  I propose to study the complex physics of topological phases by an all
optical implementation of a discrete-time quantum walk. The main novel
ingredient is the use of parametric amplifiers in the random network which can
in turn be used to emulate intra-atomic interactions and thus analyze many-body
effects in topological phases even when using light as the quantum walker. I
plan to characterize the intensity probability distribution and the spatial
correlations of the output interference pattern for different input states, as
well the robustness of localized boundary states characterizing topological
insulators to different sources of noise. In particular, I expect to determine
whether a non-local order parameter associated with a given topological
entanglement measure can be determined in order to characterize topological
order, and possible applications in entanglement topological protection. One of
the most promising applications of the proposed research includes the study of
topological phases in photosynthetic energy transferring processes
characterizing biological systems.
