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Two non-identical quantum emitters, when placed within a cavity andcoherently excited at the two-photon resonance, can reach stationary states ofnearly maximal entanglement. In Vivas-Via\~na et al., we introduce afrequency-resolved Purcell effect stabilizing entangled $W$ states amongstrongly interacting quantum emitters embedded in a cavity. Here, we delvedeeper into a specific configuration with a particularly rich phenomenology:two interacting quantum emitters under coherent excitation at the two-photonresonance. This scenario yields two resonant cavity frequencies where thecombination of two-photon driving and Purcell-enhanced decay stabilizes thesystem into the sub- and superradiant states, respectively. By considering thecase of non-degenerate emitters and exploring the parameter space of thesystem, we show that this mechanism is merely one among a complex family ofphenomena that can generate both stationary and metastable entanglement whendriving the emitters at the two-photon resonance. We provide a globalperspective of this landscape of mechanisms and contribute analyticalcharacterizations and insights into these phenomena, establishing connectionswith previous reports in the literature and discussing how some of theseeffects can be optically detected.

Dissipative stabilization of maximal entanglement between non-identical emitters via two-photon excitation