Lehmann-Symanzik-Zimmermann Reduction Approach to Multi-Photon Scattering in Coupled-Resonator Arrays

TL;DR

This paper introduces a quantum field theoretical method based on Lehmann-Symanzik-Zimmermann reduction to analyze multi-photon scattering in coupled-resonator arrays with artificial atoms, providing explicit S-matrices for complex quantum networks.

Contribution

It applies the LSZ reduction approach to derive multi-photon scattering matrices in coupled-resonator arrays, including complex network configurations, which is a novel analytical framework.

Findings

Derived bound states for single photons in T-type CRA

Explicit multi-photon S-matrices for various CRA configurations

Applicable to complex quantum networks like H-type CRA waveguides

Abstract

We present a quantum field theoretical approach based on the Lehmann-Symanzik-Zimmermann reduction for the multi-photon scattering process in a nano-architecture consisting of the coupled resonator arrays (CRA), which are also coupled to some artificial atoms as the controlling quantum node. By making use of this approach, we find the bound states of single photon for an elementary unit, the T-type CRA, and explicitly obtain its multi-photon scattering S-matrix in various situations. We also use this method to calculate the multi-photon S-matrices for the more complex quantum network constructed with main T-type CRA's, such as a H-type CRA waveguide.