Analysis of weakly-driven multi-emitter cQED systems

In this work, we show that a weakly driven multi-emitter cQED system can be analyzed by approximating the driving coherent state with a single- and two-photon Fock state, and using the Scattering matrix formalism to analyze the response of this system to these Fock states. This is a significantly more computationally feasible approach than the master equation formalism, allowing the analysis of multi-emitter systems with ~50 emitters. We use this approach to analyze the transmission and second order correlations induced in the incident coherent state by the multi-emitter system. In particular, we show that for identical emitters, increasing the number of emitters does not improve the polaritonic photon blockade. Moreover, we analyze the impact of inhomogeneous broadening on the second order correlation function of the light emitted by the multi-emitter system with large number of emitters, and analyze the emergence and behaviour of subradiant photon blockade in such multi-emitter systems.