  We have investigated vacuum Rabi oscillation of an atom coupled with
single-mode cavity field exactly, and compared the results with that of J-C
model. The results show that, there is damping Rabi oscillation for an atom,
even in strong coupling regime. For small detuning and weak coupling case, the
probability for the atom in excited state oscillates against time with
different frequency and amplitude from that of J-C model. It exhibits the
counter-rotating wave interaction could significantly effect the dynamic
behavior of the atom, even under the condition in which the RWA is considered
to be justified. On the other hand, the results also reveal that the
counter-rotating wave interaction could obviously modify the decay rate in
strong coupling regime. And there is Rabi oscillation for initially unexcited
atom, which is contrary to that of J-C model.
