  Self-rotation occurs in an exciton-polariton condensate in a two-dimensional
semiconductor microcavity pumped by a nonresonant Gaussian laser beam. A wave
packet of the condensate spontaneously rotates around the center of the pumped
region at a constant frequency breaking the rotation symmetry of the system.
When two self-rotating condensates are created with an appropriate distance,
synchronization occurs between the dynamics of the self-rotating condensates.
