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.
@article{arxiv.1012.5599,
title = {Quantum behaviour of a flux qubit coupled to a resonator},
author = {A. N. Omelyanchouk and S. N. Shevchenko and Ya. S. Greenberg and O. Astafiev and E. Ilichev},
journal= {arXiv preprint arXiv:1012.5599},
year = {2010}
}