Influence of the dissipation on the N-level atom interacting with a two two-level atoms in presence of qubit-qubit interaction

The interacting of two qubits and an N-level atom based on su(2) Lie algebra in the presence of both qubit-qubit interaction and dissipation term is considered. The effects of the qubit-qubit interaction and the dissipation term on the dynamics of the proposed system are discussed in detail for certain values of the number of levels. The dynamical expressions of the observable operators are obtained using the Heisenberg equation of motion. The population inversion and linear entropy, as well as the concurrence formula as a measure of entanglement between the two qubits are calculated and discussed. The roles of the number of levels, the qubit-qubit coupling parameter and the dissipation rate on these quantities are also discussed. We explore the sudden birth and sudden death of the entanglement phenomena with and without the dissipation term.