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We investigate theoretically the coupling of a cavity mode to a continuousdistribution of emitters. We discuss the influence of the emittersinhomogeneous broadening on the existence and on the coherence properties ofthe polaritonic peaks. We find that their coherence depends crucially on theshape of the distribution and not only on its width. Under certain conditionsthe coupling to the cavity protects the polaritonic states from inhomogeneousbroadening, resulting in a longer storage time for a quantum memory based onemitters ensembles. When two different ensembles of emitters are coupled to theresonator, they support a peculiar collective dark state, also very attractivefor the storage of quantum information.

Strongly coupling a cavity to inhomogeneous ensembles of emitters : potential for long lived solid-state quantum memories