| For better disclosing the quantum properties in the system of atom interacting with field, strengthening the content of the traditional quantum optics, and better understanding and developing the quantum information theory itself, this paper introduces the entropy theory ,and the fidelity theory of the quantum information theory to the system of atom interacting with field, taking advantage of computation, data processing,demonstration, and comparison etc.First, with the frequency of the field varying with time in the sinusoidal form, the computation of entropy in the system of atom interaction with field is investigated, the field entropy is oscillatory and more than zero at any times exceptfor the start moment. The frequency parametersμhave effects on the field entropy,with the increasing ofμ,the regular pattern of the field entropy evolution is moreobvious, and the field entropy curve is regulated by the "sinusoidal wave", with the increasing of the frequency parametersω, the frequency of the field entropy curve is slowly.Second, the fidelity of quantum information for the multi-photon Jaynes-Cummings model with the frequency of the field varying with time in thesinusoidal form have studied, Results show that the frequency parametersμ. have obviously effects on the fidelity, with the increasing ofμ, with the detuningparameters increase, the fidelity of system,photon of field and atom are also increase. and the frequency parametersωof the field varying with time only effect the frequency of the curve. with the increasing of the frequency parametersω, the frequency of the fidelity curve also increase. Third, we investigated the influence of the AC-Stark shift on the evolution of the fidelity. It is shown that AC-Stark shift is negligible effects on the fidelity of the systems,the field and the atom, with the minish of the AC-Stark shift, the detuning parameter increase, the atom-field entanglement weaken, and the fidelity of the systems,the field and the atom increase.
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