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In this paper, the interaction between a $\Lambda$-type three-level atom andtwo-mode cavity field is discussed. The detuning parameters and cross-Kerrnonlinearity are taken into account and it is assumed that atom-field couplingand Kerr medium to be $f$-deformed. Even though the system seems to becomplicated, the analytical form of the state vector of the entire system forconsidered model is exactly obtained. The time evolution of nonclassicalproperties such as quantum entanglement and position-momentum entropicuncertainty relation (entropy squeezing) of the field are investigated. In eachcase, the influences of the detuning parameters, generalized Kerr medium andintensity-dependent coupling on the latter nonclassicality signs are analyzed,in detail.

journal of the optical society of america. b, optical physics/journal of the optical society of america. b, online

Entanglement dynamics and position-momentum entropic uncertainty  relation of a $\Lambda$-type three-level atom interacting with a two-mode  cavity field in the presence of nonlinearities