  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.
