Effect of dissipation and dipole-dipole interplay on Hilbert-Schmidt distance and Bell's inequality correlations of two qubits interacting with two-mode cavity field

An analytical description is obtained for a system composed of two two-level atoms (qubits) coupled via dipole-dipole interplay by Su(1, 1) and Su(2) Lie group. Both qubits interact with two-mode open cavity through a non-degenerate two-photon process. We explore the influence of the dissipation rate on the non-classical correlation (NCC), based on the Hilbert-Schmidt distance and Bell's inequality correlations. The robustness of the generated NCCs depend not only on the dipole-dipole interplay but also on the dissipation rate and the initial coherence intensity. The NCCs can be enhanced for some selected values of the dipole-dipole interaction.