Na Young Kim ^a,b*

^a Institute for Quantum Computing, University of Waterloo, 200 University Ave. West, Waterloo, ON, N2L 3G1, Canada
^b Department of Electrical and Computer Engineering, Department of Physics and Astronomy, Department of Chemistry, University of Waterloo, 200 University Ave. West, Waterloo, ON, N2L 3G1, Canada
^c Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada

* Corresponding author: nayoung.kiim@uwaterloo.ca

Microcavity exciton-polaritons are hybrid quantum quasi-particles as an admixture of cavity photons and quantum-well excitons. We engineer exciton-polariton-lattice systems, where we seek the beauty of non-zero momentum boson order arising from the intrinsic open-dissipative nature of the condensate as well as the topology of lattices. In this work, we quantify the hopping integrals of the lowest-band exciton-polaritons in terms of two physical parameters: nearest-neighbor site distance, d (3,4,5 and 7 𝜇m), and detuning values Δ ( - 19 ~ 9 meV) in engineered two-dimensional honeycomb lattices.  The artificial lattices are formed by an etching-overgrowth technique to module the cavity layer thickness to induce a photon confinement. The lattice potential depths vary 3-5 meV at different Δ values, and we construct the band structures of the exciton-polaritons via a low-power angle-resolved photoluminescence spectroscopy. The hopping integrals of nearest-neighbor and next-nearest neighbor sites in the lowest bands are extracted from the measured band structures by the tight-binding Hamiltonian fittings.