Abstract In this paper, we study the properties of two kinds of SU(1.1) coherent statesof light with Bargman index k=1/4 andk=3/4 and show that they posses diffe-rent quantum statistical properties. The atomic dynamical behavior in a two-photonJaynes-Cummings model with initial SU(1,1) coherent state field are discussed. Weshow that the time evolution of atomic inversion displays peculiar periodic oscilla-tion and pulse which...