  In this paper, the interaction between a $\Lambda$-type three-level atom and
two-mode cavity field is discussed. The detuning parameters and cross-Kerr
nonlinearity are taken into account and it is assumed that atom-field coupling
and Kerr medium to be $f$-deformed. Even though the system seems to be
complicated, the analytical form of the state vector of the entire system for
considered model is exactly obtained. The time evolution of nonclassical
properties such as quantum entanglement and position-momentum entropic
uncertainty relation (entropy squeezing) of the field are investigated. In each
case, the influences of the detuning parameters, generalized Kerr medium and
intensity-dependent coupling on the latter nonclassicality signs are analyzed,
in detail.
