where 𝑔 c = 𝜇 LL ′ √︀ 1/(2ℏ𝜖 0 𝒱) is the Jaynes-Cummings type coupling strength (without the √ 𝜔 k -dependence). There are also 𝑁 -1 dark states that do not mix with the photonic degrees of freedom (DOF) under this approximation. Details of this standard analysis are provided in the Supplementary Material, Sec. III.