Abstract
In this paper we use the atomic version of the quantum Fisher information to estimate the quantum state of the parity deformed Jaynes Cummings Model (PD-JCM) that describing the interaction between a SQ (single qubit) and parity deformed field. The nonclassical properties of the field are identified by the evolution of the second-order correlation function. The von Neumann entropy is provided for the non-local correlation between the SQ and parity deformed field. Also, the single qubit quantum Fisher information within the phase shift estimator is obtained and compared with the von Neumann entropy during the interaction time. We examine the effect of the deformation parameter and time-dependent coupling or qubit speed on the dynamical behavior of the proposed quantities. The results verified that the dynamical behavior of the proposed quantities can be controlled by the qubit speed, deformation parameter and time-dependent coupling or qubit speed parameters.