Collective quantum coherent oscillations in a globally coupled array of qubits

Abstract

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 \(\omega_1 \simeq \omega_2\).