In this paper, we study the dynamics of two coupled qubits interacting with a two-mode parametric
amplifier cavity through the nonlinear interactions of the photon processes under the intrinsic
decoherence. The nonlinear unitary interactions lead to generating different types of nonlocal
correlations via Bell nonlocality, trace-norm measurement-induced non-locality (MIN), and Buresdistance
entanglement. Based on the intrinsic decoherence, the two-qubit states have stationary
amounts of the MIN-correlation and Bures distance entanglement with more stability. It is found that
the qubit–qubit interaction coupling is affected as additional decoherence. It leads to more oscillations
and stability. The enhancement of the amount of the generated nonlocal correlations depends on the
superposition of Barut-Girardello coherent states. The phenomenon of sudden birth/death and the
Bell non-locality can be enhanced when the two-mode parametric amplifier cavity is initially prepared
in the coherent states.