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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 $Δ_i$ and we take into account a spread of parameters $Δ_i$. Non-interacting qubits display coherent quantum beatings with N different frequencies, i.e. $ω_i=Δ_i/\hbar$ . 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 $ω_1=\barΔ/\hbar$ and $ω_2=\tildeω_R$, where $\tildeω_R$ is the resonant frequency of the cavity renormalized by interaction. The amplitude of these oscillations can be strongly enhanced in the resonant case when $ω_1 \simeq ω_2$.