  We investigate the relaxation dynamics of a single artificial atom
interacting, via multiple coupling points, with a continuum of bosonic modes
(photons or phonons) in a one-dimensional waveguide. In the non-Markovian
regime, where the travelling time of a photon or phonon between the coupling
points is sufficiently large compared to the inverse of the bare relaxation
rate of the atom, we find that a boson can be trapped and form a stable bound
state. More interestingly, if the number of coupling points is more than two,
the bound state can oscillate persistently by exchanging energy with the atom
despite the presence of the dissipative environment. We propose several
realistic experimental schemes to generate such oscillating bound states.
