Abstract
The geometric phase and quantum entanglement for a nonlinear field-atom system are described quantitatively in terms of different parameters. Specifically, considering a deformed Schrodinger cat interacting with a qubit and taking into account the time dependent of the system coupling. The results show that the initial state setting, atomic motion, photon number and deformation play important roles in the evolution of the system dynamics, nonlocal correlation and geometric phase. An interesting correlation between the entanglement and geometric phase is observed during the time evolution. The presented system is very useful to generate and maintain high amount of entanglement through controlling the phase variation of the system under consideration. We test this observation with experimentally accessible parameters and some new aspects are obtained.