Two–Level System and Some Approximate Solutions in the Strong Coupling Regime

In this paper we treat the 2–level system interacting with outer fields without the rotating wave approximation and construct some approximate solutions in the strong coupling regime. In this paper we consider the 2–level system interacting with outer fields (a radiation field for example ) and treat this system without the rotating wave approximation (RWA). Usually we assume the RWA and solve the equation. This approximation is appropriate in the weak coupling regime, however in the strong coupling one it is not applicable. See for example [1] and [2]. How can we treat the system in the strong coupling regime ? Shahriar et al treated this problem in [3], [4] and [5] and constructed some approximate solutions which contained what they called the Bloch–Siegert oscillation. By the way we have treated some important models coming from quantum optics in the strong coupling regime, see [6], [7] and [8] (also [9] for an experiment in the strong coupling ∗E-mail address : [email protected] 1 regime). This method is also applicable in the case, so we construct some approximate solutions which are completely different from those of Shahriar et al. We believe that our solutions are more general. Let {σ1, σ2, σ3} be Pauli matrices : σ1 = 