Storage states in ultracold collective atoms

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.