  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.
