Abstract
The computational quantum field theory (CQFT) is applied to study the dependence of the total EPP number on the time interval under the spatially localized double cosine-Gaussian pulse and the alternating-sign double-Gaussian pulse. The total EPP number damply oscillates with the time interval, and the oscillation frequency is about the energy gap ($2m{c}^{2}$) for all of the scenarios. This characteristic oscillation of the total EPP number is consistent with a formula, which is related to the amplitude mode in the BCS superconductors. Besides, we find that the Ramsey interference effect is not responsible for the characteristic oscillation by studying the double-Gaussian pulse with the same sign. Finally, when the favorable time interval is applied, the EPP number is much larger than the sum of the EPP number obtained in two single pulses. The favorable time interval mainly depends on the pulse duration and the carrier envelope phase (the quantity in cosine-Gaussian pulse).
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