The effect of Stark shift on the correlation between two qubits and a two-mode of the cavity-field

A physical model in which a pair of two-level atoms interacting with a two-mode cavity field is investigated in the presence of Stark shift. The two atoms are initially prepared in a product state or a maximal mixture state, while the two modes of the field are in a pair coherent state. The physical properties of the atomic system are studied by using the Quantum-Memory-Assisted Entropic Uncertainty Relation (QMA-EUR), Relative Entropy of Quantum Coherence (REoC), Geometric Quantum Discord (GQD), and concurrence. The physical properties of photon statistics are investigated by using the bunching and anti-bunching tow-mode radiation field. We found that the atomic properties depend on the initial state and the strength of the Stark shift. The general behaviour of QMA-EUR is opposite the other three atomic measurements, such as the QMA-EUR increases then concurrence, GQD, and REoC decrease. The photon statistics are independent of the Stark shift, while it is stable at the maximum entangled state.