Optimizing nonlocality generation in a two-qubit system coupled off-resonantly to a nonlinear coherent cavity under decoherence

Steerability has recently been formalized as a quantum-information task involving arbitrary bipartite states, which can reveal a hierarchy of quantum entanglement, steering, and Bell nonlocality. Additionally, nonlinear atom–cavity interactions and atomic mutual interactions are considered a potential tool for creating two-qubit nonlocality, steerability, and entanglement. Therefore, by using the intrinsic decoherence model, this work investigates the time-dependent generation of atomic nonlocality, as measured by the CHSH-Bell inequality function, EPR steering, and negativity, between coupled two-level atoms interacting resonantly and off-resonantly with a lossless Kerr-like medium cavity filled by a superposition of coherent fields. Moreover, the mutual interaction between the two-level atoms is controlled by considering both Anti-Ferromagnetic Ising atom-atom coupling and dipole–dipole coupling. The time-dependent generation of atomic nonlocality can be optimized by increasing the non-classicality of the initial coherent cavity state, the lossless Kerr-like medium cavity, anti-ferromagnetic Ising atom-atom coupling, atom–cavity detuning dipole–dipole coupling, and the intrinsic atom–cavity decoherence. It has been found that the capability of the interaction between two atoms inside a coherent cavity to realize two-qubit atomic nonlocality can be enhanced by increasing the anti-ferromagnetic Ising atom-atom coupling, atom–cavity detuning, dipole–dipole coupling, as well as the non-classicality of the superposition of two coherent states. Conversely, this ability can be weakened by increasing the lossless Kerr-like medium cavity and the intrinsic atom–cavity decoherence. Moreover, it has been shown that the generated atomic nonlocalities confirm the hierarchy principle between Bell-nonlocality, steerability, and entanglement. Additionally, through the dynamics of steerability and entanglement, the phenomena of sudden birth and sudden death occur, and their occurrence depends on increasing the atom–cavity interaction parameters.