  We analyze a chain of coupled nonlinear optical cavities driven by a coherent
source of light localized at one end and subject to uniform dissipation. We
characterize photon transport by studying the populations and the photon
correlations as a function of position. When complemented with input-output
theory, these quantities provide direct information about photon transmission
through the system. The position of single- and multi-photon resonances
directly reflect the structure of the many-body energy levels. This shows how a
study of transport along a coupled cavity array can provide rich information
about the strongly correlated (many-body) states of light even in presence of
dissipation. By means of a numerical algorithm based on the time-evolving block
decimation scheme adapted to mixed states, we are able to simulate arrays up to
sixty cavities.
