The fidelities of quantum states and the cross-correlation function between atoms in the non-degenerate two photons Tavis-Cummings model in two-mode vacuum field are studied b means of quantum theory. The influence of dipole-dipole interaction between atoms and different atomic initial states on the fidelities of quantum states and the cross-correlation function between atoms are discussed. The result shows that the two no-correlation atoms initially situated in excited state behave correlated character in the condition of interaction with two-mode vacuum optical field and dipole-dipole interaction between atoms. While the two atoms initially situated in ground state behave no-correlation, and the quantum state of all system, optical field and atoms do not lose fidelities during evolution.