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 ene
rgetically 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.
Dirac particles, massless relativistic entities, obey linear energy dispersions and hold important implication in particle physics. Recent discovery of Dirac fermions in condensed matter systems including graphene and topological insulators raises gr
eat interests to explore relativistic properties associated with Dirac physics in solid-state materials. In addition, there are stimulating research activities to engineer Dirac paricles to eludicte their physical properties in a controllable setting. One of the successful platforms is the ultracold atom-optical lattice system, whose dynamics can be manipulated in a clean environment. A microcavity exciton-polariton-lattice system provides an alternative route with an advantage of forming high-orbital condensation in non-equilibrium conditions, which enables to explore novel quantum orbital order in two dimensions. Here we directly map the liner dispersions near the Dirac points, the vertices of the first hexagonal Brillouin zone from exciton-polariton condensates trapped in a triangular lattice. The associated velocity values are ~ 0.9 - 2*10^8 cm/s, which are consistent with the theoretical estimate 1*10^8 cm/s with a 2 mu m-lattice constant. We envision that the exciton-polariton condensates in lattices would be a promising solid-state platform, where the system order parameter can be accesses in both real and momentum spaces. We furthermore explore unique phenomena revealing quantum bose nature such as superfluidity and distinct features analogous to quantum Hall effect pertinent to time-reversal symmetry.
