A scheme is presented for the teleportation of an unknown atomic state between two separated cavities. The scheme involves two interaction-detection cycles and uses resonantly coupled atoms with an additional ground state not coupled to the cavity field. Remarkably, the damping of one basis state is balanced by that of the other basis state and the state with photon loss in the first interaction-detection cycle is eliminated by the second cycle. Therefore, the fidelity of teleportation is independent of the teleported state and insensitive to the atomic spontaneous emission, cavity decay, and detection inefficiency, which is obviously in contrast to the original scheme by Bose et al. Phys. Rev. Lett. 83 5158 (1999).
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