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The possibility of investigating macroscopic coherent quantum states in polariton condensates and of engineering polariton landscapes in semiconductors has triggered interest in using polaritonic systems to simulate complex many-body phenomena. However, advanced experiments require superior trapping techniques that allow for the engineering of periodic and arbitrary potentials with strong on-site localization, clean condensate formation, and nearest-neighbor coupling. Here we establish a technology that meets these demands and enables strong, potentially tunable trapping without affecting the favorable polariton characteristics. The traps are based on a locally elongated microcavity which can be formed by standard lithography. We observe polariton condensation with non-resonant pumping in single traps and photonic crystal square lattice arrays. In the latter structures, we observe pronounced energy bands, complete band gaps, and spontaneous condensation at the M-point of the Brillouin zone.
Bosonic condensation belongs to the most intriguing phenomena in physics, and was mostly reserved for experiments with ultra-cold quantum gases. More recently, it became accessible in exciton-based solid-state systems at elevated temperatures. Here, we demonstrate bosonic condensation driven by excitons hosted in an atomically thin layer of MoSe2, strongly coupled to light in a solid-state resonator. The structure is operated in the regime of collective strong coupling between a Tamm-plasmon resonance, GaAs quantum well excitons, and two-dimensional excitons confined in the monolayer crystal. Polariton condensation in a monolayer crystal manifests by a superlinear increase of emission intensity from the hybrid polariton mode, its density-dependent blueshift, and a dramatic collapse of the emission linewidth, a hallmark of temporal coherence. Importantly, we observe a significant spin-polarization in the injected polariton condensate, a fingerprint for spin-valley locking in monolayer excitons. Our results pave the way towards highly nonlinear, coherent valleytronic devices and light sources.