# Microwave Scattering in the Subohmic Spin-Boson Systems of Superconducting Circuits

## TL;DR

This paper investigates quantum critical phenomena in microwave scattering within subohmic spin-boson systems, linking reflection coefficients to dynamic susceptibility, and proposes superconducting circuit experiments to observe these effects.

## Contribution

It introduces a method to relate microwave reflection to quantum critical behavior and proposes experimental setups in superconducting circuits for observing these phenomena.

## Key findings

- Quantum phase transition at critical coupling.
- Reflection coefficient linked to dynamic susceptibility.
- Proposed superconducting circuit experiments.

## Abstract

We study quantum critical phenomena in the microwave scattering of the subohmic spin-boson system, which exhibits a quantum phase transition at a critical system-reservoir coupling. By relating the reflection coefficient of a microwave with the dynamic susceptibility of the subohmic spin-boson system, we clarify the appearance of quantum critical phenomena in microwave scattering. Further, we propose experimental setups to realize the subohmic spin-boson system in a superconducting circuit composed of a charge qubit and a dissipative transmission line.