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

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