Light propagation in waveguide lattices has been the subject of considerable interest during the last few years. Such array structures provide a versatile platform upon which one can observe a host of processes, such as optical Bloch oscillations, Zener tunneling, Rabi oscillations, Talbot revivals, and discrete solitons, to mention a few [1, 58, 40, 12]. The discrete diffraction properties of such configurations can mold the ow of light in a predictable manner, hence providing altogether new opportunities for applications. Quite recently light propagation in random and quasi-random arrays have also been considered-ranging from ballistic to the Anderson localization regime [49, 12]. In addition, quantum correlations in regular lattice structures have been investigated for both classical and completely quantum states [28]. Yet, despite of all the efforts put in this area, only a few of the reported lattices are known to have closed form solutions [26, 58]. In fact, integrable discrete systems are rather rare and any new addition to this class will further facilitate such fundamental studies. In the present work we introduce two new types of integrable photonic lattices exhibiting new families of physical processes like those occurring in quantum optics. We predict the emergence of classical analogues to coherent and displaced quantum states. These classical states arise as the impulse response of Glauber-Fock photonic lattices [40], whose inter-channel coupling constants obey a square root law. In addition, we provide the first observation of classical intensity distributions in optical arrays that are totally analogous to quantum coherent and displaced Fock states. Bloch-like oscillations and revivals are also predicted in such Glauber-Fock photonic lattices. Special consideration is devoted to describing quantum correlations of single photon and path entangled states propagating in these novel integrated optical structures. In summary, we realized a Glauber-Fock photonic lattice to directly observe an optical analogue for the displacement of Fock states and investigated a new family of photon correlations occurring in this optical system.