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We study the single-photon collective dynamics in a waveguide systemconsisting of the photon channel with a finite bandwidth and an ensemble ofquantum emitters. The size of the volume of these quantum emitters is ignorablewhen compared with the wavelength of the radiation photons. Based on theanalytical calculations beyond the Wigner-Weisskopf and Markovian theories, wepresent exact solutions to the time evolution of the excited emitters withcollective effects. Different from the trapping effect caused by photon-emitterbound states, we find that the dark states in the systems lead to a universaltrapping behavior independent of the bosonic bath and the coupling strengthbetween photons and emitters. Instead, the trapping is solely determined by thenumber of initially excited emitters and the total number of emitters. Wedemonstrate that such a trapping law can persist even when there are more thanone type of emitters in the system. Our findings lead to the prediction thatsingle-photon collective emissions can be strongly suppressed if the number ofexcited emitters is much less than the total number of emitters in the system.

Dark-state induced trapping law in single-photon emission from multiple quantum emitters