where D characterizes the spatial extent of a given mode (along the k ∥ direction). Using the experimental molecular density and the effective number of molecules coupled to a given mode, one can estimate D ≈ 10 -1 ∼ 100 µm, with details provided in Supplementary Note 10, section A. We want to emphasize that τ ∥ differs from the cavity lifetime τ c which considers the photon loss in the k ⊥ direction due to leaking outside the cavity. As a result of τ ∥ , the thermal photon number should be modified as n(ω k ) → n eff (ω k ) with the following expression