We investigate a two-level system in a cavity QED by considering the effects of amplitude damping, phase damping and driving field. We have studied the non-Markovianity in resonance and non-resonance limits in the presence of these effects using Breuer–Laine–Piilo (BLP) non-Markovianity measure (NBLP). The evolution of the system is derived using the time convolutionless (TCL) master equation. In some conditions, it is shown that in the presence of a driving field, the NBLP increases in the resonance and non-resonance limits. We have also found the exact solution of the master equation in order to investigate the effect of temperature- and environment excited states. We have shown that the behaviour of non-Markovianity is very different from what one can see from the TCL approach. We have also presented some explanation about the behaviour of non-Markovianity in the exact solution using quantum discord (QD).

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