  It is now routine to make Bose-Einstein condensates of polaritons with long
enough lifetime and low enough disorder to travel ballistically for hundreds of
microns in quasi-one-dimensional (1D) wires. We present observations of a
polariton condensate injected at one point in a quasi-1D ring, with a
well-defined initial velocity and direction. A clear precession of the circular
polarization is seen, which arises from an effective spin-orbit coupling term
in the Hamiltonian. Our theoretical model accurately predicts the
experimentally observed behavior, and shows that "zitterbewegung" behavior
plays a role in the motion of the polaritons.
