Collective quantum coherent oscillations in a globally coupled array of qubits

We report a theoretical study of coherent collective quantum dynamic effects in an array of N qubits (two-level systems) incorporated into a low-dissipation resonant cavity. Individual qubits are characterized by energy level differences $\Delta_i$ and we take into account a spread of parameters $\Delta_i$. Non-interacting qubits display coherent quantum beatings with N different frequencies, i.e. $\omega_i=\Delta_i/\hbar$ . 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 $C_i(t)$ to obtain two collective quantum-mechanical coherent oscillations, characterized by frequencies $\omega_1=\bar{\Delta}/\hbar$ and $\omega_2=\tilde{\omega}_R$, where $\tilde{\omega}_R$ is the resonant frequency of the cavity renormalized by interaction. The amplitude of these oscillations can be strongly enhanced in the resonant case when $\omega_1 \simeq \omega_2$.