  We investigate the quantum dynamics of systems involving small numbers of
strongly interacting photons. Specifically, we develop an efficient method to
investigate such systems when they are externally driven with a coherent field.
Furthermore, we show how to quantify the many-body quantum state of light via
correlation functions. Finally, we apply this method to two strongly
interacting cases: the Bose-Hubbard and fractional quantum Hall models, and
discuss an implementation of these ideas in atom-photon system.
