  he 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 $\Delta-\varepsilon$ 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.
