  We study formation of superfluid 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
complex 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 access to the
excited states of the polariton condensate. We demonstrate both theoretically
and experimentally formation of vortices in double concentric ring polariton
condensates in the complex annular trap potential.
