Quantum theory of the low-frequency linear susceptibility of interferometer-type superconducting qubits

We use the density matrix formalism to analyze the interaction of interferometer-type superconducting qubits with a high quality tank circuit, which frequency is well below the gap frequency of a qubit. We start with the ground state characterization of the superconducting flux and charge qubits. Then, by making use of a dressed state approach we describe the qubits' spectroscopy when the qubit is irradiated by a microwave field which is tuned to the gap frequency. The last section of the paper is devoted to continuous monitoring of qubit states by using a DC SQUID in the inductive mode.Comment: 11 pages, 5 figures; the title and abstract are slightly changed; several typos are corrected; in order to make our argumentation more clear we added some comments in the introduction and other section