  We study the collective response of a group of dissipative Rydberg atoms to a
periodic modulation of the Rydberg excitation laser. Focusing on the emergent
collective-jump dynamics, where the system stochastically switches between
states with distinct Rydberg excitations, we show that the counting statistics
of the state switching is qualitatively changed by the periodic drive. The
impact is most prominent when the driving frequency is comparable to the
emergent collective-jump rate, as the jumps tend to synchronize with the
external drive, and their counting statistics exhibits a series of suppressed
subharmonics of the driving frequency. These phenomena are manifestations of a
novel type of stochastic resonance, where a cooperative collective state
switching is facilitated by quantum fluctuations in a many-body open system.
Such a collective quantum stochastic resonance further leads to an enhanced
signal-to-noise ratio in the power spectrum of the Rydberg excitations, for
which the synchronized collective jumps are viewed as the output signal. We
confirm the many-body quantum nature of the resonance by devising a cluster
model, under which the role of many-body correlations is analyzed by changing
the size of the atom clusters.
