Incomplete spontaneous decay in a waveguide caused by polarization selection

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.