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In this article, we consider the time evolution of the quantum Fisher information in the context of the interaction between two-level atom and two-modes electromagnetic field. We discuss the correlation between the quantum Fisher information, its flow and quantum entanglement for the system under consideration. Analytic results under certain parametric conditions are obtained, by means of which we analyze the influence of different parameters on the von Neumann entropy and quantum Fisher information.We investigate different forms of the two-mode field states such as uncorrelated two-mode coherent states and two-mode squeezed vacuum states. We explore an interesting monotonic relation between the quantum Fisher information and nonlocal correlation behavior of the atom-two modes field interaction under the estimator parameter and field type effect during the time evolution

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