Quantum Molecular Dynamics Study of a Two-Level Model with a Periodic External Field

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Abstract
Periodic and quasi-periodic response of a two-level model to an external field is studied numerically and analytically, where the methods of (1) Fourier analysis, (2) stroboscopic representation and (3) projection of an orbit are used. In general, the model shows a quasi-periodic motion. However, when the intensity of the external field E takes a specific value, the motion becomes a periodic motion whose periodicity is N times bigger than that of the external field. The structure of this synchronization phenomenon for E≲0.5 is expressed by N[(ω-Ω)2 + (µE/2)2]1/2 = nω; (n = 1,2,3,···), where ω is the angular frequency of the external field, Ω is the Bohr frequency and µ is the electric moment. We find that the motion is described approximately by three modes for a weak external field. This approximate solution is better than Rabi's solution based on the rotating-wave approximation.

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