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We study the quantum transport of multi-photon Fock states in one-dimensionalBose-Hubbard lattices implemented in QED cavity arrays (QCAs). We propose anoptical scheme to probe the underlying many-body states of the system byanalyzing the properties of the transmitted light using scattering theory. Tothis end, we employ the Lippmann-Schwinger formalism within which an analyticalform of the scattering matrix can be found. The latter is evaluated explicitlyfor the two particle/photon-two site case using which we study the resonanceproperties of two-photon scattering, as well as the scattering probabilitiesand the second-order intensity correlations of the transmitted light. Theresults indicate that the underlying structure of the many-body states of themodel in question can be directly inferred from the physical properties of thetransported photons in its QCA realization. We find that a fully-resonanttwo-photon scattering scenario allows a faithful characterization of theunderlying many-body states, unlike in the coherent driving scenario usuallyemployed in quantum Master equation treatments. The effects of losses in thecavities, as well as the incoming photons' pulse shapes and initialcorrelations are studied and analyzed. Our method is general and can be appliedto probe the structure of any many-body bosonic models amenable to a QCAimplementation including the Jaynes-Cummings-Hubbard, the extended Bose-Hubbardas well as a whole range of spin models.

Few-photon transport in many-body photonic systems: A scattering approach