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Semiconductor-microcavity polaritons are composite quasiparticles of excitonsand photons, emerging in the strong coupling regime. As quantum superpositionsof matter and light, polaritons have much stronger interparticle interactionscompared with photons, enabling rapid equilibration and Bose-Einsteincondensation (BEC). Current realizations based on 1D photonic structures, suchas Fabry-P\'erot microcavities, have limited light-trapping ability resultingin picosecond polariton lifetime. We demonstrate, theoretically,above-room-temperature (up to 590 K) BEC of long-lived polaritons in MoSe$_2$monolayers sandwiched by simple TiO$_2$ based 3D photonic band gap (PBG)materials. The 3D PBG induces very strong coupling of 40 meV (Rabi splitting of62 meV) for as few as three dichalcogenide monolayers. Strong light-trapping inthe 3D PBG enables the long-lived polariton superfluid to be robust againstfabrication-induced disorder and exciton line-broadening.

Photonic Architectures for Equilibrium High-Temperature Bose-Einstein Condensation in Dichalcogenide Monolayers