Abstract
We study the dynamics of exciton-polariton condensates in reconfigurable potentials created by an incoherent optical pump. The mode selection in the effective optically induced trap is shown to be determined by the largest growth rates of the linear eigenmodes of the effective complex potential created by the pump. We demonstrate that selection of higher order nonlinear modes with nonzero orbital angular momenta in such traps leads to formation of vortices in a single-component condensate and spin textures in exciton-polariton condensates consisting of two polarization components. We also show that cross-polarization coupling can lead to the synchronization of the modes belonging to different polarizations. We highlight clear signatures of the various spontaneously formed trapped states in the cavity photoluminescence spectrum, which should aid in their experimental observations.