Realizing limit cycles in dissipative bosonic systems

We propose a general mechanism for generating limit cycle (LC) oscillations by coupling a linear bosonic mode to a dissipative nonlinear bosonic mode. By analyzing the stability matrix, we show that LCs arise due to a supercritical Hopf bifurcation. We find that the existence of LCs is independent of the sign of the effective nonlinear interaction. The bosonic model can be realized in three-level systems interacting with a quantized light mode as realized in atom-cavity systems. Using such a platform, we experimentally observe LCs in an atom-cavity system with attractive optical pump lattice, thereby confirming our theoretical predictions for the minimal model and interactions needed to generate LCs for a class of driven-dissipative systems.