Phases of the electronic two-level model under rotating wave approximation

We present the time evolution of the electronic two-level model in rotating wave approximation and calculate the Aharonov-Anandan phase of the vector states with cyclic evolution either within the period of an external monochromatic electric field or the period corresponding to the generalized Rabi frequency. The Aharonov-Anandan phase in the most general case is shown to be dependent on the initial vector state, unless the system evolves in the adiabatic regime; in the latter case, the Aharonov-Anandan phase recovers Berry's phase. In the quasi-resonant regime of the electronic two-level model, the different relations between Gamma and the frequency omega of the electric field correspond to distinct regimes of the coupling between this external field and matter.