# Microwave transmission through an artificial atomic chain coupled to a superconducting photonic crystal

## TL;DR

This paper investigates the transmission properties of a three-level artificial atomic chain coupled to a superconducting microwave photonic crystal, revealing long-range interactions, a tunable dip in transmission, and photon correlation oscillations, with implications for quantum technologies.

## Contribution

It introduces a model for understanding the transmission dip and long-range interactions in artificial atomic chains coupled to microwave photonic crystals, validated by numerical results.

## Key findings

- Transmission dip frequency scales linearly with atom number and interaction strength.
- Oscillations between photon bunching and antibunching observed in correlations.
- Model remains valid despite variations in coupling strengths and phase differences.

## Abstract

Emitters strongly coupled to a photonic crystal provide a powerful platform for realizing novel quantum light-matter interactions. Here we study the optical properties of a three-level artificial atomic chain coupled to a one-dimensional superconducting microwave photonic crystal. A sharp minimum-energy dip appears in the transmission spectrum of a weak input field, which reveals rich behavior of the long-range interactions arising from localized bound states. We find that the dip frequency scales linearly with both the number of the artificial atoms and the characteristic strength of the long-range interactions when the localization length of the bound state is sufficiently large. Motivated by this observation, we present a simple model to calculate the dip frequency with system parameters, which agrees well with the results from exact numerics for large localization lengths. We observe oscillation between bunching and antibunching in photon-photon correlation function of the output field. Furthermore, we find that the model remains valid even though the coupling strengths between the photonic crystal and artificial atoms are not exactly equal and the phases of external driving fields for the artificial atoms are different. Thus, we may infer valuable system parameters from the dip location in the transmission spectrum, which provides an important measuring tool for the superconducting microwave photonic crystal systems in experiment. With remarkable advances to couple artificial atoms with microwave photonic crystals, our proposal may be experimentally realized in currently available superconducting circuits.