The Jaynes-Cummings model (JCM) is an very important model for describing interaction between quantized electromagnetic fields and atoms in cavity quantum electrodynamics (QED). This model is generalized in many different direction since it predicts many novel quantum effects that can be verified by modern physics experimental technologies. In this paper, the Berry phase and entropy of the ground state for arbitrary photon number n of a two-atom Jaynes-Cummings model with Kerr like medium are investigated. It is found that there are some correspondence between their images, especially the existence of a curve in the ∆ − ε plane along which the energy, Berry phase and entropy all reach their special values. So it is available for detecting entanglement by applying Berry phase.

Negativity has been adopted to investigate the entanglement in a system composed of a two-level atom and a two-mode cavity field. Effects of Kerr-like medium and the number of photon inside the cavity on the entanglement are studied. Our results show that atomic initial state must be superposed, so that the two cavity field modes can be entangled, moreover, we also conclude that the number of photon in the two cavity mode should be equal. The interaction between modes, namely, the Kerr effect, has a significant negative contribution. Note that the atom frequency and the cavity frequency have an indistinguishable effect, so a corresponding approximation has been made in this article. These results may be useful for quantum information in optics systems.Keywords: Negativity; Kerr-like medium; Jaynes-Cummings model. 1 Quantum computation, one of the most fascinating applications of quantum mechanics, has the potential to outperform their classical counterparts in solving hard problems using much less time. There has been an ongoing effort to search for various physical systems that maybe propitious to implement quantum computation. Several prospective approaches for scalable quantum computation have been identified [1,2,3,4]. Compared to other physical systems, the optic quantum can be easily realized in experiments. In quantum optics, the Jaynes-Cummings (JC) model is one of the exactly solvable models describing the interaction between a single-mode radiation field and a two-level atom. It has been realized experimentally in 1987 [5]. There are many ongoing experimental and theoretical investigations on the various extensions of the JC model, such as a bimodal cavity field [6,7], two atoms [8,9], multilevel atoms [10,11], and so on. A two-level atom interacting with a two-mode cavity field is discussed here.In view of the resource character of the entanglement, more attention has been paid to its quantification, such as the concurrence, the negativity, the relative entropy of entanglement etc. Entanglement between two qubits in arbitrary state has been quantified by concurrence [12,13,14]. It is generally considered that the two-atomic Wehrl entropy [15] can be used to quantify the entanglement in the JC model when these modes are initially prepared in the maximally entangled states [16,17]. Here we use negativity as the measure and deal with the mixed state entanglement [18]. Many efforts have been put on the study of the two-mode JC model, but Kerr effect [19,20,21,22] has not been considered, and this is the main motivation of the present paper. The scaled units are used in this work. The interaction between the field and atom are considered in an ideal and closed cavity, namely, the field damping and the radioactive damping [23] are ignored.The system we considered here is an effective two-level atom with upper and lower states denoted by | ↑> and | ↓>, respectively. The corresponding frequencies are ω a and ω b , moreover, we denote ω α as the transition frequency between states | ↑> and | ↓>. where ...