  A comparison between the single particle spectrum of the discrete
Bardeen-Cooper-Schrieffer (BCS) model, used for small superconducting grains,
and the spectrum of a paradigmatic model of Single Excitation Superradiance
(SES) is presented. They are both characterized by an equally spaced energy
spectrum (Picket Fence) where all the levels are coupled between each other by
a constant coupling which is real for the BCS model and purely imaginary for
the SES model. While the former corresponds to the discrete BCS-model
describing the coupling of Cooper pairs in momentum space and it induces a
Superconductive regime, the latter describes the coupling of single particle
energy levels to a common decay channel and it induces a Superradiant
transition. We show that the transition to a Superradiant regime can be
connected to the emergence of an imaginary energy gap, similarly to the
transition to a Superconductive regime where a real energy gap emerges. Despite
their different physical origin, it is possible to show that both the
Superradiant and the Superconducting gaps have the same magnitude in the large
gap limit. Nevertheless, some differences appear: while the critical coupling
at which the Superradiant gap appears is independent of the system size $N$,
for the Superconductivity gap it scales as $(\ln N)^{-1}$. The presence of a
gap in the imaginary energy axis between the Superradiant and the Subradiant
states shares many similarities with the "standard" gap on the real energy
axis: the superradiant state is protected against disorder from the imaginary
gap as well as the superconducting ground state is protected by the real energy
gap. Moreover we connect the origin of the gapped phase to the long-range
nature of the coupling between the energy levels.
