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 loss and gain of polariton BEC induces a variety of steady states with different configuration, 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.