# Electromagnetic waves propagation through an array of superconducting qubits: manifestations of non-equilibrium steady states of qubits

## TL;DR

This paper presents a theoretical analysis of electromagnetic wave propagation through superconducting qubit arrays, revealing nonlinear effects and non-equilibrium steady states that influence wave transmission in complex ways.

## Contribution

It introduces a dynamic nonlinear wave equation for qubit arrays and explores the nonlinear transmission phenomena and steady states under moderate microwave power.

## Key findings

- Resonant suppression of transmission in linear regime
- Enhanced transmission in narrow frequency regions
- Transitions between high and low transmission states in nonlinear regime

## Abstract

We report a theoretical study of the electromagnetic waves (EWs) propagation through an array of superconducting qubits, i.e. coherent two-level systems, embedded in a low-dissipative transmission line. We focus on the near-resonant case as the frequency of EWs $\omega \simeq \omega_q$, where $\omega_q$ is the qubit frequency. In this limit we derive the effective dynamic nonlinear wave equation allowing one to obtain the frequency dependent transmission coefficient of EWs, $D(\omega)$. In the linear regime and a relatively wide frequency region we obtain a strong resonant suppression of $D(\omega)$ in both cases of a single qubit and chains composed of a large number of densely arranged qubits. However, in narrow frequency regions a chain of qubits allows the resonant transmission of EWs with greatly enhanced $D(\omega)$. In the nonlinear regime realized for a moderate power of applied microwave radiation, we predict and analyze various transitions between states characterized by high and low values of $D(\omega)$. These transitions are manifestations of nonequilibrium steady states of an array of qubits achieved in this regime.