Dynamical d-wave condensation of exciton-polaritons in a two-dimensional square-lattice potential

Macroscopic order appears as the collective behaviour of many interacting particles. Prime examples are superfluidity in helium(1), atomic Bose-Einstein condensation(2), s-wave(3) and d-wave superconductivity(4) and metal-insulator transitions(5). Such physical properties are tightly linked to spin and charge degrees of freedom and are greatly enriched by orbital structures(6). Moreover, high-orbital states of bosons exhibit exotic orders distinct from the orders with real-valued bosonic ground states(7). Recently, a wide range of related phenomena have been studied using atom condensates in optical lattices(8-10), but the experimental observation of high-orbital orders has been limited to momentum space(11,12). Here we establish microcavity exciton-polariton condensates as a promising alternative for exploring high-orbital orders. We observe the formation of d-orbital condensates on a square lattice and characterize their coherence properties in terms of population distributions both in real and momentum space.