Abstract: Spin-boson models describe the interaction between a 2-level quantum system and finitely many distinguished modes of a bosonic field. In this talk I will discuss two prototypical examples, the Rabi model and the Jaynes-Cummings model, which despite their age are still very popular in several fields of quantum physics.
Notably, in the context of cavity Quantum Electro Dynamics (QED) they provide an approximate yet accurate description of the dynamics of a 2-level atom in a resonant microwave cavity, as in recent experiments of S.Haroche.
In the first part of the talk I will focus on the controllability properties of these models, analyzing two different types of control operators acting on the bosonic part, corresponding - in the application to cavity QED - to an external electric and magnetic field, respectively. I will review some recent results and prove the approximate controllability of the Jaynes-Cummings model with these controls.
In the second part, I will consider the Rotating Wave Approximation (RWA), which consists of neglecting high oscillating terms of the Rabi Hamiltonian in the weak coupling regime, to obtain the Jaynes-Cummings Hamiltonian as an approximation. I will discuss this problem as an adiabatic limit to prove that the evolution operators of the two dynamics are norm close within a particular physical regime.