Quantum Walk Topology and Spontaneous Parametric Down Conversion

TL;DR

This paper explores how topological phases in quantum walks can be studied using nonlinear optical elements, specifically analyzing the relationship between lattice topology and photon correlations in spontaneous parametric down-conversion.

Contribution

It introduces a novel approach combining quantum walk topology with nonlinear optics to investigate many-body effects in topological phases using light.

Findings

Analysis of the interplay between lattice topology and photon correlations.

Description of detection methods for experimental implementation.

Abstract

In a recent detailed research program we proposed to study the complex physics of topological phases by an all optical implementation of a discrete-time quantum walk. The main novel ingredient proposed for this study is the use of non-linear parametric amplifiers in the network which could 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. In this paper, and as a first step towards the implementation of our scheme, we analize the interplay between quantum walk lattice topology and spatial correlations of bi-photons produced by spontaneous parametric down-conversion. We also describe different detection methods suitable for our proposed experimental scheme.