Cooperative effects in Josephson junctions in a cavity in the strong coupling regime

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We analyze the behavior of systems of two and three qubits made by Josephson junctions, treated in the two level approximation, driven by a radiation mode in a cavity. The regime we consider is a strong coupling one recently experimentally reached for a single junction. Rabi oscillations are obtained with the frequency proportional to integer order Bessel functions in the limit of a large photon number, similarly to the case of the single qubit. A selection rule is derived for the appearance of Rabi oscillations. A quantum amplifier built with a large number of Josephson junctions in a cavity in the strong coupling regime is also described.