  Spontaneous decay of an excited atom in a waveguide is essentially modified
by the spatial structure of vacuum reservoir. This is particularly exciting in
view of a range of applications for quantum information science. We found out
that spontaneous decay can be incomplete, so the time dependence of the excited
state population asymptotically approaches to a nonzero value, under the
conditions when the atomic transition frequency is larger than the cutoff
frequency of a waveguide and far from the vicinities of the cut-offs.
Discovered effect is explained by the emergence of the dark state, which is
non-decaying due to polarization selection rules. It was revealed for
single-mode waveguide with rectangular cross section both in single-atom case
and diatomic case when the long-range dipole-dipole interaction plays a
significant role.
