As shown in Ref. 49, the analytic solution is also available for Ĥs . For the zero-detuning case ε = ℏω c , the Rabi splitting is ℏΩ R = ε + -ε -= 2 √ N ℏg c , and the strong coupling limit is achieved when Ω R ≫ 1 2 (Γ + κ), where Ω R is the cavity loss rate (linewidth of the cavity transmission spectra, τ c = 1/Γ is the cavity lifetime) and κ is the exciton linewidth.