Moir\'e-Polaritons in a Dark Bose-Einstein Condensate

Quantum mixtures of moir\'e excitons have arisen as a platform for realizing novel phases of light and matter. Here, we study moir\'e polaritons coupled to a Bose-Einstein condensate of dark-state excitons confined to a moir\'e superlattice. We develop a variational approach to analyze the optical response of the system and demonstrate that strong exciton-exciton interactions significantly modify the character of moir\'e polaritons, leading to sizable energy shifts of the avoided crossing between the principal polariton branches, and the emergence of an additional, stable repulsive-polariton bound state.