In this article, we propose two new quantum field states, displaced binomial state and displaced negative binomial state. Their photon number distributions and sub-Poissonian properties are discussed. The results show that the displaced binomial state is a kind of intermediate quantum state between the coherent state and displaced number state and it may be sub-Poissonian and super-Poissonian at different parameters. The displaced negative binomial state is always super-Poissonian and is an intermediate state between coherent state and displaced Sussking-Glogower phased state. Finally, we study the dynamical evolution of atomic population inversion in the intensity-dependent interaction between these two states and two-level atoms.