  We excite exciton-polariton condensates in half-moon shapes by the
non-resonant optical excitation of GaAs-based cylindrical pillar microcavities.
In this geometry, the {\pi}-jump of the phase of the condensate wave function
coexists with a gradual {\pm \pi} phase variation between two horns of the
half-moon. We switch between clockwise and counter-clockwise phase currents by
slightly shifting the excitation spot on the surface of the pillar. Half-moon
condensates are expected to reveal features of two-level quantum systems
similar to superconducting flux qubits
