This study analytically explored two coupled two-level atomic systems (TLAS) as two
qubits interacting with two modes of an electromagnetic field (EMF) cavity via two-photon transitions
in the presence of dipole–dipole interactions between the atoms and intrinsic damping. Using special
unitary su(1, 1) Lie algebra, the general solution of an intrinsic noise model is obtained when an EMF
is initially in a generalized coherent state. We investigated the population inversion of two TLAS and
the generated quantum coherence of some partitions (including the EMF, two TLAS, and TLAS–EMF).
It is possible to generate quantum coherence (mixedness and entanglement) from the initial pure state.
The robustness of the quantum coherence produced and the sudden appearance and disappearance
of coherence depended not only on dipole–dipole coupling but also on the intrinsic noise rate.
The growth of mixedness and entanglement may be enhanced by increasing dipole–dipole coupling,
leading to more robustness against intrinsic noise.