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The interaction between two $\Xi$-type three-level atoms and a single-modecavity field in the intensity dependent coupling regime has been studied. Exactanalytical solution of the wave function for the considered atoms-field systemhas been obtained by using the Laplace transform technique when the atoms areinitially prepared in the excited state and the field is in a coherent state.The presented structure has the potential ability to generate various newclasses of entangled states depending on the chosen nonlinearity function. Twoforms of intensity-dependent coupling as well as constant coupling areconsidered. Some important physical properties such as quantum entanglement,quantum statistics and quadrature squeezing of the corresponding states areinvestigated, numerically, by which the nonclassicality features of theproduced entangled state are well-established. In particular, the effect ofintensity-dependent coupling on the degree of entanglement between differentbipartite partitions of the system (that is, "atom$+$atom"-field and"field$+$atom"-atom) using the linear entropy is investigated. At the sametime, by paying attention to the negativity as a useful measure, theentanglement between the two atoms is studied in detail.

Entanglement, quantum statistics and squeezing of two $\Xi$-type three-level atoms interacting nonlinearly with a single-mode field