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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.

An analytical solution is obtained for a system consisting of two atoms interacting
with a nondegenerate parametric amplifier of a cavity field containing a Kerr like medium
in the presence of Stark shift terms. The nonlinearity of the interaction leads to the generation
of different nonlocal correlations (NLCs) beyond entanglement concurrence, which
are measured by uncertainty-induced quantum nonlocality and maximal Bell’s function. It
is found that the generation of the NLCs, due to the atom-cavity unitary interaction, can be
controlled by the nonlinearity of the Kerr like medium and the Stark shift. The Kerr like
medium and the Stark shift lead to reduce the regularity and the amount of the generated
nonlocal correlations. The reduction in the generated nonlocal correlations, due to the Kerr
like medium, is increased by the increase in the Stark shift parameter and vice versa.

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In this contribution, we investigate the bipartite non-classical correlations (NCCs) of a system formed
by two nitrogen-vacancy (N-V) centers placed in two spatially separated single-mode nanocavities
inside a planar photonic crystal (PC). The physical system is mathematically modeled by timedependent
Schrödinger equation and analytically solved. The bipartite correlations of the two N-V
centers and the two-mode cavity have been analyzed by skew information, log-negativity, and Bell
function quantifiers. We explore the effects of the coupling strength between the N-V-centers and
the cavity fields as well as the cavity-cavity hopping constant and the decay rate on the generated
correlation dynamics. Under some specific parameter values, a large amount of quantum correlations
is obtained. This shows the possibility to control the dynamics of the correlations for the NV-centers
and the cavity fields.

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In this paper, we use the su(1,1)-algebraic treatment to explore the effects of the intrinsic decoherence in a twomode
cavity containing a two-level atom. Each field is resonant with the qubit through a four-photon process.
The role of the intrinsic decoherence and the superposition of the initial generalized Barut-Girardello coherent
state on the quantum effects is investigated via different quantifiers as: atomic inversion, linear entropy and
negativity. It is found that the non-linearity of the four-photon process leads to generate non-classical effects
with a high oscillatory behavior. The superposition of the Barut-Girardello coherent state controls the dynamics
of the purity loss and the entanglement. It is found that the nonclassical effects are very sensitive to the nonlinear
interactions between the qubit and the two-mode cavity.

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