  We study the dynamics of a driven Dicke model, where the collective spin is
rotated with a constant velocity around a fixed axis. The time evolution of the
mean photon number and of the atomic inversion is calculated using, on the one
hand, a numerical technique for the quantum dynamics of a small number of
two-level atoms, on the other hand, time-dependent mean-field theory for the
limit of a large number of atoms. We observe a reduction of the mean photon
number as compared to its equilibrium value. This dynamically generated
darkness is particularly pronounced slightly above the transition to a
superradiant phase. We attribute the effect to a slowing down of the motion in
the classical limit of a large ensemble and to an interplay of dynamic and
geometric phases in the quantum case.
