrons than barrier excitation due to increased tunneling distances at potential barrier junctions (Fig. 7). This indicates higher energy utilization in oscillation step wells compared to barriers, offering valuable insights for reducing positron generation thresholds.

Our study elucidates the relationship between vacuum positron production rates and the sequence and spacing of multiple laser beams. We discover through proper arrangement, multiple subcritical laser beams can mimic the effect of a supercritical field. However, when different localization potential heights are equivalent, fewer laser beams result in the production of more particles, a phenomenon determined by the local electric field strength in space. Concurrently, we also find that even with consistent potential height and electric field strength, positron production varies depending on the shape of the potential edge, with significant differences in production rates. Compared with the static state well, the oscillating step potential wells in spatial terms show a more pronounced enhancement effect on positron numbers. The generation of particle numbers escalates exponentially with each additional laser beam. When maintaining the same number of laser beams, if the bottom width of the potential well is increased, the positron production fluctuates at small widths, stabilizing at a width of 20/c, attributed to the energy level of bound states within the localized electric field’s extent. Employing multiple subcritical laser beams can create various forms of potential wells or barrier structures with spatial localization potential, which in turn induces different numbers of positrons in the vacuum. This has significant implications and reference value for enhancing the efficiency of laser energy utilization.