  Two non-identical quantum emitters, when placed within a cavity and
coherently excited at the two-photon resonance, can reach stationary states of
nearly maximal entanglement. In Vivas-Via\~na et al., we introduce a
frequency-resolved Purcell effect stabilizing entangled $W$ states among
strongly interacting quantum emitters embedded in a cavity. Here, we delve
deeper into a specific configuration with a particularly rich phenomenology:
two interacting quantum emitters under coherent excitation at the two-photon
resonance. This scenario yields two resonant cavity frequencies where the
combination of two-photon driving and Purcell-enhanced decay stabilizes the
system into the sub- and superradiant states, respectively. By considering the
case of non-degenerate emitters and exploring the parameter space of the
system, we show that this mechanism is merely one among a complex family of
phenomena that can generate both stationary and metastable entanglement when
driving the emitters at the two-photon resonance. We provide a global
perspective of this landscape of mechanisms and contribute analytical
characterizations and insights into these phenomena, establishing connections
with previous reports in the literature and discussing how some of these
effects can be optically detected.

Quantum Physics;Atomic Physics