Theory of dressed states in quantum optics

The dual Dyson series [M. Frasca, Phys. Rev. A 58 3439 (1998)] is used to d evelop a general perturbative method for the study of atom-field interactio n in quantum optics. In fact, both the Dyson series and its dual, by renorm alization-group methods to remove secular terms from the perturbation serie s, give the opportunity for a full study of the solution of the Schrodinger equation in different ranges of the parameters of the given Hamiltonian. I n view of recent experiments with strong laser fields, this approach seems well-suited to give a clarification and an improvement of the applications of the dressed states as currently done through the eigenstates of the atom -field interaction, showing that these are just the leading order of the du al Dyson series when the Hamiltonian is expressed in the interaction pictur e. Ln order to best exploit the method, a study is accomplished of the well -known Jaynes-Cummings model in the rotating-wave approximation, whose exac t solution is known, comparing the perturbative solutions obtained by the D yson series and its dual with the same approximations obtained by Taylor ex panding the exact solution. Finally, a full perturbative study of high-orde r harmonic generation is given, obtaining, through analytical expressions, a clear account of the power spectrum using a two-level model, even If the method can be successfully applied to a more general model that can account for ionization too. The analysis shows that to account for the power spect rum it is necessary to go to first order in the perturbative analysis. The spectrum obtained gives a way to measure experimentally the shift of the en ergy levels of the atom interacting with the laser field by looking at the shifting of hyper-Raman lines. [S1050-2947(99)03807-X].