Exact treatment of the Jaynes–Cummings model under the action of an external classical field

We consider the usual Jaynes–Cummings model (JCM), in the presence of an external classical field. Under a certain canonical transformation for the Pauli operators, the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture, exact solutions for the time-dependent dynamical operators are obtained. In order to calculate the expectation values of these operators, the wave function has been constructed. It has been shown that the classical field augments the atomic frequency ω0ω0 and mixes the original atomic states. Changes of squeezing from one quadrature to another is also observed for a strong value of the coupling parameter of the classical field. Furthermore, the system in this case displays partial entanglement and the state of the field losses its purity.

► The time-dependent JCM, in the presence of the classical field, is still one of the essential problems in the quantum optics.
► A new approach is applied through a certain canonical transformation.
► The classical field augments the atomic frequency ω0ω0 and mixes the original atomic states.