Single-photon nonreciprocal excitation transfer with non-Markovian retarded effects

We study at the single-photon level nonreciprocal excitation transfer between emitters coupled with a common waveguide. Non-Markovian retarded effects are taken into account due to large separation distance different emitter-waveguide coupling ports. It is shown that of small-atom dimer can be obviously by introducing them coherent channel nontrivial phase. prove for models nonreciprocity cannot coexist decoherence-free giant-atom structure although latter markedly lengthens lifetime emitters. In view this, we further propose trimer which supports both (directional circulation) and greatly lengthened lifetime. Such model also exhibits incommensurate entanglement initial states in case however reciprocal. believe proposals this paper potential applications large-scale quantum networks information processing.