Strong coupling of two quantum emitters to a single light mode: the dissipative Tavis-Cummings ladder

A criterion for strong coupling between two quantum emitters and a single resonant light mode in a cavity is presented. The criterion takes into account the escape of cavity photons and the spontaneous emission of the emitters, which are modeled as two level systems. By using such criterion, the dissipative Tavis-Cummings ladder of states is constructed, and it is shown that the inclusion of one more emitter with respect to the Jaynes-Cummings (single emitter) case increases the effective parameter region in which $n^{\text{th}}$ order Rabi splitting is observed.