Synchronization of two cavity-coupled qubits measured by entanglement

Some nonlinear radiations such as superfluorescence can be understood as cooperative effects between atoms. We regard cooperative radiations as a manifested effect secondary to the intrinsic synchronization among the two-level atoms and propose the entanglement measure, concurrence, as a time-resolved measure of synchronization. Modeled on two cavity-coupled qubits, the evolved concurrence monotonically increases to a saturated level. The finite duration required for the rising to saturation coincides with the time delay characteristic to the initiation of superfluorescence, showing the role of synchronization in establishing the cooperation among the qubits. We verify concurrence to be a good measure of synchronization by comparing it with asynchronicity computed from the difference between the density matrices of the qubits. We find that the feature of time delay agrees in both measures and is determined by the coupling regimes of the cavity-qubit interaction. Specifically, synchronization is impossible in the weak coupling regime.