We present here a theoretical analysis of the interaction between an ideal two-level quantum system and a super-oscillatory pulse, like the one proposed and successfully synthesized in [J. Opt. 23, 075604 (2021) [CrossRef] ; arXiv:2106.09192 (2021)]. As a prominent feature, these pulses present a high efficiency of the central super-oscillatory region in relation to unavoidable sidelobes. Our study shows an increase in the effective bandwidth of the pulse in the super-oscillatory region, and not only the appearance of a local frequency higher than its highest Fourier-frequency component, as in the usual description of the phenomenon of super-oscillations. Beyond introducing the concept of effective super-bandwidth, the presented results could be relevant for experimental applications and opening new perspectives for laser–matter interaction.

中文翻译：

---

激光脉冲中的有效超带宽

我们在此对理想的两能级量子系统与超振荡脉冲之间的相互作用进行了理论分析，就像在 [J. 选择。23 , 075604 (2021) [CrossRef] ; arXiv:2106.09192 (2021)]。作为一个显着特征，这些脉冲呈现出与不可避免的旁瓣相关的中央超振荡区域的高效率。我们的研究表明，超振荡区域中脉冲的有效带宽增加，而不仅仅是出现高于其最高傅立叶频率分量的局部频率，就像对超振荡现象的通常描述一样。除了引入有效超带宽的概念外，所呈现的结果可能与实验应用相关，并为激光-物质相互作用开辟了新的视角。