  We explore the exciton-polariton condensation in the two degenerate orbital
states. In the honeycomb lattice potential, at the third band we have two
degenerate vortex-antivortex lattice states at the inequivalent K and
K'-points. We have observed energetically degenerate condensates within the
linewidth ~ 0.3 meV, and directly measured the vortex-antivortex lattice phase
order of the order parameter. We have also observed the intensity
anticorrelation between polariton condensates at the K- and K'-points. We
relate this intensity anticorrelation to the dynamical feature of polariton
condensates induced by the stochastic relaxation from the common particle
reservoir.
