Non-classical light in a Jx photonic lattice

We report the study of non-classical light in a photonic lattice having a parabolic coupling distribution, also known as a J(x) photonic lattice. We focus on a two-photon Fock state, a two-photon N00N state, a single-mode squeezed state and a coherent state as inputs to the lattice. We investigate the possibility of a perfect transfer of the mean photon number as well as the quantum state from one waveguide mode to another. We study photon-photon correlation for the two-photon N00N state. For the single-mode squeezed state we perform a detailed study of the evolution of the squeezing factor and entanglement between the waveguide modes. Our findings suggest a perfect transfer of the average photon number in all cases and a perfect transfer of the quantum state in the cases of the two-photon Fock state and the two-photon N00N state only, but not in the cases of the squeezed and coherent states. Our results should have applications in the physical implementation of photonic continuous-variable quantum-information processing.