Strongly correlated photon transport in nonlinear photonic lattice with disorder: Probing signatures of the localization transition

TL;DR

This paper investigates how few-photon states propagate in a disordered nonlinear photonic lattice, revealing signatures of many-body localization through scattering measurements and analyzing their robustness.

Contribution

It introduces a diagrammatic scattering technique to identify localization signatures in photon transport within disordered nonlinear lattices.

Findings

Two-photon transmission shows clear signatures of many-body localization.

Transmission probabilities closely match eigenstate participation ratios.

Signatures remain robust against local dissipation effects.

Abstract

We study the transport of few-photon states in an open disordered nonlinear photonic lattice. More specifically, we consider a waveguide quantum electrodynamics (QED) setup where photons are scattered from a chain of nonlinear resonators with onsite Bose-Hubbard interaction in the presence of an incommensurate potential. Applying our recently developed diagrammatic technique that represents scattering matrix (S-matrix) with scattering diagrams and associated propagators, we compute the two-photon transmission probability and show that it carries signatures of the underlying many-body localization transition of the system. We compare the calculated probability to the participation ratio of the eigenstates and find close agreement for a range of interaction strengths. We analyze the robustness of the transmission signatures against local dissipation and briefly discuss possible implementation using current superconducting circuit technology.