Dressing of superconducting qubits by their interaction with a low frequency photon reservoir

Dressing of states of superconducting qubits by their interaction with low frequency photons is investigated. We show that the derivative of the self-energy function of a qubits state at its eigenenergy is equal to the total probability to find the system in the virtual states where the reservoir degrees of freedom manifest themselves explicitly. This parameter determines the strongness of the qubit-reservoir interaction. The results of calculations of the self-energy function show that contributions to the dressed states of qubits can be very significant. (paper)