Analytic approach to dynamics of the resonant and off-resonant Jaynes-Cummings systems with cavity losses

An analytic approach to investigate the zero-temperature time evolution of the Jaynes-Cummings system with cavity losses is developed. With 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 analyses not only on 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.