"Freely" falling two-level atom in a running laser wave.

The time evolution of a two-level atom which is simultaneously exposed to the field of a running laser wave and a homogeneous gravitational field is studied. The result of the coupled dynamics of internal transitions and center-of-mass motion is worked out exactly. Neglecting spontaneous emission and performing the rotating wave approximation we derive the complete time evolution operator in an algebraical way by using commutation relations. The result is discussed with respect to the physical implications. In particular the long time and short time behaviour is physically analyzed in detail. The breakdown of the Magnus perturbation expansion is shown.