Abstract
We estimate the quantum state of a two-level atom and the coherent field in a Kerr medium subject to the cavity damping. The density matrix of the field is considered within the framework of the dispersive approximation. We study dynamical properties of the linear entropy, Wehrl entropy, and the Wehrl phase density during the time of interaction. The effects of the Kerr medium and cavity damping on the time evolution of different quantities are examined. The results refer to the sensitivity of these aspects to changes either in the decay parameter or in the Kerr-like medium and Stark-shift parameters. Linear entropy and nonclassical properties of the field quantified by the Wehrl entropy are also very sensitive to the Kerr medium and Stark-shift parameter.