Double ring polariton condensates with polariton vortices

We study formation of persistent currents of exciton polaritons in annular polariton condensates in a cylindrical micropillar cavity under the spatially localised nonresonant optical pumping. Since polariton condensates are strongly nonequilibrium systems, the trapping potential for polaritons, formed by the pillar edge and the reservoir of optically induced incoherent excitons, is not real in general case. Its imaginary part includes the spatially distributed gain from the pump and losses of polaritons in the condensate. We show that engineering the gain-loss balance in the micropillar plane gives one an access to the excited states of the polariton condensate. We demonstrate, both theoretically and experimentally, the formation of vortices in double concentric ring polariton condensates in the case of complex annular trap potential.