The dynamics of coupled atom and field assisted by continuous external pumping

The dynamics of a coupled system comprised of a two-level atom and cavity field assisted by continuous external classical field (driving Jaynes-Cummings model) is studied. When the initial field is prepared in a coherent state, the dynamics strongly depends on the algebraic sum of both fields. If this sum is zero (the compensative case) in the system only the vacuum Rabi oscillations occur. The results with the dissipation and external field detuning from the cavity field are also discussed.