Spontaneous formation of time-periodic vortex cluster in nonlinear fluids of light

We demonstrate spontaneous formation of a nonlinear vortex cluster state in a microcavity exciton-polariton condensate with time-periodic sign flipping of its topological charges at the GHz scale. When optically pumped with a ring-shaped nonresonant laser, the trapped condensate experiences intricate high-order mode competition and fractures into two distinct trap levels. The resulting mode interference leads to robust condensate density beatings with periodic appearance of orderly arranged phase singularities. Our work opens new perspectives on creating structured free-evolving light, and singular optics in the strong light-matter coupling regime.