Strong-coupling BCS models of Josephson qubits

The strong-coupling version of the BCS theory for superconductors is used to derive microscopic models for all types of small Josephson junctions--charge qubit, flux qubit and phase qubit. Applied to Josephson qubits it yields a more complicated structure of the lowest-lying energy levels than that obtained from phenomenological models based on quantization of the Kirchhoff equations. In particular, highly degenerate levels emerge, which act as probability sinks for the qubit. The alternative formulae concerning spectra of superconducting qubits are presented and compared with the experimental data. In contrast to the existing theories those formulae contain microscopic parameters of the model. In particular, for the first time, the density of Cooper pairs at zero temperature is estimated for an Al-based flux qubit. Finally, the question whether small Josephson junctions can be treated as macroscopic quantum systems is briefly discussed.