The JC Hamiltonian in Eq. 2 and its eigenenergies (Eq. 5) correspond to the ideal cavity situation where the cavity photon loss and the matter de-excitation process (eg, due to the non-radiative decay) are not considered. In a realistic experimental setup, the cavity photon only has a finite lifetime before it leaks outside the cavity. The condition to achieve strong coupling, (i.e. where one can observe the Rabi splitting in absorption spectra) depends on the relation between the excitation lifetimes in the cavity and the coupling strength g c .