SIMPLE VECTORIAL MODEL FOR THE SPECTRUM OF A 2-LEVEL ATOM IN AN INTENSE LOW-FREQUENCY FIELD

An ansatz is proposed for the analytic solution of the Heisenberg equa tions of a two-level atom in a classical, linearly polarized and inten se low-frequency field. According to this ansatz, the motion of the ve ctor representing the state of the atom on the Bloch sphere consists o f a fast precession around a direction, which in turn basculates slowl y around an axis perpendicular to the field. The time evolution of the atomic state, which is obtained analytically by this vectorial model, is shown to compare quite satisfactorily with the exact numerical sol ution of the Heisenberg equations. The limits of validity of the ansat z are discussed. The spectrum of the light scattered by the two-level atom is evaluated analytically using the ansatz and it is shown to rep roduce very precisely the exact spectrum evaluated numerically. It is shown that the slow component of the motion of the atomic Bloch vector yields the high-order harmonic part of the spectrum, whereas the fast precession gives rise to the hyper-Raman part. The appearance of the overall spectrum is discussed as a function of the various physical pa rameters of the model. The insight provided by the vectorial model is exploited to investigate the manifest universality of the main feature s of the overall spectrum and to suggest experiments to test the valid ity of the vectorial model. [S1050-2947(98)03808-6].