  We present a complete theoretical description of atomic storage states in the
multimode framework by including spatial coherence in atomic collective
operators and atomic storage states. We show that atomic storage states are
Dicke states with the maximum cooperation number. In some limits, a set of
multimode atomic storage states has been established in correspondence with
multimode Fock states of the electromagnetic field. This gives better
understanding of both the quantum and coherent information of optical field can
be preserved and recovered in ultracold medium. In this treatment, we discuss
in detail both the adiabatic and dynamic transfer of quantum information
between the field and the ultracold medium.
