  Dicke superrandiance is a cooperative phenomenon which arises from the
collective coupling of an ensemble of atoms to the electromagnetic radiation.
Here we discuss the quantifying of quantum coherence for the Dicke model of
superradiance in the mean-field approximation. We found the single-atom
$l_1$-norm of coherence is given by the square root of the normalized average
intensity of radiation emitted by the superradiant system. This validates
quantum coherence as a useful figure of merit towards the understanding of
superradiance phenomenon in the mean-field approach. In particular, this result
suggests probing the single-atom coherence through the radiation intensity in
superradiant systems, which might be useful in experimental realizations where
is unfeasible to address atoms individually. Furthermore, given the nonlinear
unitary dynamics of the time-dependent single-atom state that effectively
describes the system of $N$ atoms, we analyze the quantum speed limit time and
its interplay with the $l_1$-norm of coherence. We verify the quantum coherence
speeds up the evolution of the superradiant system, i.e., the more coherence
stored on the single-atom state, the faster the evolution. These findings
unveil the role played by quantum coherence in superradiant systems, which in
turn could be of interest for communities of both condensed matter physics and
quantum optics.
