Spontaneous parametric downconversion and quantum walk topology

Abstract

We propose a novel scheme for the all-optical quantum simulation of topological phases by means of implementation of a discrete-Time quantum walk architecture. The main novel ingredient is the inclusion of the nonlinear process of spontaneous parametric downconversion (SPDC) along the quantum network. By means of a simple theoretical model, the interplay between quantum walk lattice topology and spatial correlations of biphotons produced by SPDC is numerically explored. We describe different optical detection methods suitable for the implementation of our proposed experimental scheme.