With the help of two-photon scattering matrix of in- and out-states, we find that the use of quantum input states in photonic quantum simulators such as those implemented in coupled cavity arrays, allows one to observe not only stronger spectroscopic signals of the underlying strongly correlated states but also a faithful representation of their intensity-intensity correlations, as compared to the conventional classical driving fields. Our analysis can be applied for many-body spectroscopy of any many-body model amenable to a photonic quantum simulation, including the Jaynes-Cummings-Hubbard, the extended Bose-Hubbard, and a whole range of spin models.
We study the quantum transport of multiphoton 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, two-site case which we use to 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 model amenable to a QCA implementation, including the Jaynes-Cummings-Hubbard model, the extended Bose-Hubbard model, as well as a whole range of spin models.