The nonlinear theory of interaction between q-deformed light field and a cascade three-level atom is established.And the formal solution of Schrdinger equation in the representation is obtained.Then,the influence of q-deformed on photon squeezing effects is studied through numerical calculation.The results show that more q deviates from 1 the stronger the controllability to squeezing effects.It reflects that q-deformed nonlinear action has influence on the quantum coherence and quantum properties.When q→1,the theory reduces to the common linear theory.The analyse with q-deformed even coherent light field reflects that q-deformed odd coherent light field not only don't have squeezing effects,but also weaken it.This conclusion is same with that q-deformed even coherent light field and q-deformed odd coherent light field have different quantum properties.
The nonlinear theory of interaction between q-deformed odd coherent light field and a cascade three-level atom is established.And the formal solution of Schrdinger equation in the representation and its average number are obtained.Then,the influence of q-deformed on photon antibunching effects is studied through numerical calculation.The results show that the q-deformed has much ability of control to the photon antibunching effects.It reflects that q-deformed nonlinear action has influence on the quantum coherence and quantum properties.When q→1,the theory reduces to the common linear theory.