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Using techniques of complex analysis in an algebraic approach, we solve thewave equation for a two-level atom interacting with a monochromatic light fieldexactly. A closed-form expression for the quasi-energies is obtained, whichshows that the Bloch-Siegert shift is always finite, regardless of whether theoriginal or the shifted level spacing is an integral multiple of the drivingfrequency, $\omega$. We also find that the wave functions, though finite whenthe original level spacing is an integral multiple of $\omega$, becomedivergent when the intensity-dependent shifted energy spacing is an integralmultiple of the photon energy. This result provides, for the first time in theliterature, an ab-initio theoretical explanation for the occurrence of theFreeman resonances observed in above-threshold ionization experiments.Comment: 24 pages, no figure; v2 typos correcte

Algebraic solution for a two-level atom in radiation fields and the Freeman resonances