Consideration of geometric phase and population transfer without using rotating-wave approximation
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Recently, Rostovtsev et al (2009 Phys. Rev. A 79 063833) established an analytical treatment of the detuned atom–field interaction without using the rotating-wave approx. imation (RWA). Using this result, here we study qualitatively the dynamics of geometric phase (GP) and population transfer in a two-level atom interacting with an external off-resonant classical field for arbitrary pulse shape without using RWA. We use this exact method (without RWA) to reexamine the variation of populations and GP and compare the result with the RWA considering two kinds of the external field. We show that it is possible to control the GP dynamics by choosing suitable parameters of the atom–field system. Interestingly, we find that the variation of the opulations and GP in the time is unchanged and it differs as we get further from the resonance. Moreover, we show that the Rabi frequency plays a role in reduction or augmentation of the periodic time interval for the GP. The solution is very suitable for atom–field systems, especially when the system is far from the resonance so that the RWA method breaks down .