  By using the non-Markovian master equation, we investigate the effect of the
cavity and the environment on the quantum Fisher information (QFI) of an atom
qubit system in a dissipation cavity. We obtain the formulae of QFI for two
different initial states and analyze the effect of the atom-cavity coupling and
the cavity-reservoir coupling on the QFI. The results show that the dynamic
behavior of the QFI is obviously dependent on the initial atomic states, the
atom-cavity coupling and the cavity-reservoir coupling. The stronger the
atom-cavity coupling, the quicker the QFI oscillates and the slower the QFI
reduces. Especially, the QFI will tend to a stable value not zero if the
atom-cavity coupling is large enough. On the other hand, the smaller the
cavity-reservoir coupling, the stronger the non-Markovian effect, the slower
the QFI decay. In other words, choosing the best parameter can improve the
accuracy of parameter estimation. In addition, the physical explanation of the
dynamic behavior of the QFI is given by means of the QFI flow.
