Structuring co- and counter-flowing currents of polariton condensates in concentric ring-shaped potentials

We investigate the current flow of microcavity polariton condensates loaded into concentric ring-shaped potentials. The tunneling of the condensates between different potential rings results in different phase-locked states, depending on the separation of the potential rings. As a consequence, the condensate currents in different rings can flow either in the same or opposite direction depending on the specific configuration of the ring-shaped potentials. In two concentric standard ring-shaped potentials, the condensates always circulate in the same direction (co-flowing current) and the vortices formed in the two rings share the same topological charge because of the azimuthally uniform distribution of their phase difference. In this case, increasing the number of the potential rings enables the excitation of Bessel-like solutions. If the two ring-shaped potentials are engineered into an eye shape with the inner ring being standard ring-shaped and the outer ring being elliptically ring-shaped, the phase differences of the condensates in the two rings along the major and minor axes of the ellipse can be opposite, which gives rise to a counter-flowing condensate currents.