In this paper, the dynamical behaviour of the geometric discord of a system consisting of a two-level atom interacting with a quantised radiation field described by the Jaynes-Cummings model has been studied. The evolution of the system has been considered in the pure dephasing regime when the field is initially in a general pure state and the atom is initially in a mixed state. Dynamics of the geometric discord, as a measure of non-classical correlation, has been compared with the dynamics of negativity, as a measure of quantum entanglement. In particular, the influence of different parameters of system such as detuning and mixedness of the initial atomic state on the dynamics of geometric discord has been evaluated for when the field is initially in coherent and number states. It is shown that for asymptotically large times, the steady state geometric discord of the system presents a non-zero optimum value at some intermediate value of detuning.

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