  Quantum emitters coupled to a waveguide is a paradigm of quantum optics,
whose essential properties are described by waveguide quantum electrodynamics
(QED). We study the possibility of observing the typical features of the
conventional waveguide QED scenario in a system where the role of the waveguide
is played by a one-dimensional subwavelength atomic array. For the role of
emitters, we propose to use anti-symmetric states of atomic dimers - a pair of
closely spaced atoms - as effective two-level systems, which significantly
reduces the effect of free-space spontaneous emission. We solve the dynamics of
the system both when the dimer frequency lies inside and when it lies outside
the band of modes of the array. Along with well-known phenomena of collective
emission into the guided modes and waveguide mediated long-range dimer-dimer
interactions, we uncover significant non-Markovian corrections which arise from
both the finiteness of the array and through retardation effects.
