Quantum behavior of a flux qubit coupled to a resonator

Abstract

The detailed theory for the system of a superconducting qubit coupled to the transmission line resonator is presented. We describe the system by solving analytically and numerically the master equation for the density matrix, which includes dissipative Lindblad term. We calculate the transmission coefficient, which provides the way to probe the dressed states of the qubit. The theoretical results are related to the experiment with the intermediate coupling between the qubit and the resonator, when the coupling energy is of the same order as the qubit relaxation rate.