Approximate controllability of the Jaynes-Cummings dynamics

We investigate the controllability of the Jaynes-Cummings dynamics in the resonant and nearly resonant regime. We analyze two different types of control operators acting on the bosonic part, corresponding—in the application to cavity Quantum Electro Dynamics—to an external electric and magnetic field, respectively. For these models, we prove approximate controllability for all values of the coupling constant g ∈ R, except those in a countable set S∗ which is explicitly characterized in the statement. The proof relies on a spectral analysis which yields the non-resonance of the spectrum for every g ∈ R S∗.