We explore the exciton-polariton condensation in the two degenerate orbitalstates. In the honeycomb lattice potential, at the third band we have twodegenerate vortex-antivortex lattice states at the inequivalent K andK'-points. We have observed energetically degenerate condensates within thelinewidth ~ 0.3 meV, and directly measured the vortex-antivortex lattice phaseorder of the order parameter. We have also observed the intensityanticorrelation between polariton condensates at the K- and K'-points. Werelate this intensity anticorrelation to the dynamical feature of polaritoncondensates induced by the stochastic relaxation from the common particlereservoir.
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