One of the initial entangled two-atom interact with a cavity in the single-mode light field. We can use the J-C mode to describe the action of atom and light field. The Hamiltonian of this system can be described as

Here is essential transition frequency of atom and is the frequency of light field; g is coupling constant of atom and light field. is spin operator of atom that,

, and

, which is excited state and base state of atom.

In this letter we discussed the entanglement state of two-atom. The initial state can be written as

At any time in the interaction picture, the state of system is depicted as

In the interaction picture, the Schrödinger equation of system is

Using the initial condition we can get

We analysis the two-atom entanglements characteristics in a vacuum field by using the partially transposed matrix of negative Eigen values (negativity) method [12]. It is defined as

Which is negative Eigen values of the partially transposed matrix, and. By this calculation method we get the result as follows.

(6)

The evolution of entanglement degree of the system is described as Figure 1.

When the cavity with single-mode numerical light field fills with Kerr medium, the Hamiltonian of the system can be written as

which describes the strength of interaction between Kerr medium and light field.

As the initial state is

At any time in the interaction picture, the state of system is depicted as

The two-atom entanglement characteristics in a vacuum field, using the partially transposed matrix of negative eigenvalues (negativity) method [12], it is defined as

The evolution of entanglement degree is described as Figures 1 and 2.

According to the picture we can see that the entanglement degree of the two-atom declines seriously in the number of particles field; sometimes sudden death of entanglement occurs (as it is shown in Figure 1). The regions of entanglement sudden death increase by the increasing particle number. The reason is that the action between atom and light field destroys the entanglement of the atoms. For the further study, we find that Kerr medium can erase the phenomenon of sudden death entanglement in numerical light field when two entangled atoms enter-act in the environment of Kerr medium and single-mode numerical light field (as it is shown in Fig-

ure 2). Further more, it can make the entangled atoms keep high entanglement degree, and can make the evolution of them near the maximal entanglement regions.