Half-quantum circulation and optical spin Hall effect in a polariton spinor ring condensate*

We have observed half-quantum circulation in a macroscopic polariton spinor condensate in a ring trap. In our experiment, the polaritons come from the strong coupling between photons and electronic excitations (excitons) in quantum wells embedded in a microcavity. The polaritons are repulsively interacting bosons with small effective mass. The ring trap is a combination of a strain-induced harmonic trap and a laser-generated central barrier. By measuring the phase and polarization of the condensate, we find that theres is a phase rotation of $\pi$ in connection with a polarization rotation of $\pi$ around a closed path. In addition, the handedness of the circular polarization component, which gives the spin of the polariton, flips from one side of the ring to the other. Such a state is allowed in a ring geometry but is prohibited in a simply-connected geometry. The direction of circulation of the flow around the ring fluctuates randomly between clockwise and counterclockwise; this corresponds to spontaneous breaking of time-reversal symmetry in the system. In contrast, the polarization pattern of the condensate is very stable which is very likely due to the optical spin Hall effect playing a role as the condensate is generated.