Quantum behaviour of a flux qubit coupled to a resonator

TL;DR

This paper provides a theoretical analysis of a superconducting flux qubit coupled to a resonator, deriving transmission properties and comparing with experimental data in the intermediate coupling regime.

Contribution

It offers an analytical solution to the master equation for the system and explores the electromagnetic transmission as a probe of dressed states.

Findings

Analytical solution for the master equation in the weakly populated resonator regime.

Derived transmission coefficient as a tool for probing dressed states.

Comparison of theoretical results with experimental data in the intermediate coupling regime.

Abstract

We present a detailed theoretical analysis for a system of a superconducting flux qubit coupled to a transmission line resonator. The master equation, accounting incoherent processes for a weakly populated resonator, is analytically solved. An electromagnetic wave transmission coefficient through the system, which provides a tool for probing dressed states of the qubit, is derived. We also consider a general case for the resonator with more than one photon population and compare the results with an experiment on the qubit-resonator system in the intermediate coupling regime, when the coupling energy is comparable with the qubit relaxation rate.