Collective quantum coherent oscillations in a globally coupled array of superconducting qubits

We report a theoretical study of coherent collective quantum dynamic effects in an array N of qubits (two-level systems) incorporated into a low-dissipation resonant cavity. Individual qubits are characterized by energy level differences Delta sub(i) and a spread of Delta sub(i) is taken into account. Noninteracting qubits display coherent quantum beatings with N different frequencies, i.e., omega sub(i) = Delta sub(i)/[Planck's over 2pi]. Virtual emission and absorption of cavity photons provides a long-range interaction between qubits. In the presence of such interaction we analyze quantum correlation functions of individual qubits C sub(i)(t) to obtain two collective quantummechanical coherent oscillations, characterized by frequencies omega sub(1) = Delta /[Planck's over 2pi] and omega sub(2) = omega sub(R), where omega sub(R) is the resonant frequency of the cavity renormalized by interaction. The amplitude of these oscillations can be strongly enhanced in the resonant case when omega sub(1) [Asymptotically = to] omega sub(2). These collective quantum oscillations can be directly observed, e.g., by measurements of frequency dependent transmission coefficient D( omega ) of electromagnetic field propagating in a transmission line coupled to the system.