This study investigates the combination of two not completely overlapping oscillating fields. The aim is to analyze the effect of the separation distance between the fields on the production of electron-positron pairs in a vacuum.The process was simulated using Computational Quantum Field Theory (CQFT) methods and the split-operator technique, based on the space-time dependent Dirac equation. The primary focus was on analyzing the impact of separation distance and frequency combinations on the pair production rate and energy spectrum.
The research found that partially overlapping subcritical oscillating fields can still effectively generate electronpositron pairs within a small separation distance. The variation in separation distance in the overlapping direction significantly affects the pair production rate. For two oscillating fields with a fixed sum of frequencies, the separation distance has a notable impact on the production rate, with different frequency combinations showing varying degrees of dependency.
Further analysis of the energy spectrum revealed that the number and position of spectral peaks are differently affected by the separation distance. Models with smaller frequency differences exhibited more concentrated energy distributions, generally presenting a single-peak structure. In contrast, models with larger frequency differences showed more dispersed energy distributions, typically presenting a dual-peak structure. As the separation distance increases, the energy spectrum structure varies with different frequency combinations, especially for larger separation distances. In cases with larger frequency differences, the high-energy peak decreases rapidly with increasing separation distance, resulting in a lower proportion of high-energy electrons, whereas the cases with smaller frequency differences exhibit less change. This phenomenon was further analyzed using particle energy transition probability distribution diagrams.
By observing the particle energy transition probability distribution diagrams, we gained preliminary insights into the differences in various frequency combinations with changes in separation distance, explaining the variations in energy spectrum structure from the perspective of multiphoton transitions.Additionally, a more detailed analysis of these diagrams based on the law of energy conservation allowed us to extract the trends in particle production corresponding to various multiphoton transition effects.It was found that for the same frequency combination, the trends of second and third-order effects with varying separation distances differ, with higher-order effects decreasing more rapidly.
By analyzing the changes in multiphoton transition probabilities for the combined fields with separation distance, as well as the changes in the individual fields’ multiphoton transition probabilities, we concluded that when the separation distance is small, the combined fields with larger frequency differences have an advantage in electron-positron pair production. However, when the separation distance is large, the combined fields with smaller frequency differences begin to play a major role due to their inherent multiphoton effects, demonstrating better stability. For different cases under the combined influence of two fields, we conducted a more in-depth analysis of the differences between various orders within the same frequency combination and the differences between the same order transitions under different frequency combinations. By proposing hypotheses and performing computational verification, it was found that the trend of normalized-overlapping photon numbers with varying separation distances under the same conditions is consistent with the trend of corresponding particle production numbers, providing a more convenient method for examining the trends in particle production with separation distance.
This study not only enriches our understanding of vacuum electron-positron pair generation in strong fields but also provides theoretical guidance and reference for designing experimental setups for pair production.