Abstract
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 Bures-distance 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.