  The schemes proposed by S. Bose et al [Phys. Rev. Lett. 83, 5158 (1999)] and
others for long distance atomic teleportation using cavity decay, gives message
state dependent fidelity on successful attempt and in case of failure message
state destroys. We propose a different scheme for teleportation of an atomic
state from one cavity to a distant cavity by reflecting optical-pulse modes of
an entangled coherent state (ECS) from single atom-cavity systems and detecting
whether light is on or off. Unit success with unit fidelity is obtained for
large mean photon number (|{\alpha}|^2). For small |{\alpha}|^2, however, there
is some probability of failure but message state does not destroy, and this
allows us to achieve unit success in a few repeated attempts. Unlike previous
schemes, our scheme also enjoys advantages of deterministic generation of ECS,
robustness of ECS against de-coherence due to photon absorption, and it does
not require many-stage cavity interactions and single photon detection ability.
