  We study the dynamics of a set of two-level systems coupled by dipolar
interactions under a resonant external Rabi drive. The two-level systems are
prepared initially in a coherent product state, and we ask how the
non-equilibrium conditions caused by the drive affect this coherence. We study
the full non-linear dynamics of the coupled two-level systems within a
classical approximation by analysing numerically the equations of motion and
determining the stability of the collective coherent state within classical
Floquet theory. We establish the behaviour analytically in the high Rabi
coupling limit by employing a Magnus expansion and spin wave analysis. Our
results show that, typically, the dipole interactions between the two-level
systems lead to instabilities that cause a breakdown of the collective Rabi
oscillations. However, we identify parameter regimes for which the two-level
systems undergo collective coherent Rabi oscillations even in the presence of
the dipole interactions.
