  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.
