Two-photon self-Kerr nonlinearities for quantum computing and quantum optics

TL;DR

This paper proposes a network of cross-Kerr regions to simulate a self-Kerr medium, enabling high-fidelity photon-photon gates with effective long-range interactions for quantum computing and optics.

Contribution

It introduces a discrete network design that simulates a self-Kerr medium with local interactions, achieving high-fidelity photon-photon gates.

Findings

High fidelity photon-photon gate demonstrated

Network approximates perfect self-Kerr interaction with many nodes

Effective long-range interactions implemented locally

Abstract

The self-Kerr interaction is an optical nonlinearity that produces a phase shift proportional to the square of the number of photons in the field. At present, many proposals use nonlinearities to generate photon-photon interactions. For propagating fields these interactions result in undesirable features such as spectral correlation between the photons. Here, we engineer a discrete network composed of cross-Kerr interaction regions to simulate a self-Kerr medium. The medium has effective long-range interactions implemented in a physically local way. We compute the one- and two-photon S matrices for fields propagating in this medium. From these scattering matrices we show that our proposal leads to a high fidelity photon-photon gate. In the limit where the number of nodes in the network tends to infinity, the medium approximates a perfect self-Kerr interaction in the one- and two-photon regime.