  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 https://doi.org/10.1088/2040-8986/abfedf and
arXiv:2106.09192. As a prominent feature, these pulses present a high
efficiency of the central super-oscillatory region in relation to the
unavoidable side-lobes. Besides, our study shows an increase of 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.
