Physica A 313 (2002) 471– 487 www.elsevier.com/locate/physa General formalism of interaction of a two-level atom with cavity eld in arbitrary forms of nonlinearities Mahmoud Abdel-Aty ∗ Mathematics Department, Faculty of Science, South Valley University, Sohag, Egypt Received 27 March 2002; received in revised form 6 May 2002 Abstract We propose a general formalism of a nonlinear Jaynes–Cummings-model by including possible forms of nonlinearities of both the eld and the intensity-dependent atom-eld coupling. We obtain an exactly analytic solution of the model, by means of which we identify and numerically demonstrate the region of parameters where signicantly large entanglement can be obtained. Under the condition of an initial coherent eld, the atomic inversion shows the collapse-revival phenomenon, which have dierent features in dierent forms of the nonlinearities. It is shown that features of the degree of entanglement is inuenced signicantly by the kinds of the nonlinearities of the single-mode eld. The inuences of the nonlinearities on the photon number distribution and phase properties are examined. c  2002 Elsevier Science B.V. All rights reserved. PACS: 32.80.-t; 42.50.Ct; 03.65.Ud; 03.65.Yz Keywords: Two-level system; Entropy; Entanglement; Phase properties 1. Overview The Hamiltonian of the Jaynes–Cummings (JC)-model [1] is the commonly preferred framework for describing the interaction of an atom (or ion or molecule) with the elec- tromagnetic eld (or the harmonic oscillation of the center of mass of the atom in an external eld). Also, the interaction between a two-level atom and the radiation eld is a quantum optical problem that lies at the heart of many problems in laser physics * Present address: Munketoft 3, 24937 Flensburg, Germany. E-mail address: abdelaty@uni-ensburg.de (M. Abdel-Aty). 0378-4371/02/$ - see front matter c  2002 Elsevier Science B.V. All rights reserved. PII:S0378-4371(02)00999-8