Motion of patterns in polariton quantum fluids with spin-orbit interaction

We report on a remarkable effect of pseudospin precession on the collective motion of exciton-polaritons in a microresonator coherently driven by a linearly polarized pump. In particular, we show that hexagonal patterns can undergo a spontaneous symmetry breaking of their polarization and start a uniform motion in the plane of the resonator. Similar to the optical spin Hall effect, this becomes possible due to a spin-orbit interaction induced by a longitudinal-transverse splitting (TE-TM splitting) of the photonic resonator mode. We derive a simple analytical expression for the drift velocity of the patterns.