  The Markovian approximation is widely applied in the field of quantum optics
due to the weak frequency dependence of the vacuum field amplitude, and in
consequence non-Markovian effects are typically regarded to play a minor role
in the optical electron-photon interaction. Here, we give an example where
non-Markovianity changes the qualitative behavior of a quantum optical system,
rendering the Markovian approximation quantitatively and qualitatively
insufficient. Namely, we study a multiple-emitter, multiple-excitation
waveguide quantum-electrodynamic (waveguide-QED) system and include propagation
time delay. In particular, we demonstrate anomalous population trapping as a
result of the retardation in the excitation exchange between the waveguide and
three initially excited emitters. Allowing for local phases in the
emitter-waveguide coupling, this population trapping cannot be recovered using
a Markovian treatment, proving the essential role of non-Markovian dynamics in
the process. Furthermore, this time-delayed excitation exchange allows for a
novel steady state, in which one emitter decays entirely to its ground state
while the other two remain partially excited.
