  We study the single-photon collective dynamics in a waveguide system
consisting of the photon channel with a finite bandwidth and an ensemble of
quantum emitters. The size of the volume of these quantum emitters is ignorable
when compared with the wavelength of the radiation photons. Based on the
analytical calculations beyond the Wigner-Weisskopf and Markovian theories, we
present exact solutions to the time evolution of the excited emitters with
collective effects. Different from the trapping effect caused by photon-emitter
bound states, we find that the dark states in the systems lead to a universal
trapping behavior independent of the bosonic bath and the coupling strength
between photons and emitters. Instead, the trapping is solely determined by the
number of initially excited emitters and the total number of emitters. We
demonstrate that such a trapping law can persist even when there are more than
one type of emitters in the system. Our findings lead to the prediction that
single-photon collective emissions can be strongly suppressed if the number of
excited emitters is much less than the total number of emitters in the system.
