Physics Letters A 319 (2003) 461–474 www.elsevier.com/locate/pla Nonclassical statistical properties of a three-level atom interacting with a single-mode field in a Kerr medium with intensity dependent coupling R.A. Zait Mathematics Department, Faculty of Science, Minia University, Minia, Egypt Received 30 August 2003; received in revised form 22 October 2003; accepted 27 October 2003 Communicated by P.R. Holland Abstract We study the interaction of a three-level atom with a single mode field in a cavity containing a Kerr-like medium. Involving intensity dependent coupling, the wave function for the atomic system of V -configuration is obtained when the atom is initially prepared in the excited state. Considering the field to be initially in a coherent state, we evaluate the entropy of the cavity field, the Mandel Q parameter, normal, amplitude-squared and amplitude-cubed squeezing and quasiprobability Q-function of the field. We discuss numerically the influence of the Kerr medium, the detunings and the presence of the intensity dependent coupling on their evolution and show that they have an important effect on the temporal behaviour of the considered statistical properties. Finally, conclusions and some features and comments are given.  2003 Elsevier B.V. All rights reserved. PACS: 03.65.Ge; 32.80.-t; 42.50.-p; 42.50.Ct 1. Introduction One of the extensively studied models in the field of quantum optics is the Jaynes–Cummings model (JCM) [1]. This model is a soluble fully quantum-mechanical model of a single two-level atom interacting with a single-mode cavity field. The relative simplicity of this model and the ease with which it can be extended through analytic expressions or numerical computa- tion, have stimulated the discovery of a number of E-mail address: zaitus@yahoo.com (R.A. Zait). remarkable properties [2]: Rabi oscillations of pop- ulation as energy exchanged between field and mat- ter; the collapse and subsequent revival of these os- cillations; the appearance of chaos in an appropriate semiclassical limit; the nonclassical statistical proper- ties of the cavity field; and the formation of macro- scopic quantum states. Moreover, experimental ob- servation of collapses and revivals, Rabi oscillations and a single-mode two-photon maser have been re- ported [3]. Therefore, the possibility of finding exact solutions to fundamental models of a quantum the- ory which describes the interaction of matter with an electromagnetic field, and the subsequent experimen- 0375-9601/$ – see front matter  2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2003.10.059