  We propose an experiment to realize radiation to atom continuous variable
quantum mapping, i.e. to teleport the quantum state of a single mode radiation
field onto the collective state of atoms with a given momentum out of a
Bose-Einstein condensate. The atoms-radiation entanglement needed for the
teleportation protocol is established through the interaction of a single mode
with the condensate in presence of a strong far off-resonant pump laser,
whereas the coherent atomic displacement is obtained by the same interaction
with the radiation in a classical coherent field. In principle, verification of
the protocol requires a joint measurement on the recoiling atoms and the
condensate, however, a partial verification involving populations, i.e.
diagonal matrix elements may be obtained through counting atoms experiments.
