  Light-matter systems allow to realize a strongly correlated phase where
photons are present. In these systems strong correlations are achieved by
optical nonlinearities, which appear due to the coupling of photons to
atomic-like structures. This leads to intriguing effects, such as the quantum
phase transition from the Mott to the superfluid phase. Here, we address the
two-dimensional Jaynes-Cummings lattice model. We evaluate the boundary of the
quantum phase transition and study polaritonic properties. In order to be able
to characterize polaritons, we investigate the spectral properties of both
photons as well as two-level excitations. Based on this information we
introduce polariton quasiparticles as appropriate wavevector, band index, and
filling dependent superpositions of photons and two-level excitations. Finally,
we analyze the contributions of the individual constituents to the polariton
quasiparticles.
