  In our previous paper [Phys. Rev. A 84, 042303 (2011)], we proposed an
efficient scheme to purify dynamically a bipartite entangled state using short
chains of atoms coupled to high-finesse optical cavities. In contrast to
conventional entanglement purification protocols, we avoid controlled-NOT gates
and thus reduce complicated pulse sequences and superfluous qubit operations.
In this paper, we significantly improve the output fidelity of remotely
entangled atoms by introducing one additional entanglement protocol in each of
the repeater nodes and by optimizing the laser beams required to control the
entire scheme. Our improved distillation scheme yields an almost unit output
fidelity that, together with the entanglement distribution and swapping, opens
an attractive route towards an efficient and experimentally feasible quantum
repeater for long-distance quantum communication.
