We investigated the quantum dynamics of systems, which involved small numbers of strongly interacting photons. Specifically, we developed an efficient method to investigate such systems when they were externally driven with a coherent field. Furthermore, we showed how to quantify the many-body quantum state of light via correlation functions. Finally, we applied that method to two strongly interacting cases: the Bose–Hubbard and fractional quantum Hall models, and discussed an implementation of those ideas in atom–photon system