The time evolutions of the population of the excited states of a driven atom coupled to the environment. The initial states of the atom are respectively in (a) ground state and (b) excited state. We consider two cases that the parameters: H^S = 0 (orange square), and H^S ≠ 0, for δ = 0 (blue dot), δ = 0.5κ (green triangle), δ = 1.5κ (pink circle), δ = 3.5κ (red star), and Ω = 4.0κ.