Dynamics Of The Two-level System Coupled With Single Model Field Beyond The Rotating Wave Approximation

The model of two-level system coupled with a single-mode field has always been a basic and important problem in physics.It widely appears in quantum optics and condensed matter physics etc.In recent years,with the development of quantum information,the system has been studied more extensively and in depth,especially the experiments to achieve the program have been continuously enriched.In this development,we note that the coupling strength between the twolevel system and field is becoming lager and lager.In quantum optics,the coupling strength is very weak,and the J-C model(Jaynes-Cummings model),which can be got after using a rotating wave approximation,is an excellent model and it can explain and predict several interesting physical phenomena theoretically.But because of its excluding counter-rotating wave terms,it bounds to lose some useful information.Especially in the case of strong coupling,J-C model is no longer suitable,when we must consider the contribution of the counter-rotating terms.In this thesis,we applied Van Vleck perturbation theory to an single-mode two-level system without bias(Rabi model),and the energy eigenvalues and their eigenfunctions up to third order in coupling were gotten.Based on the results,we discussed the collapse and revival phenomena,and some novel results were obtained.Especially,when the coupling is strong enough,the equilibrium position of the two-level system's inversion is no longer at 0,but an upward shift appears.Besides, we discussed the applicability of Van Vleck perturbation theory and found for Rabi model,the energy eigenvalues must be calculated up to third order in coupling,but the eigenfunctions only need to second order.