Coherent states and their generalizations, displaced Fock states, are of fundamental importance to quantum optics. Here we present a direct observation of a classical analogue for the emergence of these states from the eigenstates of the harmonic oscillator. To this end, the light propagation in a Glauber-Fock waveguide lattice serves as equivalent for the displacement of Fock states in phase space. Theoretical calculations and analogue classical experiments show that the square-root distribution of the coupling parameter in such lattices supports a new family of intriguing quantum correlations not encountered in uniform arrays. Because of the broken shift invariance of the lattice, these correlations strongly depend on the transverse position. Consequently, quantum random walks with this extra degree of freedom may be realized in Glauber-Fock lattices.
We show that using the properties of the photon Green's function one can successfully describe the propagation of arbitrary nonclassical optical radiation through structured materials. In contrast to the similar input-output approach, our method is not restricted neither to the spatial homogeneous matter nor to the specific direction of light beam incidence or outcoupling. Several quantum states of light are addressed in detail, such as Fock, Glauber, and different squeezed light states, and their Green functions are given. Furthermore, it is demonstrated how scattering of light at a slab can be described with Poynting's energy flow vector, and how experimental setups can be modeled.
Abstract The main objective of this work is to investigate, analyze and examine in detail the behavior of quantum light in a photonic lattice having a square root law distribution for the coupling constant known as a Glauber-Fock photonic lattice. We investigate the light dynamics for both small and large size lattices for the case of spatially extended path entangled input state. We also study the squeezed state inputs, where we focus on finite size lattices. We analyze in detail the behavior of the non-classical features such as squeezing and photon correlations at the output of the system. The results and findings show the transport and revival of these features as non-classical light propagates across the waveguide array. Our findings should have applications in the areas of photonic quantum information processing and simulation and are implementable with current technology.