Emergent limit cycles and chaos in extended driven-dissipative atomic arrays*

We analyze the driven-dissipative dynamics of periodic atomic arrays in free space, where the atoms interact via light-induced dipole-dipole interactions. Based on a mean-field model, we find that solely tuning the lattice spacing and the driving strength gives access to different types of non-linear dynamics. Besides the expected steady-state that can be reached at infinite times, we determine parameter regimes in which persistent limit cycles as well as chaotic many-body dynamics can be accessed. We link this property to the occurrence of a bistable regime in parameter space. Intriguingly, the dissipative nature of the studied system gives rise to chaotic dynamics without imposing randomness externally and also for finite size systems of the size currently available in state-of-the art experimental setups.