Electron-position pair creation under combined oscillation fields with different frequencies

We study the creation of electron-positron pairs in vacuum induced by multi-photon transition process with combined oscillating fields. According to computational quantum field theory and split operator technique, we numerically solve spatiotemporally dependent Dirac equation. The effects frequencies on yields energy distributions are investigated.First, show that even for subcritical fields, goal generating continuously can be achieved combining two also find when sum is close <inline-formula><tex-math id="M3">\begin{document}$ 2.3c ^ 2 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20221660_M3.jpg"/><graphic xlink:href="2-20221660_M3.png"/></alternatives></inline-formula> (a.u.), yield created reaches a maximum value. In case only one filed involved single photon dominant, pair optimal at this frequency. way, fields fixed id="M4">\begin{document}$ 2.3c^2 xlink:href="2-20221660_M4.jpg"/><graphic xlink:href="2-20221660_M4.png"/></alternatives></inline-formula> later simulations. For example, id="M5">\begin{document}$\omega_1=1.1c^{2},\; \omega_2= 1.2c^{2}$\end{document}</tex-math><alternatives><graphic xlink:href="2-20221660_M5.jpg"/><graphic xlink:href="2-20221660_M5.png"/></alternatives></inline-formula>; id="M6">\begin{document}$\omega_1=1.0c^{2},\; 1.3c^{2}$\end{document}</tex-math><alternatives><graphic xlink:href="2-20221660_M6.jpg"/><graphic xlink:href="2-20221660_M6.png"/></alternatives></inline-formula>; id="M7">\begin{document}$ \omega_1=0.8c^{2}, xlink:href="2-20221660_M7.jpg"/><graphic xlink:href="2-20221660_M7.png"/></alternatives></inline-formula><inline-formula><tex-math id="M7-1">\begin{document}$ 1.5c^{2} xlink:href="2-20221660_M7-1.jpg"/><graphic xlink:href="2-20221660_M7-1.png"/></alternatives></inline-formula>; id="M8">\begin{document}$\omega_1=0.5c^{2},\; 1.8c^{2}$\end{document}</tex-math><alternatives><graphic xlink:href="2-20221660_M8.jpg"/><graphic xlink:href="2-20221660_M8.png"/></alternatives></inline-formula>; id="M9">\begin{document}$\omega_1=0.4c^{2},\; 1.9c^{2}$\end{document}</tex-math><alternatives><graphic xlink:href="2-20221660_M9.jpg"/><graphic xlink:href="2-20221660_M9.png"/></alternatives></inline-formula> applied following study.The time evolutions under different frequency combinations investigated. It found each other, growth rate id="M10">\begin{document}${\rm{d}}N/{\rm{d}}t$\end{document}</tex-math><alternatives><graphic xlink:href="2-20221660_M10.jpg"/><graphic xlink:href="2-20221660_M10.png"/></alternatives></inline-formula> presents an obvious periodic variation, showing “beat” - like structure. structure synchronized synthesized electric field. Meanwhile, long-term id="M11">\begin{document}${\rm{d}}N/{\rm{d}}t$\end{document}</tex-math><alternatives><graphic xlink:href="2-20221660_M11.jpg"/><graphic xlink:href="2-20221660_M11.png"/></alternatives></inline-formula> increases significantly difference becomes larger.The studied. small (eg, id="M12">\begin{document}$\omega_1=1.0c^{2},\; xlink:href="2-20221660_M12.jpg"/><graphic xlink:href="2-20221660_M12.png"/></alternatives></inline-formula>), distribution particles shows quasi-monoenergetic feature, most distributed around id="M13">\begin{document}$ 1.1c^{2}-1.2c^{2} xlink:href="2-20221660_M13.jpg"/><graphic xlink:href="2-20221660_M13.png"/></alternatives></inline-formula>. large id="M14">\begin{document}$\omega_1=0.5c^{2},\; xlink:href="2-20221660_M14.jpg"/><graphic xlink:href="2-20221660_M14.png"/></alternatives></inline-formula>), total greatly increases. range broadened generation more energetic particles.By analyzing comparing probability transitions between negative positive energy, main reason spectrum-broadening yield-increasing enhancement process. Beside two-photon (<inline-formula><tex-math id="M15">\begin{document}$ \omega_{1}+\omega_{2} xlink:href="2-20221660_M15.jpg"/><graphic xlink:href="2-20221660_M15.png"/></alternatives></inline-formula>), which high all cases, higher-order id="M16">\begin{document}$2\omega_{1}+\omega_{2},\;3\omega_{1}+\omega_{2},\;4\omega_{1}+\omega_{2}$\end{document}</tex-math><alternatives><graphic xlink:href="2-20221660_M16.jpg"/><graphic xlink:href="2-20221660_M16.png"/></alternatives></inline-formula>) will arise same order as transition. These enhance pairs, especially high-energy pairs. second narrow width id="M17">\begin{document}$ W=2/c xlink:href="2-20221660_M17.jpg"/><graphic xlink:href="2-20221660_M17.png"/></alternatives></inline-formula>), conservation momentum breaks down, corresponding asymmetric important, further enhances production broadens distribution.For wide id="M18">\begin{document}$ W=5/c xlink:href="2-20221660_M18.jpg"/><graphic xlink:href="2-20221660_M18.png"/></alternatives></inline-formula>), high-order suppressed compared id="M19">\begin{document}$ xlink:href="2-20221660_M19.jpg"/><graphic xlink:href="2-20221660_M19.png"/></alternatives></inline-formula>). However, still have important influence productions distributions.