Attractive-repulsive interaction in coupled quantum oscillators

We study the emergent dynamics of quantum self-sustained oscillators induced by the simultaneous presence of attraction and repulsion in the coupling path. We consider quantum Stuart-Landau oscillators under attractive-repulsive coupling and construct the corresponding quantum master equation in the Lindblad form. We discover an interesting symmetry-breaking transition from quantum limit cycle oscillation to a quantum inhomogeneous steady state. This transition is contrary to the previously known symmetry-breaking transition from a quantum homogeneous state to an inhomogeneous steady state. The result is supported by the analysis on the noisy classical model of the quantum system in the weak quantum regime. Remarkably, we find the generation of entanglement associated with the symmetry-breaking transition that has no analog in the classical domain. This study enriches our understanding of the collective behaviors shown by coupled oscillators in the quantum domain.