  A new analytic approach to investigate the zero-temperature time evolution of
the Jaynes-Cummings system with cavity losses is developed. With the realistic
coupling between the cavity and the environment assumed, a simple master
equation is derived, leading to the explicit analytic solution for the resonant
case. This solution is suitable for the analyses not only on the single
excitation states but also on many excitation states, which enables us to
investigate the photon coherent state and to observe sharp collapses and
revivals under dissipation. For the off-resonant case, on the other hand, the
present study presents an analytic, systematic method instead. We examine the
small and large detuning limits and discuss the condition where the widely-used
phenomenological treatment is justified. Explicit evaluations of the time
evolutions for various initial states with finite detuning are also presented.
