Quantum averaging and resonances: Two-level atom in a one-mode quantized field
M. Amniat-Talab, S. Guérin, Hans Rudolf Jauslin · Journal of Mathematical Physics · 2005
We construct a nonperturbative approach based on quantum averaging combined with resonant transformations to detect the resonances of a given Hamiltonian and to treat them. This approach, which generalizes the rotating-wave approximation, takes into account the resonances at low field and also at high field (nonlinear resonances). This allows us to derive effective Hamiltonians that contain the qualitative features of the spectrum, i.e., crossings and avoided crossings, as a function of the coupling constant. At a second stage the precision of the spectrum can be improved quantitatively by standard perturbative methods like contact transformations. We illustrate this method by determining the spectrum of a two-level atom interacting with a single-mode quantized field.