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Dynamically generated darkness in the Dicke model

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.