We have studied the non-resonance interaction between a V-type three-level atom and two-mode cavity with Kerr medium. The results show that if the detunings of the two-mode cavities are equal (δ1＝δ2), when initial strength ξ of the two cavities remains unchanged and photon difference q of the two mode cavities is decreased, the non-classical coherence degree between the two mode cavities is increased; when q remains unchanged and ξ is increased, the non-classical coherence degree between the two mode cavities is decreased. When Δδ=|δ2-δ1|=0 and q and ξ remain unchanged, the non-classical coherence degree is decreased with the increase of Kerr effect, and the value of Δδ has an importance influence on the non-classical coherence degree. The results also show that when δ1=δ2, the second-order coherence degree of the cavity 1 shows g211222222>1. On the other hand, the amplitude evolution of the second-order coherence degree of two-mode cavity is decreased due to the influence of Kerr effect.
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