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We study the dynamics of a set of two-level systems coupled by dipolarinteractions under a resonant external Rabi drive. The two-level systems areprepared initially in a coherent product state, and we ask how thenon-equilibrium conditions caused by the drive affect this coherence. We studythe full non-linear dynamics of the coupled two-level systems within aclassical approximation by analysing numerically the equations of motion anddetermining the stability of the collective coherent state within classicalFloquet theory. We establish the behaviour analytically in the high Rabicoupling limit by employing a Magnus expansion and spin wave analysis. Ourresults show that, typically, the dipole interactions between the two-levelsystems lead to instabilities that cause a breakdown of the collective Rabioscillations. However, we identify parameter regimes for which the two-levelsystems undergo collective coherent Rabi oscillations even in the presence ofthe dipole interactions.

Stable Collective Dynamics of Two-Level Systems Coupled by Dipole Interactions