On the Transition Probability for the Near or Exact Resonance with the RWA

Abstract

Rotating wave approximation (RWA) has been used to evaluate the transition probability and solve the Schrodinger equation approximately in quantum optics. Examples include the invalidity of the traditional adiabatic condition for the adiabaticity invoking a two-level coupled system near resonance. Here, using a two-state system driven by an oscillatory force, we derive the exact transition probability by solving the Schrodinger equation analytically for a general wave function. Our results reveal that the application of the RWA may lead to false conclusions on the transition probability for the near resonance with weak coupling, especially when the coupling strength is about a half of the transition frequency. We also investigate conditions for which RWA may work or fail.