Abstract
The nonlinear theory of interaction between the q analogue of a single-mode field and a Ξ-type three-level atom has been established. And the formal solution of the Schrödinger equation in the representation and its average number are obtained. Then, the photon squeezing effects are studied through numerical calculation. The results show that the q deformation nonlinear action has a lot of influence on the quantum coherence and quantum properties. When q approaches 1, the theory reduces to the common linear theory.
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