In this paper, the interactions between a one-dimensional model atom and intense laser field is approximately described by a map. Both the classical version and quantum version of this map are studied. It is shown that besides classical stable islands which can bound some phase space region against ionization and then are responsible for the atomic stabilization, there is another structure in phase space, the unstable manifold, which can determine the ionization process of the system. Quantumly, the quantum quasienergy eigenstates (QE state) under absorptive boundaries, which directly related to the ionization process, are calculated. We define the QE state with smallest ionization rate as QE0 state, which represents the stabilization degree. The Wigner distribution of such QE0 state show clear fringe structures. Finally we show that the classical description and quantum description are in a correspondence manner.
