, where N is the number of included electronic states. Recall that the strong coupling in cavity QED is commonly defined as g c ≫ κ, where g c is the matter-cavity coupling strength and κ is the cavity loss (if matter deexcitation rate is much smaller than the cavity loss). In this example (Fig. ), the absorption spectra (calculated using Eq. 147) is shown for different cases of cavity strength λ and cavity loss rate κ, which will turn the light-matter couplings from the weak coupling (no Rabi splitting) to the strong coupling regimes (has Rabi splittings). The excitonic character (orange) and the photonic character (blue) are depicted in the color bar in Fig. . For each sub-panel, (i) at a low coupling strength (λ = 0.01 a.u.) and cavity loss κ = 10 meV, the Rabi splitting is not visible in the spectral reso-lution, and the feature is dominated by the excitonic character; (ii) at a larger coupling strength (λ = 0.1 a.u.) and the same κ = 10 meV, the Rabi splitting is clearly visible; however, the second excited state is not affected by the presence of the cavity due to the large energetic separation (detuning) between the UP state and the second electronic excited state. Now, the main polaritonic absorption features are mixed between electronic and photonic contributions. (iii) at a very large coupling strengths (λ = 0.43 a.u.), the UP polariton state now strongly mixed with the second excited electronic state and forms the ULP and the UUP polariton states. Further, one can fix the coupling strength λ and gradually increase the loss rate κ. (iv) For the case of the very strong coupling λ = 0.43 a.u., the cavity loss rate is increased from κ = 10 meV to κ = 100 meV, effectively increasing the spectral signature of the cavity modes centered at ω c . Here, the character of the absorption is dominated by the photonic DOF (blue color), and the width of each main feature in the absorption becomes much broader compared to the case in (iii). (v) At an even larger cavity loss rate κ = 320 meV, the identities of the LP and ULP start to disappear, leaving only a single broad peak centered at ω c with dominating photonic character. This effectively returns the system back to the weak coupling regime, due to the light-matter coupling strength is now much smaller than cavity loss. The second excited electronic state is nearly unperturbed now due to the decoupling between the cavity modes and the electronic states. Note that the absorption spectra is arbitrarily scaled to showcase the features and may not reflect the exact nature of the spectra.