Decoherence of Single-Excitation Entanglement over DLCZ Quantum Networks Caused by Slow-Magnetic-Field Fluctuations and Protection Approach

Atomic spin-wave (SW) memory is a building block for quantum repeater. However, due to decoherence caused by atomic motions and magnetic-field gradients, SW retrieval efficiency decays with storage time. Slow magnetic-field fluctuations (SMFFs) lead to shot-to-shot phase noises of SWs, but have not been considered in previous repeater protocols. Here, we develop a SW model including a homogeneous phase noise caused by SMFFs, and then reveal that such phase noise induces decoherence of single-excitation entanglement between two atomic ensembles in a repeater link. For verify this conclusion, we experimentally prepare single-excitation entanglement between two SWs in a cold atomic ensemble and observe entanglement decoherence induced by SMFFs. Limited by SMFFs, the evaluated lifetime of the single-excitation entanglement over a repeater link is ~135 ms, even if the link uses optical-lattice atoms as nodes. We then present an approach that may overcome such limitation and extend this lifetime to ~1.7 s.