Transport regimes of biphoton-state quantum walks in ordered and disordered arrays of nonlinear waveguides

TL;DR

This paper investigates how biphoton states in nonlinear waveguide arrays exhibit different transport regimes, revealing superballistic and superdiffusive behaviors, and how disorder affects these regimes, including localization phenomena.

Contribution

It demonstrates that driven quantum walks of biphoton states do not always propagate ballistically and identifies the impact of disorder on transport regimes and localization.

Findings

Biphoton quantum walks show superballistic and superdiffusive regimes.

Disorder induces Anderson localization and suppresses superballistic transport.

Transport behavior depends on the presence and type of disorder.

Abstract

A quantum walk in an ordered medium exhibits ballistic propagation. A related process is the driven quantum walk, in which the number of walkers varies along the propagation. In this work, we show that a driven quantum walk of biphoton states in an array of nonlinear waveguides does not propagate ballistically, but instead presents two transport regimes: superballistic and superdiffusive. We also study the effects of off-diagonal and diagonal disorder. In addition to the observation of Anderson localization, both types of disorder lead to the disappearance of the superballistic regime.