# One-Dimensional Photon Transport Through a Two-Terminal Scattering Cluster: Tight-Binding Formalism

## TL;DR

This paper develops a transfer matrix formalism for one-dimensional single photon transport in a parallel resonator waveguide system, revealing quantum interference effects and conditions for perfect reflection controllable by photon-atom interactions.

## Contribution

It introduces a novel transfer matrix approach for photon transport in parallel resonator waveguides and analyzes quantum interference effects and reflection control.

## Key findings

- Perfect reflection occurs depending on the number of coupled waveguides.
- Photon-atom interactions can shift the reflection window across photon energies.
- Quantum interference significantly influences photon transport behavior.

## Abstract

Employing tight-binding approximation we derive a transfer matrix formalism for one-dimensional single photon transport through a composite scattering center, which consists of parallel connected resonator optical waveguides. By solving the single-mode eigenvectors of the Hamiltonian, we investigate the quantum interference effects of parallel couplings on the photon transport through this parallel waveguide structure. We find a perfect reflection regime determined by the number of coupled resonator waveguides. Numerical analysis reveals that by changing atom transition frequency, the window of perfect reflection may shift to cover almost all incoming photon energy, indicating the effective control of single photon scattering by photon-atom interaction.