  We study the quantum transport of multi-photon Fock states in one-dimensional
Bose-Hubbard lattices implemented in QED cavity arrays (QCAs). We propose an
optical scheme to probe the underlying many-body states of the system by
analyzing the properties of the transmitted light using scattering theory. To
this end, we employ the Lippmann-Schwinger formalism within which an analytical
form of the scattering matrix can be found. The latter is evaluated explicitly
for the two particle/photon-two site case using which we study the resonance
properties of two-photon scattering, as well as the scattering probabilities
and the second-order intensity correlations of the transmitted light. The
results indicate that the underlying structure of the many-body states of the
model in question can be directly inferred from the physical properties of the
transported photons in its QCA realization. We find that a fully-resonant
two-photon scattering scenario allows a faithful characterization of the
underlying many-body states, unlike in the coherent driving scenario usually
employed in quantum Master equation treatments. The effects of losses in the
cavities, as well as the incoming photons' pulse shapes and initial
correlations are studied and analyzed. Our method is general and can be applied
to probe the structure of any many-body bosonic models amenable to a QCA
implementation including the Jaynes-Cummings-Hubbard, the extended Bose-Hubbard
as well as a whole range of spin models.
