Correlated two-photon transport in a one-dimensional waveguide side-coupled to a nonlinear cavity

TL;DR

This paper analytically studies how two photons interact and become correlated when passing through a nonlinear cavity coupled to a one-dimensional waveguide, revealing potential bound states and quantum correlations.

Contribution

It provides an exact analytical solution for two-photon scattering states in a nonlinear waveguide-cavity system, highlighting photon correlation effects.

Findings

Quantum correlations emerge after scattering

Two-photon bound states can form in the system

Analytic solutions describe transmitted and reflected states

Abstract

We investigate the transport properties of two photons inside a one-dimensional waveguide side-coupled to a single-mode nonlinear cavity. The cavity is filled with a nonlinear Kerr medium. Based on the Laplace transform method, we present analytic solution of quantum states of the transmitted and reflected two photons, which are initially prepared in a Lorentzian wave packet. The solution reveals how quantum correlation between the two photons emerge after the scattering by the nonlinear cavity. In particular, we show that the output wave function of the two photons in position space can be localized in the relative coordinates, which is a feature that may be interpreted as a two-photon bound state in this waveguide-cavity system.