Spontaneous Formations of Dynamical Steady States in Polariton Condensates

We present a numerical analysis on dynamical steady states of polariton Bose–Einstein condensates (BECs) in an incoherent exciton reservoir driven by a ring-shaped optical pump. The balance between the loss and gain of polariton BEC induces a variety of steady states with different configurations, including approximate Gaussian distribution and topological defects, such as vortex–antivortex pairs, vortices with a winding number, and solitons. Besides, the system becomes unstable under fast decay rates and small pumping ring, where BECs can no longer exist in the long-time limit. We also confirm the soliton is dynamically stable in this system, with a steady polariton current induced by the repulsive polariton–polariton and polariton–exciton interactions