I. INTRODUCTION Cavity Quantum Electrodynamics (CQED) aims at describing light-matter interaction when light and matter reduce to canonical systems, i.e. when light can be modeled by a single mode of the electromagnetic field and matter by a single two-level system. To achieve this situation, one should couple a given transition of the matter field to a monomode cavity. The losses and dephasing times of each system should happen on a time scale much longer than the coupling timescale. Energy can thus be coherently exchanged between the atom and the cavity, allowing to implement fundamental tests of quantum mechanics, and opening the way to quantum information processing. On the way to the quantum regime, Purcell enhancement, which occurs when the emitter lifetime is modified as a consequence of its resonant coupling to the cavity mode, is a well known milestone [1]. Historically, first CQED evidences were demonstrated with atoms coupled to microwave [2] and optical [3] cavities, respectively. These systems are characterized by a very long radiation lifetime of the isolated emitter, which in the spectral domain corresponds to a very narrow dipole resonance coupled to a broad cavity. This picture has been the usual paradigm for CQED so far. On the other hand, CQED experiments can now be performed with solid-state emitters (so called artificial atoms ) and cavities. The strong coupling regime has been reached for the excitonic transition of quantum dots [4] and nanocrystals [5, 6] coupled to optical semiconductor cavities, as well as for superconducting qubits coupled to microwave cavities [7]. In all of these systems, the cavity mode quality factor can be very large, while solid state emitters are intrinsically coupled to the matrix they are embedded in. In fact, decoherence and phase relaxation unavoidably broaden any transition between the discrete states of such artificial atoms. These new conditions open an unexplored regime for CQED so far, where the emitter’s linewidth can be of the same order of magnitude, or even broader than the cavity mode one. Different mechanisms contribute to the decoherence-induced broadening of artificial atoms, among which phonon-assisted mechanisms [8], or spectral diffusion [9]. If spectral diffusion happens on a timescale much shorter than the typical spontaneous emission timescale, it can safely be modeled by a simple pure dephasing channel in the master equation describing the dynamics of the system. Because of its simplicity, the scheme of a two-level system undergoing pure dephasing can be regarded as an appealing tool to explore this new 2